Trade, economic geography and the choice of product quality

Regional Science and Urban Economics 54 (2015) 18–27

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Regional Science and Urban Economics journal homepage: www.elsevier.com/locate/regec

Trade, economic geography and the choice of product quality☆ P.M. Picard a b

CREA, University of Luxembourg, Luxembourg CORE, Université catholique de Louvain, Belgium

a r t i c l e

i n f o

Article history: Received 20 June 2014 Received in revised form 8 April 2015 Accepted 3 June 2015 Available online 18 June 2015 Keywords: Monopolistic competition Endogenous quality Economic geography

a b s t r a c t The present paper studies the effect of the choice of product quality on trade and location of firms. We discuss a model where consumers have preferences for the quality of a set of differentiated varieties. Firms do not only develop and sell manufacturing varieties in a monopolistic competitive market but also determine the quality level of their varieties by investing in research and development. We explore the price and quality equilibrium properties when firms are immobile. We then consider a footloose capital model where capital is allocated to the manufacturing firms in the region offering the highest return. We show that the larger region produces varieties of higher quality and that the quality gap increases with larger asymmetries in region sizes and with larger trade costs. Finally, the home market effect is mitigated when firms choose their product quality. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The present paper studies the effect of the choice of product quality on trade and location of firms. In particular, this paper discusses the role of the size of regions in firms' choice of location and product quality. It is well-known that firms' mobility fosters spatial polarization of economic activity (Krugman, 1991). It is however less clear how differences in region sizes affect the quality produced in each region. Recently, Picard and Okubo (2012) highlight that firms endowed with higher qualities choose to locate in the larger region. Yet, product quality is not an exogenous factor. Firms invest in research and development to improve their product quality and this investment is likely to affect their decisions about plant locations. Such a relationship between quality and location is a topic that has lacked attention. In this paper we build a quality-augmented version of Ottaviano et al.'s (2002) model where consumers have preferences for the quality of manufacturing varieties. Each firm produces a distinct variety and competes under monopolistic competition. We first consider a trade framework where firms are immobile and choose their product quality. This allows us to discuss the effect of region sizes and trade cost on the choice of product quality and trade patterns. We then consider an economic geography framework in which firms choose both their product quality and location, which highlights the role of investment in product quality in the dispersion of economic activities. We obtain the following results. In the first framework, we show that the larger region hosts the firms that produce varieties of higher ☆ I am particularly grateful to R. Amir. P. Belleflamme, K. Behrens, J. Brueckner, T. Okubo, F. Robert-Nicoud, Y. Murata, M. Parenti, M. Pfluger and D. Zeng for helpful comments on this topic. This project has been supported by the grant F2R-CRE-PUL-10EGQH at the University of Luxembourg.

http://dx.doi.org/10.1016/j.regsciurbeco.2015.06.002 0166-0462/© 2015 Elsevier B.V. All rights reserved.

quality and that the quality gap between regions increases with larger regional asymmetries and larger trade costs. Hence, the size of the local market is an important determinant of the average product quality and the added value of the goods that are produced in a particular region. In this paper, such a result does not hinge on income effects but rather on a market size and competition effect. On the one hand, firms get higher returns from their investment when they locate in the region where demand is larger. On the other hand, investments in product quality foster competition and make the larger region more competitive. Hence, incentives to invest in quality are mitigated by a harsher competition in larger regions. Quite interestingly, we show that the co-agglomeration of firms and consumers in the same locale is good for average quality and good for cost of living. Although firms agglomerating in the larger region face a harsher competition, they benefit from a larger market, which increases their incentives to invest in quality. Therefore, global quality rises. Finally, the model highlights the existence of complementarity effects between trade costs and returns to investments in quality improvements. Quality investments reinforce the impact of trade costs on prices and consumptions. In the second framework, we consider the location choice of firms that simultaneously choose their product quality. We show that the location equilibrium exists and is unique. In this location and quality equilibrium, the firms that choose to produce high quality varieties are the ones that locate in the larger market. As standard in the economic geography literature, a fall in trade cost entices a larger number of firms to locate in the larger region. More interestingly, we show that firms invest more in quality on average and the quality gap decreases as trade costs fall. Removing trade barriers is always good for quality because firms have access to larger markets and more easily recoup their investment costs. This market access effect always dominates the negative effect that quality investments have on competition. We also show

