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Entrepreneurship and conflict generating product price changes
European Economic Review 78 (2015) 158–174
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Entrepreneurship and conflict generating product price changes A.G. Schweinberger a,1, A.D. Woodland b,n a b
Previously at: Department of Economics, University of Konstanz, Fach D 150, D-78457 Konstanz, Germany School of Economics, University of New South Wales, Sydney 2052, Australia
a r t i c l e in f o
abstract
Article history: Received 18 June 2013 Accepted 28 April 2015 Available online 25 May 2015
This paper addresses the issue of the impact of changes in world prices upon the welfare of households in small open economies. Making use of a model of a small open economy with one monopolistically competitive industry, we derive conditions under which an exogenous increase in the world price of the monopolistically competitive good, arising from a shift in demand, is conflict generating between the owners of unskilled and skilled labour in the short run but Pareto improving in the long run. Output adjustments at the intensive margin make for conflict generation, but the converse holds for adjustments at the extensive margin in the long run. The analysis highlights the importance of the induced increase in the number of domestic varieties and of the skilled labour intensity in the production of goods relative to its intensity in the setting up of firms. & 2015 Elsevier B.V. All rights reserved.
JEL classification: F12 F16 Keywords: Entrepreneurship Product price changes Conflict generation between the owners of firms and workers Monopolistic competition Pareto improvements in welfare
1. Introduction In which sense, if any, is trade liberalization conflict generating between different agents? By trade liberalization we mean not only the move from an autarkic to a free trade equilibrium but also changes in domestic prices due to the reduction of tariffs or other trade impediments and to changes in trading equilibrium in the rest of the world. It seems that this question raises one of the most fundamental and time honoured issues at the centre of theoretical and empirical work in positive and normative international economics.2 The literature that focuses on this issue is huge. It ranges from the simple Stolper-Samuelson theorem and its generalizations to very recent contributions that make use of monopolistic competition models with heterogeneous firms (e.g., Egger and Kreickemeier, 2009). As is well known (e.g., Hillman, 1989), the Stolper–Samuelson theorem and its key insight that product price changes have conflict generating effects on the owners of capital and labour respectively, represent the keystone of international political economy. Even more recent articles that have spawned an impressive
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Corresponding author at: School of Economics, University of New South Wales, Sydney 2052, Australia. Tel.: þ 61 2 9385 9707; fax: þ 61 2 9313 6337. E-mail address: [email protected] (A.D. Woodland). 1 Deceased. Professor Albert Schweinberger died on 10 August, 2013, after the initial submission of this paper and prior to the subsequent revision. I gratefully acknowledge my great debt to Albert for his initiation of, and insightful contribution to, this paper and sincerely trust that the revision would have met with Albert's approval. The economics profession has lost an outstanding scholar and an excellent researcher, and I have lost a dear friend and colleague. With sadness, I dedicate this paper to Albert Schweinberger's memory. 2 The above statement applies, of course, a fortiori to international political economy. http://dx.doi.org/10.1016/j.euroecorev.2015.04.008 0014-2921/& 2015 Elsevier B.V. All rights reserved.
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literature on international political economy (Grossman and Helpman, 1994) make use of models of the economy with intrinsic conflict generating effects, i.e., a generalized Ricardo-Viner or sector specific factor model.3 Much more recently, Melitz (2003) introduced heterogeneous firms into the rich literature on monopolistic competition models. This has led to the unearthing of new sources of conflict generation associated with trade liberalization: workers employed in certain firms gain because of a rise in productivity due to the selection effect of trade liberalization but other workers lose because they become unemployed. Equally important, trade liberalization gives rise to an increase in the wage inequality of workers employed in the same industry (see Egger and Kreickemeier, 2009). It may be argued that the new sources of conflict generation are, in a certain sense, inherent in monopolistic competition models with heterogeneous firms. Clearly the novel insights are bound to have profound consequences not only for the modeling of the effects of trade liberalization on factor markets but also on international political economy in general and the explanation of trade policies in the presence of vested interest groups in open economies in particular. This brings us to the main tenet of the present paper. While there can be no doubt that many interesting and real world relevant results regarding the conflict generating effects of trade liberalization are obtained from such models, an increase in product differentiation (increase in varieties) due to trade liberalization could mitigate or even more than offset the conflict generating effects mentioned above.4 Arguably, the number of varieties may be under-produced in the autarkic equilibrium. In this context, recall that the number of varieties can be interpreted as a privately produced public good. Furthermore, Broda and Weinstein (2006) provide very impressive evidence that the increase in the number of varieties associated with trade liberalization must be regarded as a source of aggregate gains from trade liberalization of overwhelming importance. The main issue addressed in our paper is as follows. Making use of a simple model of monopolistic competition, we ask whether product price changes associated with trade liberalization are conflict generating if we allow for trade liberalization to imply an increase in the number of domestic firms and product varieties. In order to focus on essentials, our model is very simple. Its primary innovation is that it relates the change in the production of varieties to the existence of entrepreneurial activities.5 We allow for two factors of production, unskilled and skilled labour. Skilled labour may be engaged in production or in entrepreneurial activity, i.e., the setting up of firms.6 Unskilled labour is used only in production. We distinguish between short and long run equilibria. Entrepreneurs can earn rent (super normal profits) in the short run equilibrium because they are the owners of firms. The existence of rents in short run equilibria provides incentives for skilled workers to become entrepreneurs. If, for example, the prices of the differentiated good varieties rise, one may conjecture that in the short run (when output adjusts only at the intensive margin and the number of domestic firms is given) the existence of super normal profits will magnify the conflict generating effects traditionally associated with the standard Stolper– Samuelson theorem. However, intuition also tells us that in the presence of entrepreneurship the long run effects (as more domestic firms are set up by entrepreneurs) may be very different. In fact, we show that, subject to certain conditions and assumptions, the long run effects may entail a Pareto improvement. This follows because the setting up of more firms implies an increase in the provision of varieties. The increased provision of varieties may be regarded as an increase in the provision of privately produced public goods. The latter conclusion hinges, of course, on the proof that the number of varieties is under-provided before trade liberalization and the assumption that there are no barriers to entry. The importance of the number of varieties available for consumption upon the welfare of households and the role of international trade in affecting the number of varieties is, of course, well known in the literature. The seminal work by Krugman (1979) established that even trade between identical countries would generate gains from trade due to consumers in each country having access to a greater variety of differentiated goods. Of special importance to the present issue, Krugman (1981) also constructed a model of trade between two countries with two types of factors of production and demonstrated circumstances (countries have sufficiently similar endowments) where both factors experienced a welfare gain in the move from autarky to free trade. Again, the key mechanism was the increase in the number of varieties available to the factors as consumers due to the opening up of trade. A feature of Krugman's model is that the number of varieties produced in each country does not change in the move from autarky to free trade. Lawrence and Spiller (1983) have a more general model of trade in which the numbers of varieties react to the opening up of trade, but they do not consider the distribution of income or welfare between factors of production. Similarly, Helpman (1981) models international trade using a Lancaster based model of differentiation of preferences but does not address the role of numbers of varieties in ameliorating income conflicting impacts of trade. Bernard et al. (2007) demonstrate that both factors of production may have increases in real incomes as a result of trade liberalization in a heterogeneous product model, the real income increases arising primarily from aggregate productivity gains.
3 It is well known from the literature (see, e.g., Hillman (1989), Weymark (1979), Ethier (1984, chapter 3), Jones (1975), Lloyd and Schweinberger (1997), Grossman and Helpman (1994) and the huge literature on political economy of globalisation) that generally product price changes associated with globalization are conflict generating. Attention is drawn to the debate between Kemp and Wan (1986) and Dixit and Norman (1986) about the possibility of the move to free trade to be a Pareto improvement without lump sum transfers by the government. 4 See, for example, the key assumption that all the heterogeneous firms produce a homogeneous good in Egger and Kreickemeier (2009). 5 As is well known, entrepreneurship in international trade is generally explained within the framework of networks (see Rauch and Watson, 2002). In Rauch and Watson (2002) skilled workers make use of their knowledge of networks acquired in production to become trade intermediaries. Their model is based upon market matching. While it would be pretentious to claim that our modeling of entrepreneurship captures all the interesting features of Rauch and Watson (2002), it does seem to us that our monopolistic competition model does capture some of their features. 6 Neary (2004) has provided a list of lacunae of models of monopolistic competition. One item is unlimited entrepreneurship. Our paper addresses this issue by relating entrepreneureship with skilled labour, which is in limited supply.
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Our paper is distinguished from this literature in several important ways. First, while the previous literature mentioned above focuses on the welfare gains arising to home consumers from access to foreign varieties as a result of the opening up of trade, we concentrate attention upon the impact of trading conditions on the number of domestic varieties of a differentiated product produced. An increase in the number of domestic varieties is a potential source of welfare gain to households. Second, while this literature has considered international trade between two large economies, we construct and analyze a monopolistic competition model of a small open economy. Since the rest of the trading world is large relative to the home country, the prices of traded goods are determined outside its control. Accordingly, a shift in demand structure in the rest of the world will change equilibrium prices and these will impact the domestic economy. Third, we link the formation of new domestic firms to entrepreneurship provided by skilled labour households, who can choose to allocate effort between entrepreneurial activities and working for wages, and concentrate attention upon the impact of world price changes on the welfare of the two household types. Fourth, we distinguish between the short run in which the number of firms is given and the long run in which the number of domestic firms adjusts to drive profits to zero. By doing so, we show that the welfare impact of world prices differs between the short and long runs and that the long run adjustment in the number of varieties produced may allow for Pareto improvements in welfare in contrast to the short run outcome.7 It seems to us that our results are relevant in the real world for two reasons. First, because of the empirical literature on the gains from trade due to an increase in varieties mentioned above and secondly from the perspective of international political economy. We believe that it is important to put forward a framework in which the conflict generating effects of trade liberalization are not built into the model but derived from more basic assumptions. In this context, we put forward the hypothesis that entrepreneurship is much more established in some East Asian countries than in Europe. It seems that there exists some prima facie evidence that lends support to our hypothesis; see e.g. Brandt et al. (2008). Arguably, the existence of political economy motives on the parts of agents and vested interest groups are less prevalent in some East Asian countries than in Europe. In our view this can be explained by the stylized fact that agents in East Asia are much more mobile between production and entrepreneurial activities and also the tendency to focus more on the long rather than the short term. The paper is structured as follows. The basic model and its main properties are the subject matter of the following Section 2. The short run effects of an increase in the price of the manufactured good on the welfare of entrepreneurs and unskilled workers are analyzed in Section 3. Section 4 focuses on the long run effects and contains the main results of the paper. Finally, in Section 5, we summarize the main conclusions and put forward suggestions for generalizations of our analytical framework allowing for different approaches to explain the distribution of power within a firm. 2. The model The model is one of a small open monopolistic competition economy that produces and trades two goods on the world market, and comprises a production sector that produces these goods using two factors of production and a household sector consisting of two types of households. The model determines the returns to factors of production, levels of output and consumption of the two goods, the number of monopolistically competitive firms and the welfare levels for the two households. 2.1. Production sector There are two factors of production that are intranationally, but not internationally, mobile: skilled and unskilled labour. While unskilled labour can only be used in production, skilled labour is mobile between production and entrepreneurial activity, i.e., the setting up of firms. The endowments of both factors are exogenous, with V1 and V2 denoting the total endowments of unskilled and skilled labour respectively. The factor markets are assumed to be perfectly competitive. Good 1 is a homogeneous product that is produced under perfect competition via a constant returns to scale technology, while good 2 is a differentiated product produced under monopolistic competition via a production function that is nonhomothetic and exhibits increasing returns to scale owing to the assumed fixed set-up cost per firm. Both goods are assumed to be produced in the short run, with a given number of firms, as well as the long run equilibrium, when the number of firms is endogenous. Being small, all firms act as price takers in the factor markets. The unit variable cost functions for the producers of the two goods are denoted by c1 ðw1 ; w2 Þ and c2 ðw1 ; w2 Þ, where w1 and w2 denote the wage rates of unskilled and skilled labour respectively, the input–output functions denoting the input of factor i per unit production of product j being aij ¼ aij ðw1 ; w2 Þ ∂cj ðw1 ; w2 Þ=∂wi by Shephard's Lemma. Good 2 is produced under monopolistic competition.8 Industry 2 comprises n firms producing n varieties of the differentiated product 2, each variety being produced by a different firm. Each variety is produced by the same technology using skilled and unskilled labour, the common unit variable cost function being c2 ðw1 ; w2 Þ. In addition, each firm requires an entrepreneur to commit a fixed amount of entrepreneurial input. Specifically, the fixed amount of entrepreneurial input 7
Baumol (2010, pp. 7–8) has provided an intuitive arguement that in the long run entrepreneurship can lead to a Pareto improvement. By adopting a monopolistic competition modeling framework, we assume away all strategic interactions between firms (see, for example, Neary, 2003, 2004, 2009; Cox and Ruffin, 2010). Consideration of strategic interactions raises issues that are well beyond the scope of our paper. 8
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needed for each firm is b units of skilled labour. Accordingly, the total cost function for a firm producing a variety of product 2 is C 2 ðw1 ; w2 ; x2 Þ ¼ c2 ðw1 ; w2 Þx2 þ w2 b;
ð1Þ
where x2 is the firm's output. Clearly, the production technology is non-homothetic due to the fixed set up cost of a firm.9,10 Since there are n firms, the amount of skilled labour available for production is V~ 2 ¼ V 2 bn, which is equal to the total endowment, V2, minus the amount of skilled labour allocated to the setting up of firms, bn. This is reflected in Eq. (5) further below describing the factor market equilibrium condition for skilled labour. Unskilled labour is only used for the production of the two goods, so its market equilibrium condition is given by (4) further below. Good 1 is produced by perfectly competitive firms who treat the market price of 1 parameterically, equilibrium requiring unit cost to equal price. Thus, the profit maximization condition for perfectly competitive firms in industry 1 is c1 ðw1 ; w2 Þ ¼ p1 1, where the price of good 1 is chosen as the numeraire and set equal to unity. For monopolistically competitive firms in industry 2, the profit maximization condition requires that marginal variable cost (unit variable cost) equals marginal revenue. The latter is denoted by the function mr 2 ðp2 Þ, which is common to all such firms. Thus, the profit maximization condition may be expressed as c2 ðw1 ; w2 Þ ¼ mr 2 ðp2 Þ. The short run equilibrium conditions for the production sector may be expressed as c1 ðw1 ; w2 Þ ¼ p1
ð2Þ
c2 ðw1 ; w2 Þ ¼ mr 2 ðp2 Þ
ð3Þ
a11 ðw1 ; w2 ÞX 1 þ a12 ðw1 ; w2 ÞX 2 ¼ V 1
ð4Þ
a21 ðw1 ; w2 ÞX 1 þ a22 ðw1 ; w2 ÞX 2 ¼ V 2 bn V~ 2 ;
ð5Þ
where X1 and X2 denote the aggregate outputs of the two products. The first two equations are the profit maximization conditions for firms in the two industries, while the last two equations are the factor market equilibrium conditions requiring the demands for the two factors to equal their available supplies. Given the factor endowments, the number of firms and prices these equations determine the two factor prices and outputs of the two goods. In the long run, free entry or exit of firms in the differentiated goods sector determines the equilibrium number of firms and varieties, n. The zero profit condition for firms π ½p2 c2 ðw1 ; w2 ÞX 2 w2 bn ¼ 0
ð6Þ
represents the long run equilibrium condition for the determination of the number of monopolistic firms, which is a key feature of monopolistic competition models. This condition requires that profit is zero in the long run; positive profits are driven to zero by the entry of new firms, while losses are driven to zero by the exit of firms. 2.2. Households There are two household types. A type 1 household only owns unskilled labour, while a household of type 2 only owns skilled labour. Moreover, household type 2 owns the firms in industry 2 and therefore is entitled to earn residual or supernormal profits.11 Both households consume good 1 and the available varieties of good 2, the number of available varieties being N ¼ n þ nn where n is the number of domestic varieties and nn is the number of imported foreign varieties. We impose functional structure on preferences, by following Dixit and Stiglitz (1977) in assuming that the varieties of good 2 enter the utility function in a symmetric and separable way. Thus, the assumed utility function is Uðc1 ; c~ 2 Þ ¼ U 1 ðc1 ; U 2 ðc~ 2 ÞÞ, where c~ 2 ¼ ðc21 ; c22 ; …; c2N Þ is the vector of consumptions of N varieties of good 2 and where the function U 2 ðc~ 2 Þ is symmetric in its arguments. To follow the standard practice in the literature and to focus our attention more keenly on the essence of our results rather than upon their generality, we assume that household preferences for P ðσ 1Þ=σ σ=ðσ 1Þ varieties have a constant elasticity of substitution (CES) structure given by U 2 ðc~ 2 Þ ¼ ð N Þ , where σ 4 1 is the i ¼ 1 c2i 12 (constant) elasticity of substitution between varieties. This separable preference structure yields an expenditure function 9 In many monopolistic competition models, it is assumed that the input vectors in setting up of firms and production are collinear (e.g., Krugman (1979), Markusen and Venables (2000), Behrens and Murata (2007) and Helpman (2006)). Some exceptions are, e.g., Chao and Takayama (1990), and Horn (1983). This special assumption rules out the modeling of entrepreneurship because, in our approach, entrepreneurship requires special skills. 10 Dinopoulos et al. (2011) specify a non-homothetic production function for varieties that introduces economies of scale through efficiency parameters for skilled and unskilled labour. However, their model does not have a fixed set up cost as we do. Our fixed set up cost for firms is used to model entrepreneurship provided by skilled labour households. 11 The assumption that the entire surplus accrues only to the owners of the firms may remind the reader of the Marxist approach (Hart, 1995, footnote 5, p. 5). P 12 An alternative specification of preferences would be to assume that the sub-utility function takes the additive form U 2 ðc~ 2 Þ ¼ N i ¼ 1 uðc2i Þ, where the 0 00 function u(x) has the properties that u ðxÞ 4 0 and u ðxÞ o 0. The additive utility function was proposed by Dixit and Stiglitz (1977) and has been used in monopolistic competition models by, for example, Krugman (1981) and Venables (1982) and more recently by Foellmi and Zweimüller (2004), Behrens and Murata (2007), Foellmi et al. (2008) and Zhelobodko et al. (2012). Other recent articles that make use of a model with monopolistic competition and a variable elasticity of demand include Melitz and Ottoviano (2008).