P.M. Picard / Regional Science and Urban Economics 54 (2015) 18–27

that market integration reduces regional disparities in terms of product quality. Better access to consumers increases the economic returns on quality investment. Finally we provide ambiguous results about the effect of investments in product quality on the spatial distribution of firms and the home market effect. The paper is structured as it follows. Section 2 discusses the literature on the topic. Section 3 exposes the model while Section 4 presents the short run equilibrium. Section 5 discusses the long run choice of quality in a trade model where the spatial structure of capital is fixed. Section 6 discusses the simultaneous choice of quality and capital location and highlights the relationships between quality on the economic geography. Section 7 concludes. The Appendix A contains all mathematical proofs. 2. Related literature This paper is closely related to several literature strands. First, quality and location is the focus of a well-known business literature about “sophistication” and “clustering”. Porter (1990, p. 188) reports some qualitative evidence that investment in product quality turns out to be more important and more successful in regions with larger demand sizes. A typical example lies in the story of the two German designers of the rotary press, Koenig and Bauer, who returned from London (U.K.) to Bavaria (Germany) in 1818 to set up their first plant because this region was one amongst the world's largest market for printing press. German competitors in the press industry responded with differentiation strategies based on quality and reliability, which made Germany the country with the highest quality and highest price premium in this market. Similarly, the emergence of a US cluster in patient monitoring equipment after World War II is mainly explained by the fact that the US wealthy private hospitals had higher demands for sophisticated monitoring than any European country with socialized medicine. Finally, the emergence of the Japanese cluster in the robotic industry is also explained by the higher demand for robotics by the Japanese management who had significantly stronger engineering background. Second, these examples show that large markets are attractive not only to more firms but also to the most sophisticated and successful ones. This statement has already been approached in the factual and empirical literature in economics. In a seminal work, Griliches (1957) suggested that technology adoption of the spread hybrid seed corn in U.S. agriculture was closely linked to profitability and therefore to the size of farmers' markets. Schmookler (1966) argued that larger markets give more incentives for product innovation. Sutton (1991) presented cross-country case studies to document the concentration of industries in larger markets. Since then, a significant body of empirical literature gives evidence about the role of market size in the incentives to invest in R&D, with a particular focus on the pharmaceutical industry (e.g., Acemoglu and Linn, 2004). Berry and Waldfogel (2010) offer evidence that larger markets include producers with higher-quality goods in the news and restaurant industries. Such evidence is supported by the results of the present model. Furthermore, the quality channel is also important in trade patterns. According to Ferreira et al. (2012), the opening of international trade in the movie industry is responsible about 75% of increase in US movie investment budgets. Our results also confirm many empirical results from studies on trade data. In particular, it is aligned with Hummels and Klenow's (2005) finding that larger countries export goods with higher quality margins and extensive margins. Although this paper does not discuss product heterogeneity within countries or firms, it indirectly relates to recent studies about the quality dispersion across importers and exporters.1 In particular, it is consistent with the finding that prices are correlated with sales and revenues. Finally, many trade studies suggest that trade is better explained by demand or quality heterogeneity than 1 See Khandelwal (2010), Baldwin and Harrigan (2011), Crozet et al. (2012), and Manova and Zhang (2012), Di Comite et al. (2014).

19

by cost heterogeneity.2 This fact motivates our analysis of the role of investment in product quality rather than cost innovation in trade patterns and firms' location. Academic research has also produced a theoretical literature about product quality and trade based on vertical differentiation to explain why higher quality products are more likely to be consumed and produced in high wage countries.3 Murphy and Shleifer (1997) develop a model where high quality products end up being produced in high human capital countries. Feenstra and Romalis (2006) extend the Heckscher Ohlin model to product qualities. Recently, Kugler and Verhoogen (2012) theoretically study the issue of endogenous quality in a trade context but focus on the impact of exchange rate devaluations. Eckel et al. (2011) discuss the impact of quality choice of multi-product monopolies and oligopolies serving consumers with linear demands that are similar to ours. The relationship between product quality and location choice is recently studied in Picard and Okubo (2012) who show that larger regions attract better quality firms.4 None of those papers studies how the firms' product quality relates to region sizes and trade costs and to the firms' location choice. This paper extends this idea in a model where product quality is a variable chosen by firms.5 This paper differs by its focus and approach from two closely related contributions. First, using a discrete choice model, Fajgelbaum et al. (2011) study the patterns of specialization in a trade framework where firms are immobile. Because they give results on the case where firms choose one out of two quality levels, they find that countries may host firms with different quality levels. However, this outcome stems from the dichotomous property of quality6 and cannot be found in this present paper where firms have access to a continuum of quality levels. Second, using Melitz and Ottaviano's (2008) framework, Antoniades (2015) discusses the impact of firms' cost and quality heterogeneity and country sizes. However, his focus is on quality ladder, product prices and entry and export decisions in a trade framework where firms are immobile. By contrast, this paper discusses the sorting of firms and the impact of capital allocation in the context of homogenous firms and non-destination-specific investment. This seems more appropriate to the study of regional issues where capital is free to move (Ottaviano and Thisse, 2004). Because the two papers share the same preferences, production functions and monopolistic competitive setting, it shares common properties with respect to the impact of country size and intensity of competition. This paper however focuses on the markup structure, the impact of co-agglomeration of firms and consumers, and the effect of quality investment on the existence of bilateral trade. It further discusses an analytical solution for firms' endogenous location and the home market effect. Finally, this paper considers investments in product quality as fixed and destination-independent costs. It follows the economic literature on innovation that mostly considers R&D investments as fixed inputs that lower cost or improve demand (Spence, 1975; Dasgupta and Stiglitz, 1980; Shaked and Sutton, 1987; etc.). This literature has highlighted the positive role of larger market size on product quality as investment costs and quality improvements spread over a larger pool of consumers. Such a property applies if quality improvements are not specific to different consumer groups. This paper extends this view to regional economics where investments are less likely to be specific to destinations because language, culture and income can fairly be assumed to be homogenous across regions (e.g., within the same country or continent). This view also applies to many industries that mostly 2 See e.g. Baldwin (2005), Greenaway (1995) and Greenaway et al. (1995), Fukao et al. (2003), and Foster et al. (2008). 3 See Linder (1961), Falvey (1981), Falvey and Kierzkowski (1987) and Flam and Helpman (1987) and Stockey (1991). 4 Okubo et al. (2010a) study a similar two-type heterogeneity model. 5 The paper relates to the various studies of the relationship between vertical and horizontal differentiation (See Gabszewicz and Wauthy, 2012; Di Comite et al., 2014). 6 In the same way, Okubo et al.'s (2010a) get similar patterns by using the assumption of two levels of marginal cost.

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P.M. Picard / Regional Science and Urban Economics 54 (2015) 18–27

trade within the same large region (e.g., automobile, equipment, pharmaceuticals, processed food, etc.). This view however contrasts with recent trade papers that concentrate on destination-specific investments in product quality (Feenstra and Romalis, 2006; Kugler and Verhoogen, 2012; Antoniades, 2015). Under this approach, innovations cannot be transferred to other destinations. Importantly, they are unrelated to market access measures that are critical in the new economic geography literature. 3. The model 3.1. Preferences We consider a world with a mass L of immobile individuals who spread across two regions, labeled by the subscripts H and F. Region H hosts a share θH ∈ [1/2, 1] of those individuals. Individuals in region j = H,F are endowed with the same quasi-linear preferences over a homogenous good and two sets V i of horizontally differentiated varieties that are each produced in regions j = H,F. As in Ottaviano et al. (2002), the utility of each individual in region j is given by the following quadratic function:

Uj ¼

XZ i

vi

^ i ðvÞqi j ðvÞdv− α

β−γ X 2 i

" Z #2 Z h i2 γ X qi j ðvÞ dv− qi j ðvÞdv 2 i vi vi

þ qoj ;