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P 1 σ 1=ð1 σÞ of the separable form E1 ðp1 ; Pðp~ 2 Þ; uÞ, where Pðp~ 2 Þ ¼ ð N is the well-known CES price index for varieties. i ¼ 1 p2i Þ P Maximization of this separable utility function subject to the budget constraint p1 c1 þ N i ¼ 1 p2i c2i ¼ I, where I is income, σ σ yields the consumer demand functions, which take the form c1 ¼ ϕ1 ðp1 ; Pðp~ 2 Þ; IÞ and c2i ¼ p2i Pðp~ 2 Þσ ϕ2 ðp1 ; Pðp~ 2 Þ; IÞ ¼ kp2i , σ where k Pðp~ 2 Þ ϕ2 ðp1 ; Pðp~ 2 Þ; IÞ. Since firms are small relative to the industry, firms take the aggregate demand given by ϕ2 and the price index Pðp~ 2 Þ as σ beyond their influence and so the perceived demand function is γðp2i Þ kp2i , where k is regarded as a constant and outside the influence of the individual firm. The resulting marginal revenue function is mr 2 ðp2i Þ ¼ p2i ðσ 1Þ=σ. As is well known, the CES functional form is very special, with the important restrictive implications that the relative love of variety is a constant, the elasticity of marginal revenue with respect to price is unity, that is, εmr2 ;p2i ∂ ln mr 2 ðp2i Þ=∂ ln p2i ¼ 1, and the markup is constant, that is, ½p2i mr 2 ðp2i Þ=p2i ¼ 1=σ.13 In a symmetric equilibrium, which applies in the current model, the prices of all varieties will be the same, the common price being denoted by the scalar p2. In this case, the marginal revenue function for each variety becomes mr 2 ðp2 Þ ¼ p2 ðσ 1Þ=σ, the price index becomes Gðp2 ; NÞ p2 N1=ð1 σÞ and the expenditure function becomes Eðp1 ; p2 ; N; uÞ E1 ðp1 ; Gðp2 ; NÞ; uÞ. Thus, the expenditure function has the properties that ∂Eðp1 ; p2 ; N; uÞ=∂p2 ¼ ∂E1 =∂p2 ∂G=∂p2 40
ð7Þ
∂Eðp1 ; p2 ; N; uÞ=∂N ¼ ∂E1 =∂p2 ∂G=∂N o0;
ð8Þ
1=ð1 σÞ
σ=ð1 σÞ
since ∂G=∂p2 ¼ N 4 0 and ∂G=∂N ¼ p2 N =ð1 σÞ o 0 under the assumption that σ 4 1. These results show that the expenditure function is increasing in p2 and decreasing in N, thus capturing the household's preference for greater product variety. The equilibrium conditions for the household sector comprise the two budget constraints, expressed as H 1 Eðp1 ; p2 ; N; u1 Þ ¼ w1 V 1 H 2 Eðp1 ; p2 ; N; u2 Þ ¼ w2 V 2 þ ½p2 c2 ðw1 ; w2 ÞX 2 w2 bn;
ð9Þ ð10Þ
where H1 and H2 denote the numbers of unskilled and skilled labour households. Since unskilled labour is only used in production, the budget constraint (9) shows that expenditure equals unskilled wage income. As indicated by the right hand side of Eq. (10), the income of household type 2 comprises skilled labour earnings and profits. Note that we assume all supernormal profits (earned in the short run) only accrue to household type 2 – the owner of firms. In the long run, free entry and exit of firms drives this profit to zero. The expenditure function, discussed above, is written as a function of the usual variables, prices and utility, but also as a function of the number of varieties, N. 2.3. International trade An important assumption of the model is that the economy is a small open monopolistically competitive economy, trading both goods freely on the international market. This means that the foreign country (or rest of the world) is very large compared to the small open economy and, hence, that the prices of all internationally traded goods are essentially determined in the foreign country. It is therefore appropriate to assume that the domestic firms in a small open economy take the common price for varieties, p2, and the number of foreign varieties, nn , as given. On the other hand, the varieties are not perfectly substitutable in demand, and so each variety has a perceived demand function c2i ¼ γðp2i Þ that is exploited by the firm in its production level choice.14 The following argument is advanced to support the small open economy assumption. Suppose that there are two countries identical in structure to our economy specified above, with the same technology and preferences but with different factor endowments, and trading both goods. Provided that endowments are not too dissimilar, free trade involves factor price equalization.15 If the foreign country is now enlarged by proportionally increasing its factor endowments, the equilibrium prices for goods will approach that country's equilibrium autarky prices. Equivalently, the importance of the home country in determining the world prices diminishes. While all home firms producing good 2 take the price index for σ good 2 as given, they maintain their perceived demand function c2i ¼ kp2i . In a symmetric equilibrium, all varieties will be equally priced at the world determined price p2. Our analysis is concerned with the situation whereby there is a shift in the structure of the foreign economy that generates an increase in the price index (common symmetric equilibrium price) for product 2 varieties. One such shift is a reduction in the weight attached to the numeraire good in the foreign utility function, thus shifting demand 13 The special nature of the CES structure for preferences over varieties and its role in simplifying many responses has been recently demonstrated and discussed by Zhelobodko et al. (2012). The CES structure rules out non-unitary price elasticities of marginal revenue, and hence rules out anti-competitive effects of price changes. See Schweinberger (1996) on the concepts of pro-and anti-competitive effects. 14 An alternative approach to modeling a small open monopolistically competitive economy is to follow Venables (1982). His approach is to assume that domestic varieties of the product are not traded internationally and that foreign varieties are imported, consumers taking the prices of foreign varieties and the number of foreign varieties as given. Other papers to follow the Venables approach include Ghosh and Sen (2012). While this approach to the model specification could be employed in the present context, we have chosen to maintain a model without such an asymmetry. 15 See Krugman (1981), Helpman (1981) and Lawrence and Spiller (1983) for monopolistic competition models of trade with factor price equalization.
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towards product 2 varieties and increasing p2. For example, let the foreign expenditure function be En ðp1 ; p2 ; N; uÞ E1 ðp1 ; αGðp2 ; NÞ; uÞ with the parameter α indicating the preference for good 2 relative to good 1. An increase in α from an initial value of unity indicates a shift in preference towards good 2 and this would have the effect of raising the equilibrium world price for all varieties of good 2. While an increase in α would proportionately increase the demands for all varieties of good 2, it would not otherwise alter the perceived demand function for varieties of firms in this industry; the perceived elasticity of demand for each variety would remain unchanged. This is the scenario that we contemplate. Other scenarios may be contemplated. In any case, this structural shift and resulting increase in p2 is taken as exogenous by the domestic firms in the small open economy. Our purpose is to analyze the impacts that this change has on the small open economy, particularly for the welfare of skilled and unskilled labour households. Accordingly, we assume that p2 changes exogenously and that nn remains fixed. Of course, a shift in demand structure leading to an increase in p2 in the foreign country may be expected to also lead to a change in the number of foreign varieties, nn , produced and these will be available to the home country's consumers. To isolate effects and to focus on home country impacts, we keep nn constant.16 2.4. Equilibrium Equations (2)–(5) and (9)–(10) describe the short run equilibrium, while these same equations together with (6) describe the long run equilibrium. In the short run, the number of monopolistic firms in industry 2, n, is given. The short run model consists of two profit maximization conditions, Eqs. (2) and (3), two factor market equilibrium conditions, Eqs. (4) and (5), as well as two income expenditure equalities (budget constraints) for the two types of households, Eqs. (9) and (10). In the short run, the model equations determine the endogenous variables comprising the two factor prices, ðw1 ; w2 Þ, the industry outputs, ðX 1 ; X 2 Þ, and utility levels for the two households, ðu1 ; u2 Þ. In the long run, the number of domestic monopolistically competitive firms, n, is endogenously determined by the zero profit (6). Equations (2)–(5) and (9)–(10) and (6) determine the two factor prices, ðw1 ; w2 Þ, the industry outputs, ðX 1 ; X 2 Þ, the utility levels for the two households, ðu1 ; u2 Þ and the number of domestic varieties of good 2, n. The model may be rewritten more compactly by using standard results from economic theory to summarize the equilibrium conditions (2)–(5) for the production sector, using expressions for the output supply functions and the factor price functions, whose properties are well known. First, if the Jacobian determinant of the production cost functions is nonvanishing, it follows from the envelope theorem that Eqs. (2)–(3) may be solved for the factor price functions wi ðp1 ; mr 2 ðp2 ÞÞ. Second, using these functions, (4)–(5) can then be solved for the output supply functions of the form X i ðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ. The properties of these factor price and output supply functions are well known.17 Accordingly, using these functions, the model may be reduced to Eqs. (9)–(10) and (6), where X i ¼ X i ðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ and wi ¼ wi ðp1 ; mr 2 ðp2 ÞÞ are determined from Eqs. (2)–(5). 3. The short run analysis We now turn to the main issue addressed in this paper: are world product price changes conflict generating? Specifically, our focus is on determining the effects of a change in the world price of good 2, arising from a shift in demand structure in the rest of the world, upon the welfare levels for the two types of households. The price change is said to be conflict generating if the welfare effects go in opposite directions for then the two household types have conflicting interests in the price change. In this section, we focus attention on the short run equilibrium as a benchmark case for the long run analysis of the following section of the paper. Before answering this question, we remind the reader about our assumption regarding the ownership of firms. In perfectly competitive models the firm ownership issue does not arise because there are no firms earning profits. The latter statement also applies to monopolistic competition models, if – following the literature – one focuses only on the long run equilibrium. In the short run, in which the number of firms is given, price changes impact profits of monopolistically competitive firms and so the ownership of firms matters for welfare analysis. Our model assumes that all firms producing good 2 are completely owned by entrepreneurs (skilled labour). Therefore, all the supernormal profits (rent) accrue only to household type 2, as indicated by the budget constraint of household type 2. Possible generalizations are sketched in Section 5 of the paper. 16 Venables (1982, pp. 225, 235) invokes the small open economy assumption in his monopolistic competition model of trade, treating the home country as a price taker. Recognizing that changes in foreign prices may change the number of foreign varieties, he develops optimal tariff formulae for the cases when the number of foreign varieties is unchanged and then does change. In the present context, it is arguable that an increase in foreign varieties will further enhance the long run welfare gains demonstrated further below. 17 See, for example, Jones (1965) for a detailed derivation of the properties of these functions for the standard two sector model. It is also possible to derive their properties by making use of a revenue function for the production sector of the form
Rðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ ¼ p1 X 1 þ mr2 ðp2 ÞX 2 ;
ð11Þ
which has all the standard properties of a revenue function (see, for example, Woodland, 1982, 49 ff). For example, it is linearly homogeneous and concave in endowments V1 and V~ 2 , and convex in p1 and mr 2 ðp2 Þ. Application of the duality approach is useful, because it yields the above model specification simplification and many potential generalizations.
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To derive the short run effects on the welfare of the two household types of an increase in the price of good 2, we firstly rewrite Eqs. (9) and (10) as H 1 Eðp1 ; p2 ; n; u1 Þ ¼ w1 V 1
ð12Þ
H 2 Eðp1 ; p2 ; n; u2 Þ ¼ w2 V~ 2 þ ½p2 mr 2 ðp2 ÞX 2 ;
ð13Þ
where it is recalled that outputs and factor prices are determined from Eqs. (4)–(3) as X i ¼ X i ðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ and wi ¼ wi ðp1 ; mr 2 ðp2 ÞÞ. The right hand side of Eq. (13) shows that, in the short run, the income of skilled worker households comprises labour earnings and profits. To determine the short run response of household welfare to a change in the world price of good 2, we totally differentiate Eqs. (12) and (13) with respect to p2, holding n fixed. This determines the effect of p2 upon the utility levels of the two households. In undertaking this task, we make use of a special feature of the model in which we adopt the assumption of CES preferences over varieties implying that ∂lnmr 2 =∂lnp2 εmr2 ;p2 ¼ 1, i.e., that the profit margin is fixed. As is well known, a fixed profit margin is a standard assumption of a huge literature on monopolistic competition. The outcome of this task gives rise to the following proposition. Proposition 1. Assume the short run model of monopolistic competition described by equations (12) and (13), with the number of firms fixed, and assume that industry 2 uses factor 2 relatively intensively. Assume also that the households' preferences for varieties have a CES structure. Then, an increase in the world price of product 2 has the following welfare effects: (a) a reduction in welfare for household type 1, and (b) an increase in welfare for household type 2. Proof. Differentiation of Eq. (12) yields the result that ∂E1 ∂w1 ∂mr 2 H1 du1 ¼ V 1 C 12 dp2 ; ∂u1 ∂mr 2 ∂p2
ð14Þ
1 where E1 Eðp1 ; p2 ; n; u1 Þ and C 12 H 1 ∂E ∂p 40 is the aggregate consumption of good 2 by households of type 1. Since we 2
∂w1 2 o0) and ∂mr assume that industry 2 is relatively factor 2 intensive (whence ∂mr ∂p2 ¼ ðσ 1Þ=σ 4 0 under CES preferences, it is 2 1 ∂w1 ∂mr 2 evident that V 1 ∂mr C 2 o0 and, hence, that du1 =dp2 o 0. Unskilled labour households suffer a loss in welfare. 2 ∂p2 A similar differentiation of Eq. (13) yields
H2
∂E2 du2 ¼ V~ 2 dw2 þ p2 mr 2 p2 dX 2 þX 2 dp2 dmr2 C 22 dp2 ; ∂u2
ð15Þ
2 where E2 Eðp1 ; p2 ; n; u2 Þ and C 22 H 2 ∂E ∂p2 4 0 is the aggregate consumption of good 2 by households of type 2. Expression (15) may be re-expressed as
H2
∂E2 b 2 þ p X 2 1 ð1 t 2 Þεmr ;p p b 2 þ t 2 p2 X 2 X b2 ; b 2 p2 C 22 p du2 ¼ w2 V~ 2 w 2 2 2 ∂u2
b 2 dw2 =w2 ), t 2 ðp2 mr 2 Þ=p2 denotes the profit margin or percentage price where the b denotes percentage change (e.g., w markup and εX 2 ;mr2 ∂lnX 2 =∂lnmr 2 . In percentage and share terms, this may be written as ∂E2 u2 du2 w2 V~ 2 t p X b t 2 p2 X 2 p C2 b 2 þ 2 2 2X b b2 2 2 p ¼ 1 ð1 t 2 Þεmr2 ;p2 p w 2þ ∂u2 E2 u2 H 2 E2 H 2 E2 t 2 H 2 E2 H 2 E2 2 b 2 þ ð1 θ2 Þ 1 ð1 t 2 Þεmr ;p p b 2 þ ð1 θ 2 ÞX b2 b 2 s2 p ¼ θ2 w 2 2 t2
ð1 θ2 Þ b2 ; ¼ θ2 εw2 ;mr2 þ ð1 θ2 ÞεX 2 ;mr2 εmr2 ;p2 þ 1 ð1 t 2 Þεmr2 ;p2 s2 p t2 ~
p C2
where θ2 wH22VE22 is the share of household 2's income arising from labour and s2 H22 E22 is household 2's expenditure share of product 2. By definition, the two shares have the properties that 0 oθ2 o 1 and 0 os2 o1. The general elasticity expression obtained above may now be simplified by invoking the assumption of CES preferences for varieties, which implies that εmr2 ;p2 ¼ 1. With this assumption, the expression simplifies to
∂E2 u2 du2 ð1 θ2 Þ b2 ½1 ð1 t 2 Þ s2 p ¼ θ2 εw2 ;mr2 þ ð1 θ2 ÞεX 2 ;mr2 þ t2 ∂u2 E2 u2 b2 ¼ ½θ2 εw2 ;mr2 þ ð1 θ2 ÞεX 2 ;mr2 þ ð1 θ2 Þ s2 p b2 : ¼ ½θ2 ðεw2 ;mr2 1Þ þ ð1 s2 Þ þð1 θ2 ÞεX 2 ;mr2 p
ð16Þ
The Stolper–Samuelson theorem indicates that εw2 ;mr2 41 (magnification effect of shadow price on the skilled wage rate), while the elasticity of supply of good 2 with respect to the shadow price of good 2 is positive, i.e., εX 2 ;mr2 40. These b 2 on the right hand properties, along with the share properties that 0 oθ2 o 1 and 0 os2 o1, ensure that the coefficient of p
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side is positive. Accordingly, we have the result that b2 ∂lnE2 u ¼ θ2 εw2 ;mr2 1 þ ð1 s2 Þ þ ð1 θ2 ÞεX 2 ;mr2 40; b2 ∂lnu2 p
ð17Þ
showing that skilled labour households experience a gain in welfare. This completes the proof.□ Proposition 1 states that the increase in the world price of good 2 generates an unambiguous conflict of interest between the two types of households – those who own unskilled labour and those who own skilled labour and firms – in the short run. The owners of skilled labour, which is used relatively intensively in the production of the differentiated good, whose price has risen, and who own the firms and so enjoy short run profits benefit from the price increase. The other factor loses because its income falls and it faces higher prices. This result is perhaps not surprising in view of the well-known Stolper– Samuelson theorem established under perfectly competitive behaviour on the part of firms, as now discussed. The importance of the result contained in this proposition is that it generalizes the validity of the Stolper–Samuelson theorem to the context of an economy with monopolistically competitive firms. The Stolper–Samuelson theorem establishes that, in a perfectly competitive two-sector model, an increase in the price of a product will raise the real income, and hence utility, of the factor that is relatively intensively used in the production of that product and reduce the real income of the other factor of production. This theorem is based upon the magnification effect of product prices upon factor prices, which implies that the increase in real income for the first mentioned factor is in terms of both products so there is a welfare gain for any valid preferences. The result is that price changes are conflict generating, since one factor gains and the other loses in welfare. In the present context, our model incorporates monopolistic competition and so the income of skilled labour includes the short run profits that will be affected (most plausibly increased) by an increase in the world price of product 2, thus potentially blurring the Stolper–Samuelson impact. However, it is important to note that we have also incorporated the very special assumption of CES preferences for varieties, implying that εmr2 ;p2 ¼ 1 so a 1% rise in p2 ensures a 1% rise in mr2 and implying that the percentage price markup is a constant. Since in our model the Stolper–Samuelson effect operates via mr2, and mr2 and p2 are proportional, the traditional Stolper–Samuelson magnification effect occurs. Also, this feature and the constant markup combine to ensure that the total income of skilled labour households rises. Thus, the Stolper–Samuelson theorem continues to hold when preferences for varieties have a CES structure.18 Can some of our results be generalized? This seems to be an important issue, which we now address briefly. A routine generalization would be to assume that both household types have a claim on supernormal profits and that the shares of entitlement are exogenous. A more interesting approach consists of endogenizing the entitlement shares by introducing an effort function with entitlement shares as arguments. Still another possibility would be to allow for Nash bargaining to determine the shares. In that case, it is well known that the distribution of power within the firm is captured by the bargaining power of the owners of the firm and workers.19 Finally, generalizations to higher dimensions appear to be straightforward if both household types own all the types of factors (but in different proportions) and all the household endowment sectors lie within the diversification cone of the economy, making use of the concept of output imputed to household endowments with various types of factors (Lloyd and Schweinberger, 1997; Woodland, 1974). 4. The long run analysis In this section, we analyze the long run implications of an increase in the world price of product 2 arising from a shift in preferences in the rest of the world. First, we consider the effect of this price increase upon the number of domestic firms in the monopolistically competitive production sector. In particular, we establish the necessary and sufficient conditions for a higher price to induce greater entrepreneurship via an increase in the number of firms, which is the intuitively plausible outcome. Second, we follow our main objective of the paper by examining the consequences of the price increase for the welfare of the two types of households. The focus, as in the short run section, is to determine whether the price increase generates income conflict between households. Before moving to these two tasks, it is useful to rewrite Eqs. (9)–(10) and (6) of the long run model as H 1 Eðp1 ; Gðp2 ; NÞ; u2 Þ ¼ w1 V 1
ð18Þ
H 2 Eðp1 ; Gðp2 ; NÞ; u2 Þ ¼ w2 V 2
ð19Þ
πðp2 ; nÞ ½p2 c2 ðw1 ; w2 ÞX 2 w2 bn ¼ 0;
ð20Þ
where, as before, X i ¼ X i ðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ
ð21Þ
18 The proof of this proposition should make clear where the CES assumption was used and so give clues as to why the Stolper–Samuelson result might break down under alternative assumptions about preferences, with different behaviour of the elasticity εmr2 ;p2 and markups. 19 See Marin and Verdier (2008) for how to model the distribution of power inside a firm, making use of principal agency theory.