ð1Þ

where qij(v) denotes the quantity of a variety v produced in region i and consumed in region j while qoj stands for the consumption of the homogenous good in region j. The parameter γ is a measure of the degree of substitution between varieties whereas β − γ (N 0) measures the consumer bias toward a more dispersed consumption of varieties. In this paper the summation operator ∑i is used as a short notation for ∑i ∈ {H,F}. ^ i ðvÞ : V i ð→α; ∞Þ;α N 0, The new element in this model is the function α that reflects the quality of variety v. It measures the consumer's willingness to pay for the product variety v; that is, the intensity of consumer's preferences for the differentiated product v with respect to the homog^ i ðvÞ is identical for all varieties, varieties are horienous good. When α ^ i ðvÞ varies, the zontally and symmetrically differentiated. When α quality and therefore the willingness to pay varies across varieties so that goods are also vertically differentiated in the sense that consumers have a higher willingness to pay for the same quantity of the vari^ i ðv0 Þ.7 We denote the average quality by ^ i ðvÞN α ety v than for v ' if α ^ H ðvÞdv þ ∫ v F α ^ F ðvÞdv. α ≡ ∫ vH α Each consumer in region j = H,F maximizes his/her utility (1) subject to his/her budget constraint: XZ i

vi

pi j ðvÞqi j ðvÞdv þ qoj ≤w j þ s j r þ qoj ;

ð2Þ

where pij(v) denotes the price of the variety v produced in region i and sold in region j while the price of the homogenous good is used as a numéraire. The consumer has an initial endowment qoj , a wage wj, and a share of capital endowment sj that is valued at the capital return r. Following Ottaviano et al. (2002), we assume that consumers have a sufficiently large endowmentqoj so that the consumption of the homogenous good is never nil. Consequently, income effects are present in the demand for homogenous goods but are absent in the demand for manufacturing varieties. In this context, the latter demand is independent of the distribution of capital ownership. 7 See Gabszewicz and Wauthy (2012) and Di Comite et al. (2014) for alternative models mixing horizontal and vertical differentation.

3.2. Production Production takes place in two sectors. In the first sector, the homogenous good is produced under perfect competition using one unit of labor per unit of output. We assume that this good can be costlessly traded between regions, which implies that its price is internationally equalized and equal to wages. As this good is taken as the numéraire, we get wj = 1 for j = H,F. In the second sector, called the manufacturing sector, each firm produces under increasing returns to scale and sells a single differentiated manufacturing variety under monopolistic competition. Firms set specific prices to each regional market where they sell their products. The profit of a manufacturing firm v established in region i is given by   ^ i ðvÞÞ−ri ðvÞ; Π i ðvÞ ¼ Lθi pii ðvÞqii ðvÞ þ Lθ j pi j ðvÞ−τ qi j ðvÞ−Iðα

v ∈ Vi; ð3Þ

where L is the total population, θi is the share of population in region i, and qij(v) and pij(v) are the consumer price and demand of variety v when it is produced in region i and consumed in region j. The firm pays a per-unit transport cost τ in numéraire while the variable input is set to zero for the sake of exposition.8 To produce the firm uses one unit of capital and rewards its owner by ri(v) units of numéraire. Finally, ^ i ðvÞ, the firm must invest Iðα ^ i ðvÞÞ units of to reach the quality level α ^ i ðvÞÞ. We further aslabor, which yields an investment cost equal to Iðα sume decreasing returns to investment in quality where each firm can improve its quality to a quality z by investing an amount IðzÞ ¼ ξðz−α Þ2

if

z≥α

of numéraire where ξ is a positive constant. The investment cost is nil otherwise: I(z) = 0 if z b α . In this expression, the parameter α N0 is the costless product quality. This is the level of quality that firms can achieve at no cost.9 Because of decreasing returns in quality investment, higher product qualities require more than proportional investment levels. Finally we assume that the quality investment is made only in the location where the production is located. For instance, quality investments are related to effort of local management, training of local labor force or local equipment. Investment yields a quality improvement that can be embedded in the products for all destination markets. Quality is here seen as a vertical differentiated characteristic that consumers rank the same way worldwide. Because there is no reason for the firms to downgrade their variety to a lower quality, they supply their products with the same quality level everywhere.10 We assume that a unit mass of capital is inelastically supplied by the individuals, each firm requires one unit of capital in order to operate and the capital market is perfectly competitive. As a result, the total mass of varieties is equal to unity and we can denote V H and V F by the intervals [0, nH] and (nH, 1]. Therefore, nH and nF ≡1 − nH denote the masses of firms producing in each region. In this paper, we discuss the firms' choice of product quality and its relationship to the spatial distribution of capital across regions. Toward this aim we envisage two frameworks. In the first one, capital is immobile so that the sets of varieties V H and V F and the masses of firms nH and nF are exogenous. The equilibrium in the capital market is obtained when local capital owners allocate their capital to the firms that offer the highest return within their own regions. In the second framework the capital location is endogenous choices. The 8 The model with zero marginal cost presents a strong homomorphism with the one ^ ðvÞ. Results are qualitatively where the marginal cost is proportional to the quality level α similar. 9 This model requires a non-zero costless quality to guarantee that consumers' willingness to pay is higher than the trade costs. 10 By contrast, Feenstra and Romalis (2006), Baldwin and Harrigan (2011) and Kugler and Verhoogen (2012) assume investment in a quality characteristics that is specific to each destination country. With such “horizontal differentiated” qualities, a firm is assumed to be unable to benefit for economies of scope in quality investment.