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wi ¼ wi ðp1 ; mr 2 ðp2 ÞÞ
ð22Þ
are determined from Eqs. (2)–(5) and V~ 2 ¼ V 2 bn. It is observed that the right hand side of the budget constraint of household 2 now has no profits, since they are zero in the long run as specified in Eq. (20). As a result, household types 1 and 2 now appear symmetrically in the model. It is also noteworthy that the zero profit condition (20) may be used to determine the number of firms, n; then, using this result, the utility levels are determined from Eqs. (18) and (19). 4.1. The effect of a price increase on the number of firms To proceed, we totally differentiate Eq. (20) with respect to p2 and n, assuming that the economy is initially in a long run equilibrium. This yields the expression ∂mr 2 dπ ¼ p2 c2 dX 2 þ X 2 1 ð23Þ dp2 w2 b dn bn dw2 ¼ 0; ∂p2 where the changes in output of good 2 and the price of skilled labour are given by dX 2 ¼
∂X 2 ∂mr 2 ∂X 2 dp2 b dn ∂mr 2 ∂p2 ∂V~ 2
ð24Þ
dw2 ¼
∂w2 ∂mr 2 dp2 : ∂mr 2 ∂p2
ð25Þ
This yields the following partial derivatives of the profit function, namely
∂X 2 ∂π ¼ b w2 þ p2 c2 o0 ∂n ∂V~ 2 ∂X 2 ∂mr 2 ∂π ∂mr 2 ðp2 Þ ∂w2 ∂mr 2 ¼ p2 c2 þ X2 1 : bn ∂p2 ∂p2 ∂mr 2 ∂p2 ∂mr 2 ∂p2
ð26Þ ð27Þ
It is evident that ∂π=∂n o 0 under our assumption that product 2 uses factor 2 relatively intensively, since then ∂X 2 =∂V~ 2 40. However, the derivative ∂π=∂p2 cannot be signed on the basis of our assumptions (the first term is positive, the last is ∂n ∂π ∂π negative and the sign of the middle term is ambiguous in general). Since ∂p ¼ ð∂p = Þ, this ambiguity of sign leads to the 2 2 ∂n conclusion that an increase in the world price of good 2 may either increase or decrease the number of domestic firms. The outcome depends on whether an increase in the world price will increase or decrease profits, given the number of firms. Further assumptions are needed to pin down the response of the number of firms to the price increase. To this end, it will be convenient to express these derivatives in percentage terms as h i ∂π ¼ bnw2 1 þφεX 2 ;V~ 2 o0 ð28Þ ∂lnn
∂π ¼ bnw2 εX 2 ;mr2 εw2 ;mr2 εmr2 ;p2 þt 2 1 1 ð1 t 2 Þεmr2 ;p2 ; ∂lnp2
ð29Þ
2 where φ bn=V~ 2 40 and t 2 p2 c2pðw1 ;w2 Þ ¼ bnw p2 X 2 is the markup for product 2. Taking the ratio of these two expressions, we 2 obtain
^ p^ 2 ¼ n=
∂π=∂lnn ðεX 2 ;mr2 εw2 ;mr2 Þεmr2 ;p2 þ t 2 1 ½1 ð1 t 2 Þεmr2 ;p2 SRGTP ; ¼ ∂π=∂lnp2 D 1 þεX 2 ;V~ 2 φ
ð30Þ
where SRGTP is defined as the numerator and D 1 þ εX 2 ;V~ 2 φ 40 as the denominator. The term SRGTP is (apart from the constant bnw2) the short run growth in total profits, being the change in profits due to a 1% increase in the price of product 2, with the number of domestic varieties (firms) held constant. The denominator D is (apart from the constant bnw2 ) the change in total profits arising from a 1% increase in the number of domestic varieties (firms), with the price of product 2 held constant. The economic interpretation of expression (30) is straightforward. The distinctive feature of the denominator D is a weighted Rybczynski effect. As is well known, the elasticity of output with respect to the relatively intensively used factor is greater than unity (εX 2 ;V~ 2 4 1), i.e., the standard Rybczynski magnification effect. The weight is given by φ bn=V~ 2 40, which may be greater, equal to or less than one, depending on the skilled labour intensity of the setting up of firms relative to production. It follows that the assumed mobility of skilled labour between entrepreneurial activities and production may either reinforce, leave unchanged, or diminish the standard magnification effect. Intuitively, a given p^ 2 4 0 implies (ceteris paribus) a smaller n^ if the entrepreneurial activity requires more skilled labour than does production (φ 4 1). Clearly, in this case, the setting up of more firms whittles away more quickly the supernormal profits of the short run equilibrium. The numerator of expression (30) given by SRGTP consists of three effects: a standard output price effect that is positive (εX 2 ;mr2 40), a standard Stolper–Samuelson effect that captures the increase in the fixed cost of setting up firms due to the rise in the wage of skilled labour (εw2 ;mr2 41), and a profit margin effect (1 pc2 εmr2 ;p2 ¼ 1 ð1 t 2 Þεmr2 ;p2 ) that is weighted by 2
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the value productivity of all firms, i.e., ζ p2 X 2 =bnw2 ¼ t 2 1 .20 In general, the numerator cannot be unambiguously signed on the basis of economic theory; consequently, an increase in price is not guaranteed to increase the number of firms in industry 2. Rearranging expression (30), we can derive a necessary and sufficient condition for an increase in p2 to entail an increase in the number of firms (and therefore varieties). This condition is specified in the following proposition. Proposition 2. Assume a long run equilibrium for our small open economy. Further, assume that the production of good 2 is intensive in factor 2 (skilled labour) relative to good 1 and that the households' preferences for varieties have a CES structure. Then a necessary and sufficient condition for an increase in the world market price of good 2 to imply an increase in entrepreneurial activity (number of firms and varieties, n) is that εX 2 ;mr2 4εw2 ;mr2 1 4 0:
ð31Þ
Proof. It follows directly from (30) and the property D 4 0 that a necessary and sufficient condition for an increase in n is that the numerator SRGTP 40. Invoking the assumption that preferences for varieties have a CES structure, whence εmr2 ;p2 ¼ 1, the expression for SRGTP simplifies to SRGTP ¼ ðεX 2 ;mr2 εw2 ;mr2 Þ þ t 2 1 ½1 ð1 t 2 Þ ¼ εX 2 ;mr2 þð1 εw2 ;mr2 Þ. Since εX 2 ;mr2 4 0 (positive supply response around the production frontier due to an increase in the shadow price) and εw2 ;mr2 4 1 (the Stolper–Samuelson magnification effect), SRGTP is not guaranteed to be positive in general. It will be positive if, and only if, εX 2 ;mr2 4 εw2 ;mr2 1, thus completing the proof.□ Proposition 2 provides a necessary and sufficient condition for an increase in the world price of good 2 to encourage entry into the differentiated good sector and to thereby increase the number of domestic firms and the number of domestic varieties produced. While it might be expected that entry would be encouraged, the condition for this outcome indicates that this is not a foregone conclusion despite our special assumption of CES preferences. The necessary and sufficient condition involves two elasticities – the output supply elasticity εX 2 ;mr2 , which measures the movement around the production frontier, and the factor price elasticity εw2 ;mr2 , which measures the responsiveness of the wage rate for skilled labour both with respect to changes in the marginal revenue. Since εmr2 ;p2 ¼ 1 under the CES assumption, these are the normal output supply elasticities and the normal Stolper–Samuelson elasticity with respect to price. The condition expressed in Proposition 2 requires the output supply elasticity to be sufficiently high, meaning that it is greater than the Stolper–Samuelson elasticity minus unity. This requirement is not guaranteed, but depends on the values of these elasticities, which, in turn, depends upon the factor endowments and the structure of the production functions.21 Proposition 2 is interesting because it generalizes the result from the literature by focussing on the crucial role played by the Stolper–Samuelson effect. The proposition unearths a hitherto ignored interdependence between entrepreneurial activities and conflict generating effects of product price changes embodied in the Stolper–Samuelson theorem. The equilibrium value of n: Before leaving this subsection, we derive a formula for the equilibrium number of varieties, n, and use this to graphically illustrate Proposition 2. The equilibrium value for the number of varieties, n, is obtained from the zero profit condition π ½p2 c2 ðw1 ; w2 ÞX 2 w2 bn ¼ t 2 p2 X 2 w2 bn ¼ 0:
ð32Þ
In this expression, X 2 ¼ X 2 ðp1 ; mr 2 ðp2 Þ; V 1 ; V 2 bnÞ. For any given p2, the factor prices are given and X2 depends linearly upon n through its effect on the amount of skilled labour used in production, V~ 2 ¼ V 2 bn, via the Rybczynski theorem. The factor market equilibrium conditions may be expressed in matrix form as AX ¼ V ð0; bnÞ0 , yielding the output vector as X ¼ A 1 V A 1 ð0; bnÞ0 , where A 1 ¼ ½aij is the inverse of A. Defining X ¼ A 1 V, we may write X 2 ¼ X 2 a22 bn. Thus, profit may be expressed as π t 2 p2 ðX 2 a22 bnÞ w2 bn ¼ t 2 p2 X 2 bðw2 þ a22 t 2 p2 Þn;
ð33Þ
which is linear in n. Setting π¼0 and solving this linear zero profit equation, the long run equilibrium value for n may be expressed as n¼
t 2 p2 X 2 X2 : ¼ w2 bðw2 þa22 t 2 p2 Þ 22 b a þ t 2 p2
ð34Þ
Given p2, the factor prices are determined and, hence, all of the terms on the right hand side are determined. Thus, the equilibrium number of varieties (firms), n, may be calculated. The linear expression for the profit function (with p2 given) may be used to illustrate Proposition 2. Fig. 1 depicts the downward sloping linear profit function expressed in (33) labeled as Π1 and with equilibrium number of varieties equal to n01 . If p2 were to increase, thus increasing mr 2 ðp2 Þ, both the intercept and slope of this line increase. The intercept rises, since the higher marginal revenue induces greater output, X 2 , around the production frontier. The slope of the profit line also 20 The value productivity of all firms can be interpreted as the gross economy rate of return from investing in the setting up of firms. The equality ζ ¼ t 1 follows directly from the long run zero profit condition π ¼0. 21 Jones (1965) provides expressions for these responses in terms of endowments, factor shares and elasticities of substitution.
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Fig. 1. The profit function and the equilibrium number of varieties.
increases (becomes more negative) because the higher marginal revenue induces a magnified positive effect on w2 that dominates the expression for the slope. Thus, the new profit function (as a function of n) line could be the one labelled Π2 or the one labelled Π3. In the case of Π2, the slope increase is sufficiently small for the equilibrium number of varieties to increase from n01 to n02 . However, in the case of Π3, the slope increase is sufficiently large that the equilibrium number of varieties decreases from n01 to n03 . This illustrates the possibilities of an increase in the world price for the differentiated product to either increase or decrease the number of varieties produced in the long run, as indicated by Proposition 2. To conclude this discussion, note that we assume throughout the remainder of the paper that the conditions implying an increase of n (in Proposition 2) in response to an increase in the world price for good 2 are satisfied.
4.2. The effect of a price increase on the welfare of households Can there be gains from trade in the sense of a Pareto improvement in an economy with many different household types without governmental intervention? This key issue in international economics has received considerable attention (making use of models of perfect competition) in the literature. To be more specific, until the work by Dixit and Norman (1980) it was argued that a Pareto improvement is only possible if the government applies a system of lump sum transfers between household types. Dixit and Norman were the first to prove that an appropriate set of employment and commodity taxes and subsidies are, subject to certain assumptions, sufficient to ensure a Pareto improvement.22 Our contention in this paper is that an important key insight of the new trade theory is that Pareto improvements are a real possibility in economies with many household types and monopolistic competition even without any form of governmental intervention. Our main current task is to derive a set of conditions under which an increase in the world price of good 2 implies a Pareto improvement in entrepreneurial economies. As is intuitively obvious, the concept of the marginal willingness to pay for an increase in the number of varieties, the “privately produced public good” plays a crucial role in this context. It may, of course, be argued (Neary, 2004) that the marginal willingness to pay for an increase in the number of varieties declines very rapidly as the number of varieties rises. On the other hand, as mentioned in the introduction, in the light of recent overwhelming empirical evidence for the US economy (Broda and Weinstein, 2006) an increase in the number of varieties should be regarded as a very important source of gains from trade. In order to determine the conditions under which the Pareto-improvement presumption is supported by the model and its assumptions, we now totally differentiate the income expenditure equalities of household types 1 and 2 in Eqs. (18) and (19) with respect to p2 and taking into account the impact of the change in the world price upon the number of domestic varieties produced. This yields Hi
∂Ei dui ∂Y i ∂Y i ∂E dn Hi i ¼ C i2 þ ; ∂ui dp2 ∂p2 ∂n ∂n dp2
i ¼ 1; 2;
ð35Þ
where ∂Ei =∂n ¼ ð∂Ei =∂GÞð∂G=∂NÞ o0 denotes the (negative of the) marginal willingness to pay for an increase in the number of varieties. In this expression, C i2 ¼ H i ð∂Ei =∂GÞð∂G=∂p2 Þ 4 0 is the aggregate consumption of good 2 by household type i, and household incomes in the long run are Y i wi V i . Before using (35) to determine the welfare effects of a price increase, it is useful to obtain some preliminary results that are presented in the following lemma. ∂w1 ∂mr2 Lemma 1. The income function Y i ðp2 ; nÞ wi V i for household type i has derivatives (a) ∂Y i =∂n ¼ 0, and (b) ∂Y i =∂p2 ¼ V i ∂mr , 2 ∂p2 with ∂Y 1 =∂p2 o 0 and ∂Y 2 =∂p2 4 0.
22 The reader may also consult Kemp and Wan (1986), who disagree with Dixit and Norman (1986). Dixit (1987) has a more general treatment of Pareto improving taxes.