P.M. Picard / Regional Science and Urban Economics 54 (2015) 18–27

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equilibrium in the capital market is then obtained when capital owners allocate their capital to the firms that offer the highest return r across regions. The model is closed by setting each individual's reward from lending her capital unit to r.11 In those frameworks, we consider that firms' product quality and location are long term decisions. In the short run, the firms set prices and consumers choose their consumption, which constitutes the product market equilibrium that we shortly present now.

^ i ðvÞ, on the average quality α and on the mass of of its own variety α firms (ni, nj) in each region. In other words, the prices p∗ii(v) and p∗ij(v) do not directly depend on the specific quality and location of any ^ 0 Þ. This independence of prices to the preother variety v ' and quality αðv cise composition of local production turns out to be a useful property in the spatial analysis in Section 6. Given the linear demand and cost specification, it is easy to show that q∗ii(v) = (b + c)p∗ii(v) and q∗ij(v) = (b + c)(p∗ij(v) − τ).12 The profit of firm v located in region i can be written as

4. Short run equilibrium

  2   2 ^ i ðvÞÞ−r i ðvÞ: −Iðα Π i ðvÞ ¼ Lðb þ cÞ θi pii ðvÞ þ θ j pi j ðvÞ−τ

4.1. Demands When individuals in region j maximize their utility (1) subject to the budget constraint (2), they display the following linear demand: h i   ^ i ðvÞ−pi j ðvÞ þ c ℙ j −α qi j ðvÞ ¼ ðb þ cÞ α

ð4Þ

for all i, j ∈ {H, F} where α is the average quality and XZ pi j ðvÞdv ℙj ¼ i

4.2. Product market equilibrium Under monopolistic competition, firms are too small to affect the aggregate variables. They set their prices pii(v) and pij(v) taking the price ^ i ðÞÞ as given. As indices (ℙi, ℙj) and the distribution of quality ðα shown in the Appendix A, equilibrium prices are then equal to ^ ðvÞ−α 1 2αb þ τn j c α þ i 2 2b þ c 2

and

ð5Þ

^ ðvÞ−α τ 1 2αb þ τni c α þ i þ : pi j ðvÞ ¼ 2 2b þ c 2 2

αb þ ðb þ cÞτn j 2b þ c

Trade models generally consider the location of factors as exogenous. In this section we discuss such a trade model where firms are able to choose their quality investments but the spatial distribution of capital is exogenous. That is, we assume that individuals invest their capital only in their own region. Because each firm requires one unit of capital, the mass of firms in each region ni is equal to the exogenous local share of capital endowment Lθisi, i = H, F. The sets of varieties then becomes VH = [0, nH] and VF = (nH, 1], where nH is exogenous in this section. This framework allows us to highlight how the firms' investment in product quality impacts on firms' prices and trade patterns. Under monopolistic competition, each firm is small in the global product market and has no influence on other firms' prices and quality levels. Hence, the firm maximizes its profit Πi(v) with respect to its own ^ i ðvÞ considering its impact on its own prices p∗ij(v) but quality level α ^ ¼ 1=2, the first order taking ℙi and α as given. Because dpi j ðvÞ=dαðvÞ condition writes as nh  i o dΠ i ðvÞ ^ i ðvÞ−α Þϑ=2 ¼ 0 ð8Þ ¼ Lðb þ cÞ θi pii ðvÞ þ θ j pi j ðvÞ−τ −ðα ^ i ðvÞ dα where ϑ ¼ 4ξ=ðLðb þ cÞÞ:

Firms selling higher quality products set higher prices. Indeed, each firm's prices increase with its idiosyncratic product quality. They however fall with larger average product quality (∂p∗ij(v)/∂α b 0) because they react to the presence of more attractive local goods by lowering their prices. Note that each firm passes-through half of the ^ i ðvÞ−α to consumers. Similarly, firms invalue of its quality advantage α flate the price of their exports pij(v) by half of the transport cost. Finally, the aggregate price index ℙi ¼

In this analysis we have assumed bilateral trade so that consumers purchased all varieties. To guarantee this, we impose that exports are positive, q∗ij(v) N 0, or equivalently, that the f.o.b. prices p∗ij(v) − τ remain positive in equilibrium. Section 5.4 discusses this condition in more detail. We are now equipped to analyze the firms' choice of quality and its impact on trade, holding the location of capital as fixed. 5. Product quality and trade

Vi

is the manufacturing price index in region j (see computations in Appendix A). In this expression, the parameter b≡ 1/β measures the price sensitivity of demand and the parameter c≡ γ/[β(β − γ)] the degree of product substitutability. When c → 0, varieties are perfectly differentiated, while they become perfect substitutes when c → ∞. Importantly, prices are linearly adjusted for the presence of idiosyncratic and average quality. Each individual indeed has a product demand for ^ i ðvÞ−pi j ðvÞ, and a variety v that falls with its quality-adjusted price, α rises with the aggregate quality-adjusted prices, (ℙj − α). The latter effect is more important when varieties are better substitutes (larger c). Product quality therefore shifts demand functions.

pii ðvÞ ¼

ð7Þ

ð6Þ

rises with the average quality and falls with the number of firms in the market. Prices are independent to the precise composition of local production. That is, each firm sets a price p∗ii(v) that depends only on the quality 11 In this model, capital owners are immobile and demand for manufacturing goods is not subject to income effects. The spatial distribution of capital ownership is irrelevant for firms' demands, profits and location incentives.

We conveniently redefine the parameter ξ because firms' investment incentives are proportional to the total size of market (i.e., L consumers)13 and because profit levels are proportional to the slope of demand functions (b + c). Hence, ϑ constitutes a measure of decreasing returns in quality investment that is normalized for a unit-mass population and unit-slope demand functions. It can be shown that the second order condition is satisfied if and only if ϑ N 1. The optimal quality is finite only if decreasing returns in quality investment are strong enough, which we assume from now. Indeed, if this condition were not satisfied, investment costs would rise at a smaller pace than the revenues associated to quality improvements and the optimal quality would be unbounded. From expression (8), the optimal quality ^ i ðvÞ−α ¼ α

 i 2h  θi pii ðvÞ þ θ j pi j ðvÞ−τ ϑ

ð9Þ

12 This linear relationship between output and markup is a natural property of profit maximization under linear demand and cost. 13 See Antoniades (2015) for a detailed discussion of the impact of global market size.

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P.M. Picard / Regional Science and Urban Economics 54 (2015) 18–27

is proportional to the average markup on the world population and inversely proportional to the cost of quality investment ϑ. The firm balances the marginal cost and the marginal revenues of its quality investment. Under linear demand functions, both outputs and marginal revenues are proportional to markups. The impact of access is clearly apparent: since higher trade costs reduce markups, the marginal revenues and therefore incentives to invest in quality get smaller as the production site is located further away from consumers. 5.1. Product quality The trade literature and new economic geography highlights the role of trade barriers and distance between firms and consumers on the incentives to produce. We here study the impact of those two factors on product quality. To highlight the effect of the location of capital and consumers, we focus on the co-agglomeration index G≡∑i = 1,2(θi − 1/2)(ni − 1/2), which increases as more consumers live and firms produce within the same region.14 This co-agglomeration index is equal to 2(θH − 1/2) (nH − 1/2), which increases with a larger mass of firms nH since θH N 1/2. We also compute that the sum θHnF + θFnH is equal to 1/2 − G, which decreases with stronger co-agglomeration of firms and consumers. Remind that the co-agglomeration index is here exogenous as the masses of consumers and firms are exogenous. Section 6 will discuss endogenous agglomeration processes. Using (5) and (9), the optimal quality is the same for all firms located ^ i ðvÞ≡α i and is given by the following formula: in the same region α α i −α ¼

τθ j 2αb cτϑ ðθH n F þ θ F nH Þ : þ − ϑ ð2b þ cÞ−2b ðϑ−1Þðϑ ð2b þ cÞ−2bÞ ϑ−1

ð10Þ

It can be shown that the optimal quality increases with larger local market (smaller θj) and smaller co-agglomeration of firms and consumers (larger (θHnF + θFnH)). It can be shown that α∗H increases with trade cost τ whereas α ∗F decreases with it. Finally, firms invest more in quality when products are less differentiated (higher c). This reflects a business stealing effect whereby the quality improvement of a variety entices consumers to switch their consumption from competing varieties and therefore gives firms too high returns from improving their own qualities. Note that since ϑ is inversely related with total market size L, the quality of each variety correlates with total market size (see Antoniades, 2015). The quality gap between regions is given by τ ð2θH −1Þ α H −α F ¼ ϑ−1

ð11Þ

which is simply proportional to the difference in region sizes. As a result, high quality products are necessarily produced in the larger region. Furthermore, higher trade costs increase the quality gap.15 This is because the markups on firms' exports decrease with higher trade costs and reduce the returns to investment in quality. This effect has a stronger impact on the firms that have a larger export share, which are the ones located in the smaller market. Finally, the above expression shows the complementary effect of trade costs and returns in quality investments. Stronger decreasing returns (smaller ϑ) exacerbate the impact of trade costs on regional asymmetries in product quality. The average quality α∗ = nHα∗H + nFα∗F can be computed as α−τ ðθH n F þ θ F nH Þ α  −α ¼ 2b ϑð2b þ cÞ−2b

ð12Þ

where the denominator is positive because ϑ N 1. We note the following 14 This index is the covariance of the numbers of consumers and firms in the case of two regions. See Ellison et al. (2010) for an index with two groups of industries and many regions. 15 Khandelwald (2010) refers to this quality gap as ‘quality ladder’.

points. The average quality decreases with larger trade cost τ. As explained above, higher trade costs reduce markups on exports and diminish the incentives to invest in quality. The average quality rises with stronger co-agglomeration of firms and consumers. We summarize our results in the following proposition. Proposition 1. (i) The larger region produces varieties of higher quality. (ii) The quality gap increases with larger asymmetries in region sizes and with larger trade costs. (iii) A higher co-agglomeration index of firms and consumers implies higher average quality. This proposition brings a contrasting perspective on global quality and firms' spatial distribution. On the one hand, the asymmetry in the spatial distribution of consumers is a cause for spatial disparities in product quality. On the other hand, disparities in firms' spatial distribution lead to a rise in the average quality. This result is novel in the literature. 5.2. Prices Because firms set the same product quality in each region, they also set the same price, p∗ii(v) = p∗ii and p∗ij(v) = p∗ij where, by (5), pii ¼

1 2α  b þ τn j c α i −α  þ 2 2 2b þ c

and

pi j ¼

1 2α  b þ τni c α i −α  τ þ : þ 2 2 2b þ c 2 ð13Þ

The first terms represent the optimal price for a hypothetical ‘average quality good’ (α ∗i = α∗). Prices therefore increase with average quality α∗. The second terms represent a markup for quality (resp. a discount if α∗i b α∗) for the firm's quality advantage (resp. disadvantage). In this model without income effects, the consumer's demand response to quality is the same across regions so that firms set the same markup (resp. discount) for quality in both markets. The markup for quality of firms located in the larger region H can be expressed as α H −α  τ ¼ ðθH −θ F Þð1−nH ÞN0; 2 2ðϑ−1Þ

ð14Þ

which increases with region size asymmetries (larger θH) but decreases for a stronger co-agglomeration index of firms and consumers (larger nH). Firms located in the smaller region get a quality discount α F −α  τ ¼− ðθH −θ F ÞnH b 0 2 2ðϑ−1Þ