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Proof. Part (a) follows because it is clear that factor prices are not affected by a change in n. Part (b) follows by showing the ∂w1 ∂w2 dependence of wi upon p2 through its effects upon mr2 and by noting that ∂mr o0 o ∂mr as a result of the assumption that 2 2 product 2 uses factor 2 relatively intensively.□ As a result of this lemma, the expressions for household welfare changes may be rewritten as ∂E du ∂w ∂E dn H i i i ¼ V i i C i2 þ H i i ; i ¼ 1; 2; ∂ui dp2 ∂p2 ∂n dp2
ð36Þ
Since we are assuming that an increase in the world price of good 2 increases the number of varieties of the good (increases dn i the number of firms, dp 40) and since the term ∂E ∂n o 0 due to the property that an increase in the number of varieties 2 reduces the expenditure needed to attain a given level of utility, the last term on the right hand side of (36) is positive; the increase in the number of varieties contributes positively to the welfare of each household type. The first term, however, 1 which measures the direct price effect on welfare, is negative for household type 1 (since ∂w ∂p2 o 0) and ambiguous in sign for 2 household type 2 (since ∂w 4 0). Whether households gain or lose depends upon the relative strengths of the direct price ∂p2 and varieties effects. Specifically, it is clear from (36) that household type 2 gains from an increase in p2 provided that 2 2 V 2 ∂w ∂p2 C 2 4 0, which will be the case when preferences for varieties have a CES structure (as will be shown below). On the 1 1 other hand, V 1 ∂w ∂p2 C 2 o 0 and so the right hand side of (36) for household type 1 has an ambiguous sign. Thus, the issue regarding household type 1 is clear-cut: under which conditions can the long run gains due to an increase in the number of varieties more than offset the income and consumption loss owing to a fall in the wage of unskilled labour and the increase in the price of good 2? To proceed further, we substitute the expression in (30) for the change in the number of varieties into (36) for the changes in welfare to get reduced form expressions, which then yield sufficient conditions for both households to benefit from an increase in the world price of good 2. These results give rise to the following proposition. Proposition 3. Consider the long run equilibrium for our model. Further, assume that the production of good 2 is relatively intensive in skilled labour, that the households' preferences for varieties have a CES structure and that the increase in the price of product 2 generates an increase in the number of domestic varieties produced (SRGTP 40). Then, an increase in the world market price of good 2 entails a Pareto improvement in welfare if: (a) SRGTP 4ILH 1 s12 εw1 ;mr2 (the short run growth in total profits exceeds the income losses of household type 1 – unskilled labour), and (b) εE1 ;n ¼ s12 Nn σ 1 1 4D 1 þεX 2 ;V~ 2 φ. Proof. To prove this proposition, we first express (36) in percentage and share terms as ! bi b ∂Ei ui u wi V i ∂wi mr 2 ∂mr 2 p2 p2 C i2 ∂E n n þ i ¼ ; b2 b2 ∂ui Ei p H i Ei ∂mr 2 wi ∂p2 mr 2 Hi Ei ∂n Ei p b n ¼ εwi ;mr2 si2 εEi ;n ; i ¼ 1; 2; b2 p
ð37Þ
where the CES implication that εmr2 ;p2 ; ¼ 1 has been used. Second, it is noted that the last term on the right hand side of (37) is positive for both household types, since it has been assumed that there is an increase in the number of domestic varieties b =p b 2 40Þ and an increase in the number of varieties reduces the expenditure needed to in response to an increase in p2 (n attain a given level of utility (εEi ;n o 0). Third, for the skilled labour household type 2 (i¼2), Eq. (37) shows that welfare increases provided that the first term ðεw2 ;mr2 s22 Þ 4 0, since the last term is positive as just shown. This first term may be expressed as ðεw2 ;mr2 1Þ þ ð1 s22 Þ 40, and is positive since εw2 ;mr2 1 4 0 by the Stolper–Samuelson theorem and the expenditure share on good 1 is positive, ð1 s22 Þ 4 0. Thus, household type 2 experiences a gain in welfare. Fourth, for the b =p b 2 ¼ SRGTP unskilled labour household type 1 (i ¼ 1Þ, substitution of the expression in (30) for n D 40 into (37), we get the reduced form expression b1 ∂E1 u1 u SRGTP ¼ εw1 ;mr2 s12 εE1 ;n b2 D ∂u1 E1 p ¼ ½εw1 ;mr2 s12 þ SRGTP SRGTPðD þεE1 ;n Þ=D:
ð38Þ
This expression for the welfare change for the unskilled labour household type 1 will be positive if (a) ½εw1 ;mr2 s12 þ SRGTP 40 and (b) D þ εE1 ;n o 0, since D 4 0 and SRGTP 40 by the assumption that there is an increase in the number of domestic varieties in response to an increase in p2. The first inequality may be expressed as ½SRGTP ILH 1 40, defining ILH1 s12 εw1 ;mr2 4 0 as the percentage income loss of unskilled labour arising from the price change, thus proving condition (a). The second inequality may be expressed as εE1 ;n 4 D, thus establishing condition (b), noting that εE1 ;n ¼ s12 Nn σ 1 1 under the assumption of CES preferences for varieties. This shows that conditions (a) and (b) are sufficient for the result that unskilled labour gains in welfare. Thus, we have established sufficient conditions for both households to benefit from an increase in the world price of good 2, completing the proof.□
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Proposition 3 yields a number of insights shedding light on the key issue addressed in this paper: could changes in product prices be conflict generating only in the short run but lead to a Pareto improvement in the long run? In particular, Proposition 3 establishes two sufficiency conditions for the long run outcome of an increase in the world price of product 2 to be a Pareto improvement in welfare, whereby both skilled and unskilled labour households experience an increase in welfare. This is in contrast to the short run outcome established in Proposition 1 that skilled labour households gained in welfare while unskilled labour households suffered a loss in welfare. The long run outcome depends heavily upon the extent to which the increase in the world price of product 2 increases the short run total profit earned by firms and then induces the entry of new firms in the long run, and the extent to which the long run increase in the number of varieties (firms) reduces the expenditure needed to attain a given level of utility by households (measured by the marginal willingness to pay for the increase in the number of varieties). If these effects are sufficiently strong, a Pareto improvement in welfare ensues; if not sufficiently strong, then unskilled labour households suffer a loss in welfare just as they did in the short run. The proposition establishes these precise conditions. Condition (a) of Proposition 3 is that the short (and long) run income loss of unskilled labour is smaller than the short run growth in total profits. The income loss of unskilled households reflects that impact that the increase in the world price has on these households, comprising the direct effect of the higher price needed to be paid for the consumption of product 2 (measured by the share of product 2 in the budget, s12 ) and the indirect effect of the change in the price of product 2, via the marginal revenue function, on the wage rate for unskilled labour (measured by the Stolper–Samuelson effect, εw1 ;mr2 o0). The term SRGTP measures the impact of the price increase upon the number of domestic varieties of the product produced in the long run, as indicated in Proposition 2. Condition (a) establishes a lower bound for this term, requiring that SRGTP 4ILH 1 . That is, condition (a) indicates that the short run growth in total profits needs to be of sufficient magnitude to ensure that there is not only an increase in the number of varieties produced (SRGTP 40 is sufficient for this), but also to outweigh the income loss experienced by unskilled labour. Subject to this assumption holding, Proposition 3 also provides a second sufficiency condition that has a straightforward interpretation. In this context, as expected, the aggregate marginal willingness to pay for an increase in varieties plays a key part. 1 Condition (b) requires the marginal willingness to pay for increased varieties, ∂Ei =∂n, measured by the elasticity ∂lnE εE1 ;n , ∂lnn to be greater than a lower bound given by D 1 þεX 2 ;V~ 2 φ 4 1. Since this lower bound is greater than unity, condition (b) implies that the elasticity of the marginal willingness to pay for increased variety by unskilled labour households needs to be sufficiently greater than unity. In the case of CES preferences for varieties being considered in the present context, this elasticity takes the form εE1 ;n ¼ s12 Nn σ 1 1. Since the first two terms in this expression are less than unity, the elasticity will only be greater than unity if the third term is sufficiently greater than unity. This, in turn, requires that 1o σ o 2 with σ sufficiently close to unity. More precisely, condition (b) may be written as 1 o σ o 1 þ Ds12 Nn . Clearly, this may be a rather tight condition. The closer D is to unity, the less stringent is condition (b) on the marginal willingness to pay for increased variety and, hence, the less stringent condition (b) is on the Pareto improvement outcome. Clearly, D is closer to unity if the production of good 2 is very much more skilled labour intensive than the setting up of firms, i.e., φ ¼ bn=V~ 2 is very small. This holds even if the production of good 2 is highly skilled labour intensive relative to good 1 and therefore the standard Rybczynski effect is significant. On the other hand the standard Rybczynski effect is, of course, magnified if φ is very high, i.e., the setting up of firms is much more skilled labour intensive than production. This accords with our intuition. Even if the income loss of household type 1 is very low relative to the short run growth in profits (accruing to skilled labour) the increase in n may be small. This follows if the setting up of firms is very skilled labour intensive and therefore even a small increase in n quickly whittles away total profits. The results contained in Proposition 3 suggest several remarks. First, from an empirical point of view, the main insight of Proposition 3 is that we have deduced a lower bound for the aggregate marginal willingness to pay for an increase in varieties that, subject to the assumptions of the proposition, implies a Pareto improvement. Note that the lower bound is expressed solely in terms of observable and measurable parameters. Second, we note that a key mechanism by which a Pareto improvement can occur is for the unskilled labour households to be provided with an increase in “real income” to compensate for the reduction in wage income and the increased price for differentiated goods. In principle, this “real-income” increase might be achieved by government action through a direct income transfer to unskilled labour households or through a carefully designed set of taxes and subsidies as in Dixit and Norman (1980) approach. Proposition 3 provides another mechanism that does not require government action, namely an increase in the number of varieties. This increase in the number of varieties provides the mechanism for an increase in “real income” sufficiently large to generate an increase in welfare due to the love of variety by households. Third, the reader is reminded that we have stated in Proposition 3 conditions for a Pareto improvement in the long run equilibrium because we believe that our simple modelling approach, focussing on entrepreneurship, may shed light on the stylized fact that in entrepreneurial economies (as in some countries of East Asia) vested interest groups and political motivation seem to play a relatively minor part (as compared with Europe). As already mentioned, from the point of view of international political economy, a key aim of our analysis has been to try to endogenize the existence or absence of vested interest groups.23
23 At this point it should be pointed out that there possibly exists a relationship between the skilled labour intensity of production relative to the setting up of firms and the skilled labour intensity of production (of good 2 relative to good 1). The interested reader may consult empirical work on this important issue, such as Bustos (2005) and Helpman (2006, p. 597).
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Fig. 2. Monopolistic equilibrium solutions over the world price grid.
Finally we should mention the following interesting interpretation of our model and Proposition 3. As is well known, there exists a huge literature on Pareto improving transfers between countries and agents within a country, see e.g., Woodland and Turunen-Red (1988). It should be noted that the setting up of more firms and the implicit increase in the number of varieties can be regarded as the provision of an incentive compatible income transfer from the owners of firms (household type 2) to the owners of unskilled labour (household type 1). This follows because the literature on the provision of public goods tells us that an increased provision of a public good is equivalent to an income transfer if the public good is under-provided to the recipient household. Most importantly, in our case, there is no need for governmental intervention except that there should be no impediments to the entry of firms into an industry such as high licensing fees.24 4.3. Illustrative example We provide an illustrative example of a small open monopolistically competitive economy in which world price increases for the differentiated good generate an increase in the number of domestic varieties produced that is sufficient to yield a Pareto improvement in welfare. This example, therefore, complements our theoretical analysis by providing concreteness to our results. The example makes use of CES functions for the production cost functions and the household utility functions. Both unit production functions embody the same elasticity of substitution, σ i ¼ 0:92, but have different distribution parameters given by (0.9 0.1) and (0.1 0.9) respectively. Preferences over the two goods are assumed homothetic and CES, with distribution parameters (0.8 0.2) and elasticity of substitution equal to 0.999 (close to a Cobb–Douglas utility function with constant expenditure shares). The elasticity of substitution between varieties was set to σ ¼1.5, the implied percentage markup being 2=3. Other settings are as follows: V 1 ¼ 1:5, V 2 ¼ 2:0, H 1 ¼ H2 ¼ 100 and b¼0.009. Fig. 2 shows results from simulation of the model over a range of world prices for product 2. The top left panel of Fig. 2 graphs indices of the utility levels enjoyed by the two (unskilled and skilled labour) households as the world price for 24 Actually, in the real world the entry into an industry is heavily regulated in many countries. This may be explained in terms of political economy reasons (Djankov et al., 2002), or in terms of environmental policies.
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product 2, p2, increases over the chosen range. This panel provides a numerical confirmation of the result in Proposition 3 that both household types may experience welfare gains when the world price rises. This Pareto improving outcome is seen to occur for a world price up to approximately p2 ¼ 0:365, after which the utility level for household type 1 (unskilled labour) falls. As is evident from the proposition, this Pareto improving outcome arises because, in the long run, the price increase induces an increase in the domestic output at the extensive margin by increasing the number of domestic varieties produced. This increase in n is depicted in the right upper panel of Fig. 2, thus numerically illustrating Proposition 2. The lower left panel of the figure shows the increase in the total number of varieties consumed by the households as the world price increases; it also shows the impact of the price increase and the resulting increase in the number of varieties on the demand price index for the differentiated good. Despite the increase in price (which raises the index), the increase in domestic (hence total) varieties is sufficiently great to reduce this price index and this is the source of the welfare gains accruing to unskilled labour households (whose income falls). As is evident from this graph, the reduction in the price index diminishes as p2 continues to increase and eventually begins to rise (not shown). Similarly, the number of domestic firms (varieties) increases at a lower rate as p2 increases further and eventually falls (not shown). This price index impact of the increase in p2 is because the increase in output of product 2 varieties at both the intensive and extensive margins increases the demand for skilled labour and entrepreneurship, causing the skilled labour wage rate to rise and increasing cost. The final panel of the figure provides indices of the long run equilibrium wage rates for unskilled and skilled labour, showing the standard result that the unskilled wage rate falls and the skilled wage rate rises as the world price of product 2 increases. 5. Conclusions Many governmental policies entail conflict generating product and factor price changes. However, in the presence of entrepreneurship the possibly anti-competitive effects of product price changes create incentives for entrepreneurial activities that involve the setting up of new firms and producing new varieties of goods. In this paper, we have shown that the entry of more domestic firms and the production of more domestic varieties may, in the long run and subject to certain assumptions (see Propositions 3), imply welfare gains for all households (owners of firms and workers) that more than offset the negative effect of conflict generating price changes on the wages of unskilled labour. Under these conditions, therefore, the increase in the number of domestic varieties produced may produce a Pareto improvement in welfare in the long run, in contrast to the conflict generation of the price changes in the short run. The Pareto improvement outcome depends on various features of our model. First, it has been assumed that all rent (surplus) of the short run equilibrium accrues only to the entrepreneurs (owners of firms). Using this assumption, we have shown that, given an increase in the world price of good 2 (the good produced under monopolistic competition), an increase in the output of good 2 at the intensive margin (when the number of firms is given) generates conflict between the owners of firms and workers, but the converse holds for an increase in output of good 2 at the extensive margin (when the number of firms and varieties is endogenous). Paradoxically, the stronger the anti-competitive effect of product price changes in the short run the higher the probability that in the long run product price changes lead to a Pareto improvement. Second, we assumed that the good produced under monopolistic competition is skilled labour intensive relative to the good produced under perfect competition. Then the lower the skilled labour intensity of the setting up of firms relative to the skilled labour intensity of production, the greater is the incentive for firm entry and, hence, the more likely is a Pareto improvement in the long run. Third, as expected, the economy and private rates of return on investment earned from the setting up of firms are also of paramount importance. Furthermore, the magnitude of an appropriately defined aggregate marginal willingness to pay for an increase in varieties on the part of consumers plays a crucial part in ensuring a Pareto improvement. To clarify this, we have derived lower bounds to the marginal willingness to pay that are consistent with a Pareto improvement and expressed purely in terms of observable and measurable parameters. Our model and results focus on a small open monopolistically competitive economy, in contrast to most of the related literature that typically deals with large trading economies. This literature has emphasized the important impact of the opening up of economies to free trade upon the increase in the number of varieties of differentiated goods available to consumers as the main source of welfare gains. While this is important, our focus has been on the impact of changes in market conditions in large economies upon the welfare of household types in small open economies, assuming away changes in the number of foreign varieties in order to concentrate on the effect of these changed trading conditions upon incentives for domestic firms to enter production. If these incentives are strong, the increase in the number of domestic firms may increase the number of domestic varieties sufficiently for the positive effect on welfare to dominate any negative effect upon incomes of unskilled labour households. Crucial to this outcome, is the ability of skilled labour to move from employment to the entrepreneurial activity of setting up new firms. Our short and long run results have the several potentially interesting economic interpretations. Subject to our assumptions, product price changes that are conflict generating between the owners of firms and unskilled workers in the short run imply in the long run a Pareto improving and incentive compatible transfer from the owners of firms to workers without any form of governmental intervention. This sheds new light on the possibility of implementing Pareto improving transfers by governments in multi-household and multi-country modelling frameworks. Another potential interpretation of our results relates to the question of why vested interest groups, which attempt to influence governmental decision making by means of political activities, are arguably much less important in some countries than in others. Our tentative answer to that complex question is that it is because entrepreneurship (which we define as a high mobility of skilled labour between
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production and the setting up of firms) plays a much more important role in some countries (such as, for example, in South East Asia) than in others (such as in Europe). There are worthwhile extensions. For example, the highly restrictive assumption that all rents of the short run equilibrium accrue only to the owners of firms should be relaxed. It is well known that many firms have policies of profit sharing. On the one hand, profit sharing should have an effort raising effect. On the other hand, there is the possibility that it could also act as a disincentive to entrepreneurship. This relates to a fundamental issue of which distributions of power within a firm are socially desirable, the distribution of power within the firm being a very active and topical research area (see, for example, Marin and Verdier, 2008). Finally, note that we are not arguing that the beneficial effects of entrepreneurial activity always welfare dominate the sources of conflict generation, such as the well-known Stolper–Samuelson effect or the selection effect emphasized in the recent models with heterogeneous firms. This is an unresolved issue, which should be analyzed in a model that allows for entrepreneurship (in the sense of our model) as well as heterogeneous firms.
Acknowledgements This paper has benefited considerably from the comments of the editor, two referees, Xiao Chen, Arghya Ghosh, Pascalis Raimondos-Møller, Martin Richardson and other participants at the Asia Pacific Trade Seminars (APTS2011) meeting in Hawaii, and Larry Qiu, Tony Venables and other participants at the Australasian Trade Workshop (ATW2014) in Perth. Woodland gratefully acknowledges the financial support provided by the Australian Research Council through its Discovery Grants program for this research (Grants DP0880291 and DP140101187). Views expressed here should not be attributed to the Australian Research Council. References Baumol, W.J., 2010. The Microtheory of Innovative Entrepreneurship. Princeton University Press, Princeton. Behrens, K., Murata, Y., 2007. General equilibrium models of monopolistic competition: a new approach. J. Econ. Theory 136, 776–787. Bernard, A.B., Redding, S.J., Schott, P.K., 2007. Comparative advantage and heterogeneous firms. Rev. Econ. 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Income Effects in the Theory of Monopolistic Competition and International Trade. Institute for Empirical Research in Economics, University of Zurich, CH -8006, Zürich. Working Paper 02/2008. Ghosh, A., Sen, P., 2012. Privatization in a small open economy with imperfect competition. J. Publ. Econ. Theory 14 (3), 441–471. Grossman, G., Helpman, E., 1994. Protection for sale. Am. Econ. Rev. 84, 833–850. Hart, O., 1995. Firms, Contracts and Financial Structure. Clarendon Lectures in Economics. Clarendon Press, Oxford. Helpman, E., 1981. International trade in the presence of product differentiation, economies of scale and monopolistic competition: a Chamberlin– Heckscher–Ohlin approach. J. Int. Econ. 11 (3), 305–340. Helpman, E., 2006. Trade, FDI, and the organisation of firms. J. Econ. Lit. XLIV, 589–630. Hillman, A., 1989. The Political Economy of Protection. Harvard Academic Press, London. Horn, H., 1983. Some implications of non-homotheticity in production in a two-sector general equilibrium model with monopolistic competition. J. Int. Econ. 14, 85–101. Jones, R.W., 1965. The structure of simple general equilibrium models. J. Polit. Econ. 73 (6), 557–572. Jones, R.W., 1975. Income distribution and effective protection in a multicommodity trade model. J. Econ. Theory 11, 1–15. Kemp, M.C., Wan Jr., H., 1986. Gains from trade with and without lump-sum compensation. J. Int. Econ. 21, 99–110. Krugman, P.R., 1979. Increasing returns, monopolistic competition, and international trade. J. Int. Econ. 9, 469–479. Krugman, P.R., 1981. Intraindustry specialization and the gains from trade. J. Polit. Econ. 89 (5), 959–973. Lawrence, C., Spiller, P.T., 1983. Product diversity, economies of scale, and international trade. Quart. J. Econ. 98 (1), 63–83. Lloyd, P., Schweinberger, A.G., 1997. Conflict generating product price changes: the imputed output approach. Eur. Econ. Rev. 41, 1569–1589. 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Entrepreneurship and conflict generating product price changes A.G. Schweinberger a,1, A.D. Woodland b,n a b
Previously at: Department of Economics, University of Konstanz, Fach D 150, D-78457 Konstanz, Germany School of Economics, University of New South Wales, Sydney 2052, Australia
a r t i c l e in f o
abstract
Article history: Received 18 June 2013 Accepted 28 April 2015 Available online 25 May 2015
This paper addresses the issue of the impact of changes in world prices upon the welfare of households in small open economies. Making use of a model of a small open economy with one monopolistically competitive industry, we derive conditions under which an exogenous increase in the world price of the monopolistically competitive good, arising from a shift in demand, is conflict generating between the owners of unskilled and skilled labour in the short run but Pareto improving in the long run. Output adjustments at the intensive margin make for conflict generation, but the converse holds for adjustments at the extensive margin in the long run. The analysis highlights the importance of the induced increase in the number of domestic varieties and of the skilled labour intensity in the production of goods relative to its intensity in the setting up of firms. & 2015 Elsevier B.V. All rights reserved.
JEL classification: F12 F16 Keywords: Entrepreneurship Product price changes Conflict generation between the owners of firms and workers Monopolistic competition Pareto improvements in welfare
1. Introduction In which sense, if any, is trade liberalization conflict generating between different agents? By trade liberalization we mean not only the move from an autarkic to a free trade equilibrium but also changes in domestic prices due to the reduction of tariffs or other trade impediments and to changes in trading equilibrium in the rest of the world. It seems that this question raises one of the most fundamental and time honoured issues at the centre of theoretical and empirical work in positive and normative international economics.2 The literature that focuses on this issue is huge. It ranges from the simple Stolper-Samuelson theorem and its generalizations to very recent contributions that make use of monopolistic competition models with heterogeneous firms (e.g., Egger and Kreickemeier, 2009). As is well known (e.g., Hillman, 1989), the Stolper–Samuelson theorem and its key insight that product price changes have conflict generating effects on the owners of capital and labour respectively, represent the keystone of international political economy. Even more recent articles that have spawned an impressive
n
Corresponding author at: School of Economics, University of New South Wales, Sydney 2052, Australia. Tel.: þ 61 2 9385 9707; fax: þ 61 2 9313 6337. E-mail address: [email protected] (A.D. Woodland). 1 Deceased. Professor Albert Schweinberger died on 10 August, 2013, after the initial submission of this paper and prior to the subsequent revision. I gratefully acknowledge my great debt to Albert for his initiation of, and insightful contribution to, this paper and sincerely trust that the revision would have met with Albert's approval. The economics profession has lost an outstanding scholar and an excellent researcher, and I have lost a dear friend and colleague. With sadness, I dedicate this paper to Albert Schweinberger's memory. 2 The above statement applies, of course, a fortiori to international political economy. http://dx.doi.org/10.1016/j.euroecorev.2015.04.008 0014-2921/& 2015 Elsevier B.V. All rights reserved.
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literature on international political economy (Grossman and Helpman, 1994) make use of models of the economy with intrinsic conflict generating effects, i.e., a generalized Ricardo-Viner or sector specific factor model.3 Much more recently, Melitz (2003) introduced heterogeneous firms into the rich literature on monopolistic competition models. This has led to the unearthing of new sources of conflict generation associated with trade liberalization: workers employed in certain firms gain because of a rise in productivity due to the selection effect of trade liberalization but other workers lose because they become unemployed. Equally important, trade liberalization gives rise to an increase in the wage inequality of workers employed in the same industry (see Egger and Kreickemeier, 2009). It may be argued that the new sources of conflict generation are, in a certain sense, inherent in monopolistic competition models with heterogeneous firms. Clearly the novel insights are bound to have profound consequences not only for the modeling of the effects of trade liberalization on factor markets but also on international political economy in general and the explanation of trade policies in the presence of vested interest groups in open economies in particular. This brings us to the main tenet of the present paper. While there can be no doubt that many interesting and real world relevant results regarding the conflict generating effects of trade liberalization are obtained from such models, an increase in product differentiation (increase in varieties) due to trade liberalization could mitigate or even more than offset the conflict generating effects mentioned above.4 Arguably, the number of varieties may be under-produced in the autarkic equilibrium. In this context, recall that the number of varieties can be interpreted as a privately produced public good. Furthermore, Broda and Weinstein (2006) provide very impressive evidence that the increase in the number of varieties associated with trade liberalization must be regarded as a source of aggregate gains from trade liberalization of overwhelming importance. The main issue addressed in our paper is as follows. Making use of a simple model of monopolistic competition, we ask whether product price changes associated with trade liberalization are conflict generating if we allow for trade liberalization to imply an increase in the number of domestic firms and product varieties. In order to focus on essentials, our model is very simple. Its primary innovation is that it relates the change in the production of varieties to the existence of entrepreneurial activities.5 We allow for two factors of production, unskilled and skilled labour. Skilled labour may be engaged in production or in entrepreneurial activity, i.e., the setting up of firms.6 Unskilled labour is used only in production. We distinguish between short and long run equilibria. Entrepreneurs can earn rent (super normal profits) in the short run equilibrium because they are the owners of firms. The existence of rents in short run equilibria provides incentives for skilled workers to become entrepreneurs. If, for example, the prices of the differentiated good varieties rise, one may conjecture that in the short run (when output adjusts only at the intensive margin and the number of domestic firms is given) the existence of super normal profits will magnify the conflict generating effects traditionally associated with the standard Stolper– Samuelson theorem. However, intuition also tells us that in the presence of entrepreneurship the long run effects (as more domestic firms are set up by entrepreneurs) may be very different. In fact, we show that, subject to certain conditions and assumptions, the long run effects may entail a Pareto improvement. This follows because the setting up of more firms implies an increase in the provision of varieties. The increased provision of varieties may be regarded as an increase in the provision of privately produced public goods. The latter conclusion hinges, of course, on the proof that the number of varieties is under-provided before trade liberalization and the assumption that there are no barriers to entry. The importance of the number of varieties available for consumption upon the welfare of households and the role of international trade in affecting the number of varieties is, of course, well known in the literature. The seminal work by Krugman (1979) established that even trade between identical countries would generate gains from trade due to consumers in each country having access to a greater variety of differentiated goods. Of special importance to the present issue, Krugman (1981) also constructed a model of trade between two countries with two types of factors of production and demonstrated circumstances (countries have sufficiently similar endowments) where both factors experienced a welfare gain in the move from autarky to free trade. Again, the key mechanism was the increase in the number of varieties available to the factors as consumers due to the opening up of trade. A feature of Krugman's model is that the number of varieties produced in each country does not change in the move from autarky to free trade. Lawrence and Spiller (1983) have a more general model of trade in which the numbers of varieties react to the opening up of trade, but they do not consider the distribution of income or welfare between factors of production. Similarly, Helpman (1981) models international trade using a Lancaster based model of differentiation of preferences but does not address the role of numbers of varieties in ameliorating income conflicting impacts of trade. Bernard et al. (2007) demonstrate that both factors of production may have increases in real incomes as a result of trade liberalization in a heterogeneous product model, the real income increases arising primarily from aggregate productivity gains.
3 It is well known from the literature (see, e.g., Hillman (1989), Weymark (1979), Ethier (1984, chapter 3), Jones (1975), Lloyd and Schweinberger (1997), Grossman and Helpman (1994) and the huge literature on political economy of globalisation) that generally product price changes associated with globalization are conflict generating. Attention is drawn to the debate between Kemp and Wan (1986) and Dixit and Norman (1986) about the possibility of the move to free trade to be a Pareto improvement without lump sum transfers by the government. 4 See, for example, the key assumption that all the heterogeneous firms produce a homogeneous good in Egger and Kreickemeier (2009). 5 As is well known, entrepreneurship in international trade is generally explained within the framework of networks (see Rauch and Watson, 2002). In Rauch and Watson (2002) skilled workers make use of their knowledge of networks acquired in production to become trade intermediaries. Their model is based upon market matching. While it would be pretentious to claim that our modeling of entrepreneurship captures all the interesting features of Rauch and Watson (2002), it does seem to us that our monopolistic competition model does capture some of their features. 6 Neary (2004) has provided a list of lacunae of models of monopolistic competition. One item is unlimited entrepreneurship. Our paper addresses this issue by relating entrepreneureship with skilled labour, which is in limited supply.
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Our paper is distinguished from this literature in several important ways. First, while the previous literature mentioned above focuses on the welfare gains arising to home consumers from access to foreign varieties as a result of the opening up of trade, we concentrate attention upon the impact of trading conditions on the number of domestic varieties of a differentiated product produced. An increase in the number of domestic varieties is a potential source of welfare gain to households. Second, while this literature has considered international trade between two large economies, we construct and analyze a monopolistic competition model of a small open economy. Since the rest of the trading world is large relative to the home country, the prices of traded goods are determined outside its control. Accordingly, a shift in demand structure in the rest of the world will change equilibrium prices and these will impact the domestic economy. Third, we link the formation of new domestic firms to entrepreneurship provided by skilled labour households, who can choose to allocate effort between entrepreneurial activities and working for wages, and concentrate attention upon the impact of world price changes on the welfare of the two household types. Fourth, we distinguish between the short run in which the number of firms is given and the long run in which the number of domestic firms adjusts to drive profits to zero. By doing so, we show that the welfare impact of world prices differs between the short and long runs and that the long run adjustment in the number of varieties produced may allow for Pareto improvements in welfare in contrast to the short run outcome.7 It seems to us that our results are relevant in the real world for two reasons. First, because of the empirical literature on the gains from trade due to an increase in varieties mentioned above and secondly from the perspective of international political economy. We believe that it is important to put forward a framework in which the conflict generating effects of trade liberalization are not built into the model but derived from more basic assumptions. In this context, we put forward the hypothesis that entrepreneurship is much more established in some East Asian countries than in Europe. It seems that there exists some prima facie evidence that lends support to our hypothesis; see e.g. Brandt et al. (2008). Arguably, the existence of political economy motives on the parts of agents and vested interest groups are less prevalent in some East Asian countries than in Europe. In our view this can be explained by the stylized fact that agents in East Asia are much more mobile between production and entrepreneurial activities and also the tendency to focus more on the long rather than the short term. The paper is structured as follows. The basic model and its main properties are the subject matter of the following Section 2. The short run effects of an increase in the price of the manufactured good on the welfare of entrepreneurs and unskilled workers are analyzed in Section 3. Section 4 focuses on the long run effects and contains the main results of the paper. Finally, in Section 5, we summarize the main conclusions and put forward suggestions for generalizations of our analytical framework allowing for different approaches to explain the distribution of power within a firm. 2. The model The model is one of a small open monopolistic competition economy that produces and trades two goods on the world market, and comprises a production sector that produces these goods using two factors of production and a household sector consisting of two types of households. The model determines the returns to factors of production, levels of output and consumption of the two goods, the number of monopolistically competitive firms and the welfare levels for the two households. 2.1. Production sector There are two factors of production that are intranationally, but not internationally, mobile: skilled and unskilled labour. While unskilled labour can only be used in production, skilled labour is mobile between production and entrepreneurial activity, i.e., the setting up of firms. The endowments of both factors are exogenous, with V1 and V2 denoting the total endowments of unskilled and skilled labour respectively. The factor markets are assumed to be perfectly competitive. Good 1 is a homogeneous product that is produced under perfect competition via a constant returns to scale technology, while good 2 is a differentiated product produced under monopolistic competition via a production function that is nonhomothetic and exhibits increasing returns to scale owing to the assumed fixed set-up cost per firm. Both goods are assumed to be produced in the short run, with a given number of firms, as well as the long run equilibrium, when the number of firms is endogenous. Being small, all firms act as price takers in the factor markets. The unit variable cost functions for the producers of the two goods are denoted by c1 ðw1 ; w2 Þ and c2 ðw1 ; w2 Þ, where w1 and w2 denote the wage rates of unskilled and skilled labour respectively, the input–output functions denoting the input of factor i per unit production of product j being aij ¼ aij ðw1 ; w2 Þ ∂cj ðw1 ; w2 Þ=∂wi by Shephard's Lemma. Good 2 is produced under monopolistic competition.8 Industry 2 comprises n firms producing n varieties of the differentiated product 2, each variety being produced by a different firm. Each variety is produced by the same technology using skilled and unskilled labour, the common unit variable cost function being c2 ðw1 ; w2 Þ. In addition, each firm requires an entrepreneur to commit a fixed amount of entrepreneurial input. Specifically, the fixed amount of entrepreneurial input 7
Baumol (2010, pp. 7–8) has provided an intuitive arguement that in the long run entrepreneurship can lead to a Pareto improvement. By adopting a monopolistic competition modeling framework, we assume away all strategic interactions between firms (see, for example, Neary, 2003, 2004, 2009; Cox and Ruffin, 2010). Consideration of strategic interactions raises issues that are well beyond the scope of our paper. 8
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needed for each firm is b units of skilled labour. Accordingly, the total cost function for a firm producing a variety of product 2 is C 2 ðw1 ; w2 ; x2 Þ ¼ c2 ðw1 ; w2 Þx2 þ w2 b;
ð1Þ
where x2 is the firm's output. Clearly, the production technology is non-homothetic due to the fixed set up cost of a firm.9,10 Since there are n firms, the amount of skilled labour available for production is V~ 2 ¼ V 2 bn, which is equal to the total endowment, V2, minus the amount of skilled labour allocated to the setting up of firms, bn. This is reflected in Eq. (5) further below describing the factor market equilibrium condition for skilled labour. Unskilled labour is only used for the production of the two goods, so its market equilibrium condition is given by (4) further below. Good 1 is produced by perfectly competitive firms who treat the market price of 1 parameterically, equilibrium requiring unit cost to equal price. Thus, the profit maximization condition for perfectly competitive firms in industry 1 is c1 ðw1 ; w2 Þ ¼ p1 1, where the price of good 1 is chosen as the numeraire and set equal to unity. For monopolistically competitive firms in industry 2, the profit maximization condition requires that marginal variable cost (unit variable cost) equals marginal revenue. The latter is denoted by the function mr 2 ðp2 Þ, which is common to all such firms. Thus, the profit maximization condition may be expressed as c2 ðw1 ; w2 Þ ¼ mr 2 ðp2 Þ. The short run equilibrium conditions for the production sector may be expressed as c1 ðw1 ; w2 Þ ¼ p1
ð2Þ
c2 ðw1 ; w2 Þ ¼ mr 2 ðp2 Þ
ð3Þ
a11 ðw1 ; w2 ÞX 1 þ a12 ðw1 ; w2 ÞX 2 ¼ V 1
ð4Þ
a21 ðw1 ; w2 ÞX 1 þ a22 ðw1 ; w2 ÞX 2 ¼ V 2 bn V~ 2 ;
ð5Þ
where X1 and X2 denote the aggregate outputs of the two products. The first two equations are the profit maximization conditions for firms in the two industries, while the last two equations are the factor market equilibrium conditions requiring the demands for the two factors to equal their available supplies. Given the factor endowments, the number of firms and prices these equations determine the two factor prices and outputs of the two goods. In the long run, free entry or exit of firms in the differentiated goods sector determines the equilibrium number of firms and varieties, n. The zero profit condition for firms π ½p2 c2 ðw1 ; w2 ÞX 2 w2 bn ¼ 0
ð6Þ
represents the long run equilibrium condition for the determination of the number of monopolistic firms, which is a key feature of monopolistic competition models. This condition requires that profit is zero in the long run; positive profits are driven to zero by the entry of new firms, while losses are driven to zero by the exit of firms. 2.2. Households There are two household types. A type 1 household only owns unskilled labour, while a household of type 2 only owns skilled labour. Moreover, household type 2 owns the firms in industry 2 and therefore is entitled to earn residual or supernormal profits.11 Both households consume good 1 and the available varieties of good 2, the number of available varieties being N ¼ n þ nn where n is the number of domestic varieties and nn is the number of imported foreign varieties. We impose functional structure on preferences, by following Dixit and Stiglitz (1977) in assuming that the varieties of good 2 enter the utility function in a symmetric and separable way. Thus, the assumed utility function is Uðc1 ; c~ 2 Þ ¼ U 1 ðc1 ; U 2 ðc~ 2 ÞÞ, where c~ 2 ¼ ðc21 ; c22 ; …; c2N Þ is the vector of consumptions of N varieties of good 2 and where the function U 2 ðc~ 2 Þ is symmetric in its arguments. To follow the standard practice in the literature and to focus our attention more keenly on the essence of our results rather than upon their generality, we assume that household preferences for P ðσ 1Þ=σ σ=ðσ 1Þ varieties have a constant elasticity of substitution (CES) structure given by U 2 ðc~ 2 Þ ¼ ð N Þ , where σ 4 1 is the i ¼ 1 c2i 12 (constant) elasticity of substitution between varieties. This separable preference structure yields an expenditure function 9 In many monopolistic competition models, it is assumed that the input vectors in setting up of firms and production are collinear (e.g., Krugman (1979), Markusen and Venables (2000), Behrens and Murata (2007) and Helpman (2006)). Some exceptions are, e.g., Chao and Takayama (1990), and Horn (1983). This special assumption rules out the modeling of entrepreneurship because, in our approach, entrepreneurship requires special skills. 10 Dinopoulos et al. (2011) specify a non-homothetic production function for varieties that introduces economies of scale through efficiency parameters for skilled and unskilled labour. However, their model does not have a fixed set up cost as we do. Our fixed set up cost for firms is used to model entrepreneurship provided by skilled labour households. 11 The assumption that the entire surplus accrues only to the owners of the firms may remind the reader of the Marxist approach (Hart, 1995, footnote 5, p. 5). P 12 An alternative specification of preferences would be to assume that the sub-utility function takes the additive form U 2 ðc~ 2 Þ ¼ N i ¼ 1 uðc2i Þ, where the 0 00 function u(x) has the properties that u ðxÞ 4 0 and u ðxÞ o 0. The additive utility function was proposed by Dixit and Stiglitz (1977) and has been used in monopolistic competition models by, for example, Krugman (1981) and Venables (1982) and more recently by Foellmi and Zweimüller (2004), Behrens and Murata (2007), Foellmi et al. (2008) and Zhelobodko et al. (2012). Other recent articles that make use of a model with monopolistic competition and a variable elasticity of demand include Melitz and Ottoviano (2008).
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P 1 σ 1=ð1 σÞ of the separable form E1 ðp1 ; Pðp~ 2 Þ; uÞ, where Pðp~ 2 Þ ¼ ð N is the well-known CES price index for varieties. i ¼ 1 p2i Þ P Maximization of this separable utility function subject to the budget constraint p1 c1 þ N i ¼ 1 p2i c2i ¼ I, where I is income, σ σ yields the consumer demand functions, which take the form c1 ¼ ϕ1 ðp1 ; Pðp~ 2 Þ; IÞ and c2i ¼ p2i Pðp~ 2 Þσ ϕ2 ðp1 ; Pðp~ 2 Þ; IÞ ¼ kp2i , σ where k Pðp~ 2 Þ ϕ2 ðp1 ; Pðp~ 2 Þ; IÞ. Since firms are small relative to the industry, firms take the aggregate demand given by ϕ2 and the price index Pðp~ 2 Þ as σ beyond their influence and so the perceived demand function is γðp2i Þ kp2i , where k is regarded as a constant and outside the influence of the individual firm. The resulting marginal revenue function is mr 2 ðp2i Þ ¼ p2i ðσ 1Þ=σ. As is well known, the CES functional form is very special, with the important restrictive implications that the relative love of variety is a constant, the elasticity of marginal revenue with respect to price is unity, that is, εmr2 ;p2i ∂ ln mr 2 ðp2i Þ=∂ ln p2i ¼ 1, and the markup is constant, that is, ½p2i mr 2 ðp2i Þ=p2i ¼ 1=σ.13 In a symmetric equilibrium, which applies in the current model, the prices of all varieties will be the same, the common price being denoted by the scalar p2. In this case, the marginal revenue function for each variety becomes mr 2 ðp2 Þ ¼ p2 ðσ 1Þ=σ, the price index becomes Gðp2 ; NÞ p2 N1=ð1 σÞ and the expenditure function becomes Eðp1 ; p2 ; N; uÞ E1 ðp1 ; Gðp2 ; NÞ; uÞ. Thus, the expenditure function has the properties that ∂Eðp1 ; p2 ; N; uÞ=∂p2 ¼ ∂E1 =∂p2 ∂G=∂p2 40
ð7Þ
∂Eðp1 ; p2 ; N; uÞ=∂N ¼ ∂E1 =∂p2 ∂G=∂N o0;
ð8Þ
1=ð1 σÞ
σ=ð1 σÞ
since ∂G=∂p2 ¼ N 4 0 and ∂G=∂N ¼ p2 N =ð1 σÞ o 0 under the assumption that σ 4 1. These results show that the expenditure function is increasing in p2 and decreasing in N, thus capturing the household's preference for greater product variety. The equilibrium conditions for the household sector comprise the two budget constraints, expressed as H 1 Eðp1 ; p2 ; N; u1 Þ ¼ w1 V 1 H 2 Eðp1 ; p2 ; N; u2 Þ ¼ w2 V 2 þ ½p2 c2 ðw1 ; w2 ÞX 2 w2 bn;
ð9Þ ð10Þ
where H1 and H2 denote the numbers of unskilled and skilled labour households. Since unskilled labour is only used in production, the budget constraint (9) shows that expenditure equals unskilled wage income. As indicated by the right hand side of Eq. (10), the income of household type 2 comprises skilled labour earnings and profits. Note that we assume all supernormal profits (earned in the short run) only accrue to household type 2 – the owner of firms. In the long run, free entry and exit of firms drives this profit to zero. The expenditure function, discussed above, is written as a function of the usual variables, prices and utility, but also as a function of the number of varieties, N. 2.3. International trade An important assumption of the model is that the economy is a small open monopolistically competitive economy, trading both goods freely on the international market. This means that the foreign country (or rest of the world) is very large compared to the small open economy and, hence, that the prices of all internationally traded goods are essentially determined in the foreign country. It is therefore appropriate to assume that the domestic firms in a small open economy take the common price for varieties, p2, and the number of foreign varieties, nn , as given. On the other hand, the varieties are not perfectly substitutable in demand, and so each variety has a perceived demand function c2i ¼ γðp2i Þ that is exploited by the firm in its production level choice.14 The following argument is advanced to support the small open economy assumption. Suppose that there are two countries identical in structure to our economy specified above, with the same technology and preferences but with different factor endowments, and trading both goods. Provided that endowments are not too dissimilar, free trade involves factor price equalization.15 If the foreign country is now enlarged by proportionally increasing its factor endowments, the equilibrium prices for goods will approach that country's equilibrium autarky prices. Equivalently, the importance of the home country in determining the world prices diminishes. While all home firms producing good 2 take the price index for σ good 2 as given, they maintain their perceived demand function c2i ¼ kp2i . In a symmetric equilibrium, all varieties will be equally priced at the world determined price p2. Our analysis is concerned with the situation whereby there is a shift in the structure of the foreign economy that generates an increase in the price index (common symmetric equilibrium price) for product 2 varieties. One such shift is a reduction in the weight attached to the numeraire good in the foreign utility function, thus shifting demand 13 The special nature of the CES structure for preferences over varieties and its role in simplifying many responses has been recently demonstrated and discussed by Zhelobodko et al. (2012). The CES structure rules out non-unitary price elasticities of marginal revenue, and hence rules out anti-competitive effects of price changes. See Schweinberger (1996) on the concepts of pro-and anti-competitive effects. 14 An alternative approach to modeling a small open monopolistically competitive economy is to follow Venables (1982). His approach is to assume that domestic varieties of the product are not traded internationally and that foreign varieties are imported, consumers taking the prices of foreign varieties and the number of foreign varieties as given. Other papers to follow the Venables approach include Ghosh and Sen (2012). While this approach to the model specification could be employed in the present context, we have chosen to maintain a model without such an asymmetry. 15 See Krugman (1981), Helpman (1981) and Lawrence and Spiller (1983) for monopolistic competition models of trade with factor price equalization.
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towards product 2 varieties and increasing p2. For example, let the foreign expenditure function be En ðp1 ; p2 ; N; uÞ E1 ðp1 ; αGðp2 ; NÞ; uÞ with the parameter α indicating the preference for good 2 relative to good 1. An increase in α from an initial value of unity indicates a shift in preference towards good 2 and this would have the effect of raising the equilibrium world price for all varieties of good 2. While an increase in α would proportionately increase the demands for all varieties of good 2, it would not otherwise alter the perceived demand function for varieties of firms in this industry; the perceived elasticity of demand for each variety would remain unchanged. This is the scenario that we contemplate. Other scenarios may be contemplated. In any case, this structural shift and resulting increase in p2 is taken as exogenous by the domestic firms in the small open economy. Our purpose is to analyze the impacts that this change has on the small open economy, particularly for the welfare of skilled and unskilled labour households. Accordingly, we assume that p2 changes exogenously and that nn remains fixed. Of course, a shift in demand structure leading to an increase in p2 in the foreign country may be expected to also lead to a change in the number of foreign varieties, nn , produced and these will be available to the home country's consumers. To isolate effects and to focus on home country impacts, we keep nn constant.16 2.4. Equilibrium Equations (2)–(5) and (9)–(10) describe the short run equilibrium, while these same equations together with (6) describe the long run equilibrium. In the short run, the number of monopolistic firms in industry 2, n, is given. The short run model consists of two profit maximization conditions, Eqs. (2) and (3), two factor market equilibrium conditions, Eqs. (4) and (5), as well as two income expenditure equalities (budget constraints) for the two types of households, Eqs. (9) and (10). In the short run, the model equations determine the endogenous variables comprising the two factor prices, ðw1 ; w2 Þ, the industry outputs, ðX 1 ; X 2 Þ, and utility levels for the two households, ðu1 ; u2 Þ. In the long run, the number of domestic monopolistically competitive firms, n, is endogenously determined by the zero profit (6). Equations (2)–(5) and (9)–(10) and (6) determine the two factor prices, ðw1 ; w2 Þ, the industry outputs, ðX 1 ; X 2 Þ, the utility levels for the two households, ðu1 ; u2 Þ and the number of domestic varieties of good 2, n. The model may be rewritten more compactly by using standard results from economic theory to summarize the equilibrium conditions (2)–(5) for the production sector, using expressions for the output supply functions and the factor price functions, whose properties are well known. First, if the Jacobian determinant of the production cost functions is nonvanishing, it follows from the envelope theorem that Eqs. (2)–(3) may be solved for the factor price functions wi ðp1 ; mr 2 ðp2 ÞÞ. Second, using these functions, (4)–(5) can then be solved for the output supply functions of the form X i ðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ. The properties of these factor price and output supply functions are well known.17 Accordingly, using these functions, the model may be reduced to Eqs. (9)–(10) and (6), where X i ¼ X i ðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ and wi ¼ wi ðp1 ; mr 2 ðp2 ÞÞ are determined from Eqs. (2)–(5). 3. The short run analysis We now turn to the main issue addressed in this paper: are world product price changes conflict generating? Specifically, our focus is on determining the effects of a change in the world price of good 2, arising from a shift in demand structure in the rest of the world, upon the welfare levels for the two types of households. The price change is said to be conflict generating if the welfare effects go in opposite directions for then the two household types have conflicting interests in the price change. In this section, we focus attention on the short run equilibrium as a benchmark case for the long run analysis of the following section of the paper. Before answering this question, we remind the reader about our assumption regarding the ownership of firms. In perfectly competitive models the firm ownership issue does not arise because there are no firms earning profits. The latter statement also applies to monopolistic competition models, if – following the literature – one focuses only on the long run equilibrium. In the short run, in which the number of firms is given, price changes impact profits of monopolistically competitive firms and so the ownership of firms matters for welfare analysis. Our model assumes that all firms producing good 2 are completely owned by entrepreneurs (skilled labour). Therefore, all the supernormal profits (rent) accrue only to household type 2, as indicated by the budget constraint of household type 2. Possible generalizations are sketched in Section 5 of the paper. 16 Venables (1982, pp. 225, 235) invokes the small open economy assumption in his monopolistic competition model of trade, treating the home country as a price taker. Recognizing that changes in foreign prices may change the number of foreign varieties, he develops optimal tariff formulae for the cases when the number of foreign varieties is unchanged and then does change. In the present context, it is arguable that an increase in foreign varieties will further enhance the long run welfare gains demonstrated further below. 17 See, for example, Jones (1965) for a detailed derivation of the properties of these functions for the standard two sector model. It is also possible to derive their properties by making use of a revenue function for the production sector of the form
Rðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ ¼ p1 X 1 þ mr2 ðp2 ÞX 2 ;
ð11Þ
which has all the standard properties of a revenue function (see, for example, Woodland, 1982, 49 ff). For example, it is linearly homogeneous and concave in endowments V1 and V~ 2 , and convex in p1 and mr 2 ðp2 Þ. Application of the duality approach is useful, because it yields the above model specification simplification and many potential generalizations.
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To derive the short run effects on the welfare of the two household types of an increase in the price of good 2, we firstly rewrite Eqs. (9) and (10) as H 1 Eðp1 ; p2 ; n; u1 Þ ¼ w1 V 1
ð12Þ
H 2 Eðp1 ; p2 ; n; u2 Þ ¼ w2 V~ 2 þ ½p2 mr 2 ðp2 ÞX 2 ;
ð13Þ
where it is recalled that outputs and factor prices are determined from Eqs. (4)–(3) as X i ¼ X i ðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ and wi ¼ wi ðp1 ; mr 2 ðp2 ÞÞ. The right hand side of Eq. (13) shows that, in the short run, the income of skilled worker households comprises labour earnings and profits. To determine the short run response of household welfare to a change in the world price of good 2, we totally differentiate Eqs. (12) and (13) with respect to p2, holding n fixed. This determines the effect of p2 upon the utility levels of the two households. In undertaking this task, we make use of a special feature of the model in which we adopt the assumption of CES preferences over varieties implying that ∂lnmr 2 =∂lnp2 εmr2 ;p2 ¼ 1, i.e., that the profit margin is fixed. As is well known, a fixed profit margin is a standard assumption of a huge literature on monopolistic competition. The outcome of this task gives rise to the following proposition. Proposition 1. Assume the short run model of monopolistic competition described by equations (12) and (13), with the number of firms fixed, and assume that industry 2 uses factor 2 relatively intensively. Assume also that the households' preferences for varieties have a CES structure. Then, an increase in the world price of product 2 has the following welfare effects: (a) a reduction in welfare for household type 1, and (b) an increase in welfare for household type 2. Proof. Differentiation of Eq. (12) yields the result that ∂E1 ∂w1 ∂mr 2 H1 du1 ¼ V 1 C 12 dp2 ; ∂u1 ∂mr 2 ∂p2
ð14Þ
1 where E1 Eðp1 ; p2 ; n; u1 Þ and C 12 H 1 ∂E ∂p 40 is the aggregate consumption of good 2 by households of type 1. Since we 2
∂w1 2 o0) and ∂mr assume that industry 2 is relatively factor 2 intensive (whence ∂mr ∂p2 ¼ ðσ 1Þ=σ 4 0 under CES preferences, it is 2 1 ∂w1 ∂mr 2 evident that V 1 ∂mr C 2 o0 and, hence, that du1 =dp2 o 0. Unskilled labour households suffer a loss in welfare. 2 ∂p2 A similar differentiation of Eq. (13) yields
H2
∂E2 du2 ¼ V~ 2 dw2 þ p2 mr 2 p2 dX 2 þX 2 dp2 dmr2 C 22 dp2 ; ∂u2
ð15Þ
2 where E2 Eðp1 ; p2 ; n; u2 Þ and C 22 H 2 ∂E ∂p2 4 0 is the aggregate consumption of good 2 by households of type 2. Expression (15) may be re-expressed as
H2
∂E2 b 2 þ p X 2 1 ð1 t 2 Þεmr ;p p b 2 þ t 2 p2 X 2 X b2 ; b 2 p2 C 22 p du2 ¼ w2 V~ 2 w 2 2 2 ∂u2
b 2 dw2 =w2 ), t 2 ðp2 mr 2 Þ=p2 denotes the profit margin or percentage price where the b denotes percentage change (e.g., w markup and εX 2 ;mr2 ∂lnX 2 =∂lnmr 2 . In percentage and share terms, this may be written as ∂E2 u2 du2 w2 V~ 2 t p X b t 2 p2 X 2 p C2 b 2 þ 2 2 2X b b2 2 2 p ¼ 1 ð1 t 2 Þεmr2 ;p2 p w 2þ ∂u2 E2 u2 H 2 E2 H 2 E2 t 2 H 2 E2 H 2 E2 2 b 2 þ ð1 θ2 Þ 1 ð1 t 2 Þεmr ;p p b 2 þ ð1 θ 2 ÞX b2 b 2 s2 p ¼ θ2 w 2 2 t2
ð1 θ2 Þ b2 ; ¼ θ2 εw2 ;mr2 þ ð1 θ2 ÞεX 2 ;mr2 εmr2 ;p2 þ 1 ð1 t 2 Þεmr2 ;p2 s2 p t2 ~
p C2
where θ2 wH22VE22 is the share of household 2's income arising from labour and s2 H22 E22 is household 2's expenditure share of product 2. By definition, the two shares have the properties that 0 oθ2 o 1 and 0 os2 o1. The general elasticity expression obtained above may now be simplified by invoking the assumption of CES preferences for varieties, which implies that εmr2 ;p2 ¼ 1. With this assumption, the expression simplifies to
∂E2 u2 du2 ð1 θ2 Þ b2 ½1 ð1 t 2 Þ s2 p ¼ θ2 εw2 ;mr2 þ ð1 θ2 ÞεX 2 ;mr2 þ t2 ∂u2 E2 u2 b2 ¼ ½θ2 εw2 ;mr2 þ ð1 θ2 ÞεX 2 ;mr2 þ ð1 θ2 Þ s2 p b2 : ¼ ½θ2 ðεw2 ;mr2 1Þ þ ð1 s2 Þ þð1 θ2 ÞεX 2 ;mr2 p
ð16Þ
The Stolper–Samuelson theorem indicates that εw2 ;mr2 41 (magnification effect of shadow price on the skilled wage rate), while the elasticity of supply of good 2 with respect to the shadow price of good 2 is positive, i.e., εX 2 ;mr2 40. These b 2 on the right hand properties, along with the share properties that 0 oθ2 o 1 and 0 os2 o1, ensure that the coefficient of p
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side is positive. Accordingly, we have the result that b2 ∂lnE2 u ¼ θ2 εw2 ;mr2 1 þ ð1 s2 Þ þ ð1 θ2 ÞεX 2 ;mr2 40; b2 ∂lnu2 p
ð17Þ
showing that skilled labour households experience a gain in welfare. This completes the proof.□ Proposition 1 states that the increase in the world price of good 2 generates an unambiguous conflict of interest between the two types of households – those who own unskilled labour and those who own skilled labour and firms – in the short run. The owners of skilled labour, which is used relatively intensively in the production of the differentiated good, whose price has risen, and who own the firms and so enjoy short run profits benefit from the price increase. The other factor loses because its income falls and it faces higher prices. This result is perhaps not surprising in view of the well-known Stolper– Samuelson theorem established under perfectly competitive behaviour on the part of firms, as now discussed. The importance of the result contained in this proposition is that it generalizes the validity of the Stolper–Samuelson theorem to the context of an economy with monopolistically competitive firms. The Stolper–Samuelson theorem establishes that, in a perfectly competitive two-sector model, an increase in the price of a product will raise the real income, and hence utility, of the factor that is relatively intensively used in the production of that product and reduce the real income of the other factor of production. This theorem is based upon the magnification effect of product prices upon factor prices, which implies that the increase in real income for the first mentioned factor is in terms of both products so there is a welfare gain for any valid preferences. The result is that price changes are conflict generating, since one factor gains and the other loses in welfare. In the present context, our model incorporates monopolistic competition and so the income of skilled labour includes the short run profits that will be affected (most plausibly increased) by an increase in the world price of product 2, thus potentially blurring the Stolper–Samuelson impact. However, it is important to note that we have also incorporated the very special assumption of CES preferences for varieties, implying that εmr2 ;p2 ¼ 1 so a 1% rise in p2 ensures a 1% rise in mr2 and implying that the percentage price markup is a constant. Since in our model the Stolper–Samuelson effect operates via mr2, and mr2 and p2 are proportional, the traditional Stolper–Samuelson magnification effect occurs. Also, this feature and the constant markup combine to ensure that the total income of skilled labour households rises. Thus, the Stolper–Samuelson theorem continues to hold when preferences for varieties have a CES structure.18 Can some of our results be generalized? This seems to be an important issue, which we now address briefly. A routine generalization would be to assume that both household types have a claim on supernormal profits and that the shares of entitlement are exogenous. A more interesting approach consists of endogenizing the entitlement shares by introducing an effort function with entitlement shares as arguments. Still another possibility would be to allow for Nash bargaining to determine the shares. In that case, it is well known that the distribution of power within the firm is captured by the bargaining power of the owners of the firm and workers.19 Finally, generalizations to higher dimensions appear to be straightforward if both household types own all the types of factors (but in different proportions) and all the household endowment sectors lie within the diversification cone of the economy, making use of the concept of output imputed to household endowments with various types of factors (Lloyd and Schweinberger, 1997; Woodland, 1974). 4. The long run analysis In this section, we analyze the long run implications of an increase in the world price of product 2 arising from a shift in preferences in the rest of the world. First, we consider the effect of this price increase upon the number of domestic firms in the monopolistically competitive production sector. In particular, we establish the necessary and sufficient conditions for a higher price to induce greater entrepreneurship via an increase in the number of firms, which is the intuitively plausible outcome. Second, we follow our main objective of the paper by examining the consequences of the price increase for the welfare of the two types of households. The focus, as in the short run section, is to determine whether the price increase generates income conflict between households. Before moving to these two tasks, it is useful to rewrite Eqs. (9)–(10) and (6) of the long run model as H 1 Eðp1 ; Gðp2 ; NÞ; u2 Þ ¼ w1 V 1
ð18Þ
H 2 Eðp1 ; Gðp2 ; NÞ; u2 Þ ¼ w2 V 2
ð19Þ
πðp2 ; nÞ ½p2 c2 ðw1 ; w2 ÞX 2 w2 bn ¼ 0;
ð20Þ
where, as before, X i ¼ X i ðp1 ; mr 2 ðp2 Þ; V 1 ; V~ 2 Þ
ð21Þ
18 The proof of this proposition should make clear where the CES assumption was used and so give clues as to why the Stolper–Samuelson result might break down under alternative assumptions about preferences, with different behaviour of the elasticity εmr2 ;p2 and markups. 19 See Marin and Verdier (2008) for how to model the distribution of power inside a firm, making use of principal agency theory.
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wi ¼ wi ðp1 ; mr 2 ðp2 ÞÞ
ð22Þ
are determined from Eqs. (2)–(5) and V~ 2 ¼ V 2 bn. It is observed that the right hand side of the budget constraint of household 2 now has no profits, since they are zero in the long run as specified in Eq. (20). As a result, household types 1 and 2 now appear symmetrically in the model. It is also noteworthy that the zero profit condition (20) may be used to determine the number of firms, n; then, using this result, the utility levels are determined from Eqs. (18) and (19). 4.1. The effect of a price increase on the number of firms To proceed, we totally differentiate Eq. (20) with respect to p2 and n, assuming that the economy is initially in a long run equilibrium. This yields the expression ∂mr 2 dπ ¼ p2 c2 dX 2 þ X 2 1 ð23Þ dp2 w2 b dn bn dw2 ¼ 0; ∂p2 where the changes in output of good 2 and the price of skilled labour are given by dX 2 ¼
∂X 2 ∂mr 2 ∂X 2 dp2 b dn ∂mr 2 ∂p2 ∂V~ 2
ð24Þ
dw2 ¼
∂w2 ∂mr 2 dp2 : ∂mr 2 ∂p2
ð25Þ
This yields the following partial derivatives of the profit function, namely
∂X 2 ∂π ¼ b w2 þ p2 c2 o0 ∂n ∂V~ 2 ∂X 2 ∂mr 2 ∂π ∂mr 2 ðp2 Þ ∂w2 ∂mr 2 ¼ p2 c2 þ X2 1 : bn ∂p2 ∂p2 ∂mr 2 ∂p2 ∂mr 2 ∂p2
ð26Þ ð27Þ
It is evident that ∂π=∂n o 0 under our assumption that product 2 uses factor 2 relatively intensively, since then ∂X 2 =∂V~ 2 40. However, the derivative ∂π=∂p2 cannot be signed on the basis of our assumptions (the first term is positive, the last is ∂n ∂π ∂π negative and the sign of the middle term is ambiguous in general). Since ∂p ¼ ð∂p = Þ, this ambiguity of sign leads to the 2 2 ∂n conclusion that an increase in the world price of good 2 may either increase or decrease the number of domestic firms. The outcome depends on whether an increase in the world price will increase or decrease profits, given the number of firms. Further assumptions are needed to pin down the response of the number of firms to the price increase. To this end, it will be convenient to express these derivatives in percentage terms as h i ∂π ¼ bnw2 1 þφεX 2 ;V~ 2 o0 ð28Þ ∂lnn
∂π ¼ bnw2 εX 2 ;mr2 εw2 ;mr2 εmr2 ;p2 þt 2 1 1 ð1 t 2 Þεmr2 ;p2 ; ∂lnp2
ð29Þ
2 where φ bn=V~ 2 40 and t 2 p2 c2pðw1 ;w2 Þ ¼ bnw p2 X 2 is the markup for product 2. Taking the ratio of these two expressions, we 2 obtain
^ p^ 2 ¼ n=
∂π=∂lnn ðεX 2 ;mr2 εw2 ;mr2 Þεmr2 ;p2 þ t 2 1 ½1 ð1 t 2 Þεmr2 ;p2 SRGTP ; ¼ ∂π=∂lnp2 D 1 þεX 2 ;V~ 2 φ
ð30Þ
where SRGTP is defined as the numerator and D 1 þ εX 2 ;V~ 2 φ 40 as the denominator. The term SRGTP is (apart from the constant bnw2) the short run growth in total profits, being the change in profits due to a 1% increase in the price of product 2, with the number of domestic varieties (firms) held constant. The denominator D is (apart from the constant bnw2 ) the change in total profits arising from a 1% increase in the number of domestic varieties (firms), with the price of product 2 held constant. The economic interpretation of expression (30) is straightforward. The distinctive feature of the denominator D is a weighted Rybczynski effect. As is well known, the elasticity of output with respect to the relatively intensively used factor is greater than unity (εX 2 ;V~ 2 4 1), i.e., the standard Rybczynski magnification effect. The weight is given by φ bn=V~ 2 40, which may be greater, equal to or less than one, depending on the skilled labour intensity of the setting up of firms relative to production. It follows that the assumed mobility of skilled labour between entrepreneurial activities and production may either reinforce, leave unchanged, or diminish the standard magnification effect. Intuitively, a given p^ 2 4 0 implies (ceteris paribus) a smaller n^ if the entrepreneurial activity requires more skilled labour than does production (φ 4 1). Clearly, in this case, the setting up of more firms whittles away more quickly the supernormal profits of the short run equilibrium. The numerator of expression (30) given by SRGTP consists of three effects: a standard output price effect that is positive (εX 2 ;mr2 40), a standard Stolper–Samuelson effect that captures the increase in the fixed cost of setting up firms due to the rise in the wage of skilled labour (εw2 ;mr2 41), and a profit margin effect (1 pc2 εmr2 ;p2 ¼ 1 ð1 t 2 Þεmr2 ;p2 ) that is weighted by 2
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the value productivity of all firms, i.e., ζ p2 X 2 =bnw2 ¼ t 2 1 .20 In general, the numerator cannot be unambiguously signed on the basis of economic theory; consequently, an increase in price is not guaranteed to increase the number of firms in industry 2. Rearranging expression (30), we can derive a necessary and sufficient condition for an increase in p2 to entail an increase in the number of firms (and therefore varieties). This condition is specified in the following proposition. Proposition 2. Assume a long run equilibrium for our small open economy. Further, assume that the production of good 2 is intensive in factor 2 (skilled labour) relative to good 1 and that the households' preferences for varieties have a CES structure. Then a necessary and sufficient condition for an increase in the world market price of good 2 to imply an increase in entrepreneurial activity (number of firms and varieties, n) is that εX 2 ;mr2 4εw2 ;mr2 1 4 0:
ð31Þ
Proof. It follows directly from (30) and the property D 4 0 that a necessary and sufficient condition for an increase in n is that the numerator SRGTP 40. Invoking the assumption that preferences for varieties have a CES structure, whence εmr2 ;p2 ¼ 1, the expression for SRGTP simplifies to SRGTP ¼ ðεX 2 ;mr2 εw2 ;mr2 Þ þ t 2 1 ½1 ð1 t 2 Þ ¼ εX 2 ;mr2 þð1 εw2 ;mr2 Þ. Since εX 2 ;mr2 4 0 (positive supply response around the production frontier due to an increase in the shadow price) and εw2 ;mr2 4 1 (the Stolper–Samuelson magnification effect), SRGTP is not guaranteed to be positive in general. It will be positive if, and only if, εX 2 ;mr2 4 εw2 ;mr2 1, thus completing the proof.□ Proposition 2 provides a necessary and sufficient condition for an increase in the world price of good 2 to encourage entry into the differentiated good sector and to thereby increase the number of domestic firms and the number of domestic varieties produced. While it might be expected that entry would be encouraged, the condition for this outcome indicates that this is not a foregone conclusion despite our special assumption of CES preferences. The necessary and sufficient condition involves two elasticities – the output supply elasticity εX 2 ;mr2 , which measures the movement around the production frontier, and the factor price elasticity εw2 ;mr2 , which measures the responsiveness of the wage rate for skilled labour both with respect to changes in the marginal revenue. Since εmr2 ;p2 ¼ 1 under the CES assumption, these are the normal output supply elasticities and the normal Stolper–Samuelson elasticity with respect to price. The condition expressed in Proposition 2 requires the output supply elasticity to be sufficiently high, meaning that it is greater than the Stolper–Samuelson elasticity minus unity. This requirement is not guaranteed, but depends on the values of these elasticities, which, in turn, depends upon the factor endowments and the structure of the production functions.21 Proposition 2 is interesting because it generalizes the result from the literature by focussing on the crucial role played by the Stolper–Samuelson effect. The proposition unearths a hitherto ignored interdependence between entrepreneurial activities and conflict generating effects of product price changes embodied in the Stolper–Samuelson theorem. The equilibrium value of n: Before leaving this subsection, we derive a formula for the equilibrium number of varieties, n, and use this to graphically illustrate Proposition 2. The equilibrium value for the number of varieties, n, is obtained from the zero profit condition π ½p2 c2 ðw1 ; w2 ÞX 2 w2 bn ¼ t 2 p2 X 2 w2 bn ¼ 0:
ð32Þ
In this expression, X 2 ¼ X 2 ðp1 ; mr 2 ðp2 Þ; V 1 ; V 2 bnÞ. For any given p2, the factor prices are given and X2 depends linearly upon n through its effect on the amount of skilled labour used in production, V~ 2 ¼ V 2 bn, via the Rybczynski theorem. The factor market equilibrium conditions may be expressed in matrix form as AX ¼ V ð0; bnÞ0 , yielding the output vector as X ¼ A 1 V A 1 ð0; bnÞ0 , where A 1 ¼ ½aij is the inverse of A. Defining X ¼ A 1 V, we may write X 2 ¼ X 2 a22 bn. Thus, profit may be expressed as π t 2 p2 ðX 2 a22 bnÞ w2 bn ¼ t 2 p2 X 2 bðw2 þ a22 t 2 p2 Þn;
ð33Þ
which is linear in n. Setting π¼0 and solving this linear zero profit equation, the long run equilibrium value for n may be expressed as n¼
t 2 p2 X 2 X2 : ¼ w2 bðw2 þa22 t 2 p2 Þ 22 b a þ t 2 p2
ð34Þ
Given p2, the factor prices are determined and, hence, all of the terms on the right hand side are determined. Thus, the equilibrium number of varieties (firms), n, may be calculated. The linear expression for the profit function (with p2 given) may be used to illustrate Proposition 2. Fig. 1 depicts the downward sloping linear profit function expressed in (33) labeled as Π1 and with equilibrium number of varieties equal to n01 . If p2 were to increase, thus increasing mr 2 ðp2 Þ, both the intercept and slope of this line increase. The intercept rises, since the higher marginal revenue induces greater output, X 2 , around the production frontier. The slope of the profit line also 20 The value productivity of all firms can be interpreted as the gross economy rate of return from investing in the setting up of firms. The equality ζ ¼ t 1 follows directly from the long run zero profit condition π ¼0. 21 Jones (1965) provides expressions for these responses in terms of endowments, factor shares and elasticities of substitution.
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Fig. 1. The profit function and the equilibrium number of varieties.
increases (becomes more negative) because the higher marginal revenue induces a magnified positive effect on w2 that dominates the expression for the slope. Thus, the new profit function (as a function of n) line could be the one labelled Π2 or the one labelled Π3. In the case of Π2, the slope increase is sufficiently small for the equilibrium number of varieties to increase from n01 to n02 . However, in the case of Π3, the slope increase is sufficiently large that the equilibrium number of varieties decreases from n01 to n03 . This illustrates the possibilities of an increase in the world price for the differentiated product to either increase or decrease the number of varieties produced in the long run, as indicated by Proposition 2. To conclude this discussion, note that we assume throughout the remainder of the paper that the conditions implying an increase of n (in Proposition 2) in response to an increase in the world price for good 2 are satisfied.
4.2. The effect of a price increase on the welfare of households Can there be gains from trade in the sense of a Pareto improvement in an economy with many different household types without governmental intervention? This key issue in international economics has received considerable attention (making use of models of perfect competition) in the literature. To be more specific, until the work by Dixit and Norman (1980) it was argued that a Pareto improvement is only possible if the government applies a system of lump sum transfers between household types. Dixit and Norman were the first to prove that an appropriate set of employment and commodity taxes and subsidies are, subject to certain assumptions, sufficient to ensure a Pareto improvement.22 Our contention in this paper is that an important key insight of the new trade theory is that Pareto improvements are a real possibility in economies with many household types and monopolistic competition even without any form of governmental intervention. Our main current task is to derive a set of conditions under which an increase in the world price of good 2 implies a Pareto improvement in entrepreneurial economies. As is intuitively obvious, the concept of the marginal willingness to pay for an increase in the number of varieties, the “privately produced public good” plays a crucial role in this context. It may, of course, be argued (Neary, 2004) that the marginal willingness to pay for an increase in the number of varieties declines very rapidly as the number of varieties rises. On the other hand, as mentioned in the introduction, in the light of recent overwhelming empirical evidence for the US economy (Broda and Weinstein, 2006) an increase in the number of varieties should be regarded as a very important source of gains from trade. In order to determine the conditions under which the Pareto-improvement presumption is supported by the model and its assumptions, we now totally differentiate the income expenditure equalities of household types 1 and 2 in Eqs. (18) and (19) with respect to p2 and taking into account the impact of the change in the world price upon the number of domestic varieties produced. This yields Hi
∂Ei dui ∂Y i ∂Y i ∂E dn Hi i ¼ C i2 þ ; ∂ui dp2 ∂p2 ∂n ∂n dp2
i ¼ 1; 2;
ð35Þ
where ∂Ei =∂n ¼ ð∂Ei =∂GÞð∂G=∂NÞ o0 denotes the (negative of the) marginal willingness to pay for an increase in the number of varieties. In this expression, C i2 ¼ H i ð∂Ei =∂GÞð∂G=∂p2 Þ 4 0 is the aggregate consumption of good 2 by household type i, and household incomes in the long run are Y i wi V i . Before using (35) to determine the welfare effects of a price increase, it is useful to obtain some preliminary results that are presented in the following lemma. ∂w1 ∂mr2 Lemma 1. The income function Y i ðp2 ; nÞ wi V i for household type i has derivatives (a) ∂Y i =∂n ¼ 0, and (b) ∂Y i =∂p2 ¼ V i ∂mr , 2 ∂p2 with ∂Y 1 =∂p2 o 0 and ∂Y 2 =∂p2 4 0.
22 The reader may also consult Kemp and Wan (1986), who disagree with Dixit and Norman (1986). Dixit (1987) has a more general treatment of Pareto improving taxes.
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Proof. Part (a) follows because it is clear that factor prices are not affected by a change in n. Part (b) follows by showing the ∂w1 ∂w2 dependence of wi upon p2 through its effects upon mr2 and by noting that ∂mr o0 o ∂mr as a result of the assumption that 2 2 product 2 uses factor 2 relatively intensively.□ As a result of this lemma, the expressions for household welfare changes may be rewritten as ∂E du ∂w ∂E dn H i i i ¼ V i i C i2 þ H i i ; i ¼ 1; 2; ∂ui dp2 ∂p2 ∂n dp2
ð36Þ
Since we are assuming that an increase in the world price of good 2 increases the number of varieties of the good (increases dn i the number of firms, dp 40) and since the term ∂E ∂n o 0 due to the property that an increase in the number of varieties 2 reduces the expenditure needed to attain a given level of utility, the last term on the right hand side of (36) is positive; the increase in the number of varieties contributes positively to the welfare of each household type. The first term, however, 1 which measures the direct price effect on welfare, is negative for household type 1 (since ∂w ∂p2 o 0) and ambiguous in sign for 2 household type 2 (since ∂w 4 0). Whether households gain or lose depends upon the relative strengths of the direct price ∂p2 and varieties effects. Specifically, it is clear from (36) that household type 2 gains from an increase in p2 provided that 2 2 V 2 ∂w ∂p2 C 2 4 0, which will be the case when preferences for varieties have a CES structure (as will be shown below). On the 1 1 other hand, V 1 ∂w ∂p2 C 2 o 0 and so the right hand side of (36) for household type 1 has an ambiguous sign. Thus, the issue regarding household type 1 is clear-cut: under which conditions can the long run gains due to an increase in the number of varieties more than offset the income and consumption loss owing to a fall in the wage of unskilled labour and the increase in the price of good 2? To proceed further, we substitute the expression in (30) for the change in the number of varieties into (36) for the changes in welfare to get reduced form expressions, which then yield sufficient conditions for both households to benefit from an increase in the world price of good 2. These results give rise to the following proposition. Proposition 3. Consider the long run equilibrium for our model. Further, assume that the production of good 2 is relatively intensive in skilled labour, that the households' preferences for varieties have a CES structure and that the increase in the price of product 2 generates an increase in the number of domestic varieties produced (SRGTP 40). Then, an increase in the world market price of good 2 entails a Pareto improvement in welfare if: (a) SRGTP 4ILH 1 s12 εw1 ;mr2 (the short run growth in total profits exceeds the income losses of household type 1 – unskilled labour), and (b) εE1 ;n ¼ s12 Nn σ 1 1 4D 1 þεX 2 ;V~ 2 φ. Proof. To prove this proposition, we first express (36) in percentage and share terms as ! bi b ∂Ei ui u wi V i ∂wi mr 2 ∂mr 2 p2 p2 C i2 ∂E n n þ i ¼ ; b2 b2 ∂ui Ei p H i Ei ∂mr 2 wi ∂p2 mr 2 Hi Ei ∂n Ei p b n ¼ εwi ;mr2 si2 εEi ;n ; i ¼ 1; 2; b2 p
ð37Þ
where the CES implication that εmr2 ;p2 ; ¼ 1 has been used. Second, it is noted that the last term on the right hand side of (37) is positive for both household types, since it has been assumed that there is an increase in the number of domestic varieties b =p b 2 40Þ and an increase in the number of varieties reduces the expenditure needed to in response to an increase in p2 (n attain a given level of utility (εEi ;n o 0). Third, for the skilled labour household type 2 (i¼2), Eq. (37) shows that welfare increases provided that the first term ðεw2 ;mr2 s22 Þ 4 0, since the last term is positive as just shown. This first term may be expressed as ðεw2 ;mr2 1Þ þ ð1 s22 Þ 40, and is positive since εw2 ;mr2 1 4 0 by the Stolper–Samuelson theorem and the expenditure share on good 1 is positive, ð1 s22 Þ 4 0. Thus, household type 2 experiences a gain in welfare. Fourth, for the b =p b 2 ¼ SRGTP unskilled labour household type 1 (i ¼ 1Þ, substitution of the expression in (30) for n D 40 into (37), we get the reduced form expression b1 ∂E1 u1 u SRGTP ¼ εw1 ;mr2 s12 εE1 ;n b2 D ∂u1 E1 p ¼ ½εw1 ;mr2 s12 þ SRGTP SRGTPðD þεE1 ;n Þ=D:
ð38Þ
This expression for the welfare change for the unskilled labour household type 1 will be positive if (a) ½εw1 ;mr2 s12 þ SRGTP 40 and (b) D þ εE1 ;n o 0, since D 4 0 and SRGTP 40 by the assumption that there is an increase in the number of domestic varieties in response to an increase in p2. The first inequality may be expressed as ½SRGTP ILH 1 40, defining ILH1 s12 εw1 ;mr2 4 0 as the percentage income loss of unskilled labour arising from the price change, thus proving condition (a). The second inequality may be expressed as εE1 ;n 4 D, thus establishing condition (b), noting that εE1 ;n ¼ s12 Nn σ 1 1 under the assumption of CES preferences for varieties. This shows that conditions (a) and (b) are sufficient for the result that unskilled labour gains in welfare. Thus, we have established sufficient conditions for both households to benefit from an increase in the world price of good 2, completing the proof.□
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Proposition 3 yields a number of insights shedding light on the key issue addressed in this paper: could changes in product prices be conflict generating only in the short run but lead to a Pareto improvement in the long run? In particular, Proposition 3 establishes two sufficiency conditions for the long run outcome of an increase in the world price of product 2 to be a Pareto improvement in welfare, whereby both skilled and unskilled labour households experience an increase in welfare. This is in contrast to the short run outcome established in Proposition 1 that skilled labour households gained in welfare while unskilled labour households suffered a loss in welfare. The long run outcome depends heavily upon the extent to which the increase in the world price of product 2 increases the short run total profit earned by firms and then induces the entry of new firms in the long run, and the extent to which the long run increase in the number of varieties (firms) reduces the expenditure needed to attain a given level of utility by households (measured by the marginal willingness to pay for the increase in the number of varieties). If these effects are sufficiently strong, a Pareto improvement in welfare ensues; if not sufficiently strong, then unskilled labour households suffer a loss in welfare just as they did in the short run. The proposition establishes these precise conditions. Condition (a) of Proposition 3 is that the short (and long) run income loss of unskilled labour is smaller than the short run growth in total profits. The income loss of unskilled households reflects that impact that the increase in the world price has on these households, comprising the direct effect of the higher price needed to be paid for the consumption of product 2 (measured by the share of product 2 in the budget, s12 ) and the indirect effect of the change in the price of product 2, via the marginal revenue function, on the wage rate for unskilled labour (measured by the Stolper–Samuelson effect, εw1 ;mr2 o0). The term SRGTP measures the impact of the price increase upon the number of domestic varieties of the product produced in the long run, as indicated in Proposition 2. Condition (a) establishes a lower bound for this term, requiring that SRGTP 4ILH 1 . That is, condition (a) indicates that the short run growth in total profits needs to be of sufficient magnitude to ensure that there is not only an increase in the number of varieties produced (SRGTP 40 is sufficient for this), but also to outweigh the income loss experienced by unskilled labour. Subject to this assumption holding, Proposition 3 also provides a second sufficiency condition that has a straightforward interpretation. In this context, as expected, the aggregate marginal willingness to pay for an increase in varieties plays a key part. 1 Condition (b) requires the marginal willingness to pay for increased varieties, ∂Ei =∂n, measured by the elasticity ∂lnE εE1 ;n , ∂lnn to be greater than a lower bound given by D 1 þεX 2 ;V~ 2 φ 4 1. Since this lower bound is greater than unity, condition (b) implies that the elasticity of the marginal willingness to pay for increased variety by unskilled labour households needs to be sufficiently greater than unity. In the case of CES preferences for varieties being considered in the present context, this elasticity takes the form εE1 ;n ¼ s12 Nn σ 1 1. Since the first two terms in this expression are less than unity, the elasticity will only be greater than unity if the third term is sufficiently greater than unity. This, in turn, requires that 1o σ o 2 with σ sufficiently close to unity. More precisely, condition (b) may be written as 1 o σ o 1 þ Ds12 Nn . Clearly, this may be a rather tight condition. The closer D is to unity, the less stringent is condition (b) on the marginal willingness to pay for increased variety and, hence, the less stringent condition (b) is on the Pareto improvement outcome. Clearly, D is closer to unity if the production of good 2 is very much more skilled labour intensive than the setting up of firms, i.e., φ ¼ bn=V~ 2 is very small. This holds even if the production of good 2 is highly skilled labour intensive relative to good 1 and therefore the standard Rybczynski effect is significant. On the other hand the standard Rybczynski effect is, of course, magnified if φ is very high, i.e., the setting up of firms is much more skilled labour intensive than production. This accords with our intuition. Even if the income loss of household type 1 is very low relative to the short run growth in profits (accruing to skilled labour) the increase in n may be small. This follows if the setting up of firms is very skilled labour intensive and therefore even a small increase in n quickly whittles away total profits. The results contained in Proposition 3 suggest several remarks. First, from an empirical point of view, the main insight of Proposition 3 is that we have deduced a lower bound for the aggregate marginal willingness to pay for an increase in varieties that, subject to the assumptions of the proposition, implies a Pareto improvement. Note that the lower bound is expressed solely in terms of observable and measurable parameters. Second, we note that a key mechanism by which a Pareto improvement can occur is for the unskilled labour households to be provided with an increase in “real income” to compensate for the reduction in wage income and the increased price for differentiated goods. In principle, this “real-income” increase might be achieved by government action through a direct income transfer to unskilled labour households or through a carefully designed set of taxes and subsidies as in Dixit and Norman (1980) approach. Proposition 3 provides another mechanism that does not require government action, namely an increase in the number of varieties. This increase in the number of varieties provides the mechanism for an increase in “real income” sufficiently large to generate an increase in welfare due to the love of variety by households. Third, the reader is reminded that we have stated in Proposition 3 conditions for a Pareto improvement in the long run equilibrium because we believe that our simple modelling approach, focussing on entrepreneurship, may shed light on the stylized fact that in entrepreneurial economies (as in some countries of East Asia) vested interest groups and political motivation seem to play a relatively minor part (as compared with Europe). As already mentioned, from the point of view of international political economy, a key aim of our analysis has been to try to endogenize the existence or absence of vested interest groups.23
23 At this point it should be pointed out that there possibly exists a relationship between the skilled labour intensity of production relative to the setting up of firms and the skilled labour intensity of production (of good 2 relative to good 1). The interested reader may consult empirical work on this important issue, such as Bustos (2005) and Helpman (2006, p. 597).
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Fig. 2. Monopolistic equilibrium solutions over the world price grid.
Finally we should mention the following interesting interpretation of our model and Proposition 3. As is well known, there exists a huge literature on Pareto improving transfers between countries and agents within a country, see e.g., Woodland and Turunen-Red (1988). It should be noted that the setting up of more firms and the implicit increase in the number of varieties can be regarded as the provision of an incentive compatible income transfer from the owners of firms (household type 2) to the owners of unskilled labour (household type 1). This follows because the literature on the provision of public goods tells us that an increased provision of a public good is equivalent to an income transfer if the public good is under-provided to the recipient household. Most importantly, in our case, there is no need for governmental intervention except that there should be no impediments to the entry of firms into an industry such as high licensing fees.24 4.3. Illustrative example We provide an illustrative example of a small open monopolistically competitive economy in which world price increases for the differentiated good generate an increase in the number of domestic varieties produced that is sufficient to yield a Pareto improvement in welfare. This example, therefore, complements our theoretical analysis by providing concreteness to our results. The example makes use of CES functions for the production cost functions and the household utility functions. Both unit production functions embody the same elasticity of substitution, σ i ¼ 0:92, but have different distribution parameters given by (0.9 0.1) and (0.1 0.9) respectively. Preferences over the two goods are assumed homothetic and CES, with distribution parameters (0.8 0.2) and elasticity of substitution equal to 0.999 (close to a Cobb–Douglas utility function with constant expenditure shares). The elasticity of substitution between varieties was set to σ ¼1.5, the implied percentage markup being 2=3. Other settings are as follows: V 1 ¼ 1:5, V 2 ¼ 2:0, H 1 ¼ H2 ¼ 100 and b¼0.009. Fig. 2 shows results from simulation of the model over a range of world prices for product 2. The top left panel of Fig. 2 graphs indices of the utility levels enjoyed by the two (unskilled and skilled labour) households as the world price for 24 Actually, in the real world the entry into an industry is heavily regulated in many countries. This may be explained in terms of political economy reasons (Djankov et al., 2002), or in terms of environmental policies.
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product 2, p2, increases over the chosen range. This panel provides a numerical confirmation of the result in Proposition 3 that both household types may experience welfare gains when the world price rises. This Pareto improving outcome is seen to occur for a world price up to approximately p2 ¼ 0:365, after which the utility level for household type 1 (unskilled labour) falls. As is evident from the proposition, this Pareto improving outcome arises because, in the long run, the price increase induces an increase in the domestic output at the extensive margin by increasing the number of domestic varieties produced. This increase in n is depicted in the right upper panel of Fig. 2, thus numerically illustrating Proposition 2. The lower left panel of the figure shows the increase in the total number of varieties consumed by the households as the world price increases; it also shows the impact of the price increase and the resulting increase in the number of varieties on the demand price index for the differentiated good. Despite the increase in price (which raises the index), the increase in domestic (hence total) varieties is sufficiently great to reduce this price index and this is the source of the welfare gains accruing to unskilled labour households (whose income falls). As is evident from this graph, the reduction in the price index diminishes as p2 continues to increase and eventually begins to rise (not shown). Similarly, the number of domestic firms (varieties) increases at a lower rate as p2 increases further and eventually falls (not shown). This price index impact of the increase in p2 is because the increase in output of product 2 varieties at both the intensive and extensive margins increases the demand for skilled labour and entrepreneurship, causing the skilled labour wage rate to rise and increasing cost. The final panel of the figure provides indices of the long run equilibrium wage rates for unskilled and skilled labour, showing the standard result that the unskilled wage rate falls and the skilled wage rate rises as the world price of product 2 increases. 5. Conclusions Many governmental policies entail conflict generating product and factor price changes. However, in the presence of entrepreneurship the possibly anti-competitive effects of product price changes create incentives for entrepreneurial activities that involve the setting up of new firms and producing new varieties of goods. In this paper, we have shown that the entry of more domestic firms and the production of more domestic varieties may, in the long run and subject to certain assumptions (see Propositions 3), imply welfare gains for all households (owners of firms and workers) that more than offset the negative effect of conflict generating price changes on the wages of unskilled labour. Under these conditions, therefore, the increase in the number of domestic varieties produced may produce a Pareto improvement in welfare in the long run, in contrast to the conflict generation of the price changes in the short run. The Pareto improvement outcome depends on various features of our model. First, it has been assumed that all rent (surplus) of the short run equilibrium accrues only to the entrepreneurs (owners of firms). Using this assumption, we have shown that, given an increase in the world price of good 2 (the good produced under monopolistic competition), an increase in the output of good 2 at the intensive margin (when the number of firms is given) generates conflict between the owners of firms and workers, but the converse holds for an increase in output of good 2 at the extensive margin (when the number of firms and varieties is endogenous). Paradoxically, the stronger the anti-competitive effect of product price changes in the short run the higher the probability that in the long run product price changes lead to a Pareto improvement. Second, we assumed that the good produced under monopolistic competition is skilled labour intensive relative to the good produced under perfect competition. Then the lower the skilled labour intensity of the setting up of firms relative to the skilled labour intensity of production, the greater is the incentive for firm entry and, hence, the more likely is a Pareto improvement in the long run. Third, as expected, the economy and private rates of return on investment earned from the setting up of firms are also of paramount importance. Furthermore, the magnitude of an appropriately defined aggregate marginal willingness to pay for an increase in varieties on the part of consumers plays a crucial part in ensuring a Pareto improvement. To clarify this, we have derived lower bounds to the marginal willingness to pay that are consistent with a Pareto improvement and expressed purely in terms of observable and measurable parameters. Our model and results focus on a small open monopolistically competitive economy, in contrast to most of the related literature that typically deals with large trading economies. This literature has emphasized the important impact of the opening up of economies to free trade upon the increase in the number of varieties of differentiated goods available to consumers as the main source of welfare gains. While this is important, our focus has been on the impact of changes in market conditions in large economies upon the welfare of household types in small open economies, assuming away changes in the number of foreign varieties in order to concentrate on the effect of these changed trading conditions upon incentives for domestic firms to enter production. If these incentives are strong, the increase in the number of domestic firms may increase the number of domestic varieties sufficiently for the positive effect on welfare to dominate any negative effect upon incomes of unskilled labour households. Crucial to this outcome, is the ability of skilled labour to move from employment to the entrepreneurial activity of setting up new firms. Our short and long run results have the several potentially interesting economic interpretations. Subject to our assumptions, product price changes that are conflict generating between the owners of firms and unskilled workers in the short run imply in the long run a Pareto improving and incentive compatible transfer from the owners of firms to workers without any form of governmental intervention. This sheds new light on the possibility of implementing Pareto improving transfers by governments in multi-household and multi-country modelling frameworks. Another potential interpretation of our results relates to the question of why vested interest groups, which attempt to influence governmental decision making by means of political activities, are arguably much less important in some countries than in others. Our tentative answer to that complex question is that it is because entrepreneurship (which we define as a high mobility of skilled labour between
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production and the setting up of firms) plays a much more important role in some countries (such as, for example, in South East Asia) than in others (such as in Europe). There are worthwhile extensions. For example, the highly restrictive assumption that all rents of the short run equilibrium accrue only to the owners of firms should be relaxed. It is well known that many firms have policies of profit sharing. On the one hand, profit sharing should have an effort raising effect. On the other hand, there is the possibility that it could also act as a disincentive to entrepreneurship. This relates to a fundamental issue of which distributions of power within a firm are socially desirable, the distribution of power within the firm being a very active and topical research area (see, for example, Marin and Verdier, 2008). Finally, note that we are not arguing that the beneficial effects of entrepreneurial activity always welfare dominate the sources of conflict generation, such as the well-known Stolper–Samuelson effect or the selection effect emphasized in the recent models with heterogeneous firms. This is an unresolved issue, which should be analyzed in a model that allows for entrepreneurship (in the sense of our model) as well as heterogeneous firms.
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