ð15Þ

whose absolute value increases with stronger region size asymmetries (larger θH) and co-agglomeration indices (larger nH). The more firms located in the larger region H, the higher the average quality and the lower the quality discount of the firms producing in the smaller market. The above price responses to firms' location allow us to anticipate the firms' incentives to locate across regions. The main channel stems from the difference between willingness to pay and trade costs. Recall that, in Ottaviano and Thisse's (2004) model, a higher homogenous quality α increases the willingness to pay and the price of each product compared above the value of trade cost. Consequently, trade barriers offer less protection against competitors, reduce the incentives to disperse across regions and foster agglomeration in the larger locale. The same process takes place here through the effects of the average quality and the quality markup and discount. On the one hand, by (12), the co-agglomeration of firms and consumers raises the average quality α∗ and therefore consumers' willingness to pay. This pushes prices up and makes trade costs less effective in protecting against competition, which fosters agglomeration. On the other hand, when co-agglomeration of firms and consumers is strong, the firms are unable to get high quality markups in the larger market. This attenuates the incentives to locate in the larger region because firms see the individual benefit of their quality advantage reduced

P.M. Picard / Regional Science and Urban Economics 54 (2015) 18–27

by more intense competition. The opposite occurs for the firms in the smaller market. Overall, one may anticipate that the quality markups and discounts exert a dispersion force on firms. To sum up, the choice of quality creates two conflicting forces: an agglomeration force because average price-trade cost ratio rises and a dispersion force because the net benefit of quality advantage diminishes as more firms agglomerate in the larger region. Those effects critically depend on the possibility that firms choose their product quality. Indeed, this discussion is irrelevant for prohibitive investments in quality (ϑ → ∞) since quality would remain the same across regions. 5.3. Exports The present analysis also allows us to disentangle the various effects of trade costs on export prices and quantities.16 Because q∗ij = (b + c)(p∗ij − τ), the export markup or f.o.b. prices (p∗ij − τ), export quantity Lθjq∗ij and export revenue Lθj(p∗ij − τ)q∗ij fluctuate in the same direction. The correlation between export quantity and revenue is consistent with the empirical literature quoted in the introduction. Differentiating this markup, we get    d   1 1 ni c b dα  1 d α i −α  þ þ : pi j −τ ¼ − þ dτ dτ 2 |fflfflfflffl 2 2b þfflc} 2b þ c dτ 2 |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} |{z} |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} ffl{zfflfflfflffl −

þ

−

ð16Þ

þ=−

A fall in trade cost has various effects on markups and exports. It firstly has the standard effects that we find in homogenous quality models. On the one hand, it raises the markups and exports because of the presence of an imperfect pass-through (first term equal to − 1/2).17 Firms indeed pass through a half of trade costs to their foreign consumers and subsidize the other half. Lower trade costs reduce such subsidy incentives and raise markups and export output. On the other hand, the fall in trade costs pushes consumer prices down in the foreign market and intensifies the price competition there, which reduces markups and exports (second term). It can readily be shown that the former effect dominates the latter. The fall in trade cost also creates two additional effects through product quality. It firstly improves market access so that firms invest more in product quality, the average product quality rises and firms set higher export prices (third negative term). This is the main effect of endogenous quality when regions have similar sizes (θH ≃ θF). In this case the total impact of lower trade costs is a rise in markups and exports. However, when regions have different sizes, a fall in trade cost affects each region's exports in a different way (fourth term). Because it reduces the market access disadvantage of the smaller region (i = F), the firms producing there have additional incentives to raise their quality level, markup, export price and output. By contrast, the firms in the larger region (i = H) benefit from a lower market access advantage and cannot raise their quality, export price and output as much. So, a fall in trade cost does not only raise markups and exports but also improves the export position of each firm in smaller region relative to those in the larger one.18 We now turn to the discussion of the existence of bilateral trade.

16 Since changes in trade costs are equivalent to bilateral changes in tariffs and changes in distances between trade partners, the following analysis applies for the study of passthrough effects of tariffs and transport costs. 17 For instance, the existence of an imperfect pass-through is reported in De Loecker et al. (2012). 18 This model includes no export selection within product category and therefore does not replicate Manova and Zhang's (2012) result about the positive correlation between trade costs and f.o.b. prices (markups here).

23

5.4. Bilateral trade Bilateral trade takes place when firms export from all regions. As shown in Behrens (2005a,b) and Okubo et al (2014), it may not be feasible for all spatial distribution of firms.19 In particular, firms located in the smaller region have lower quality and sell at a competitive disadvantage. Those firms are the first that stop exporting. The export quantities q∗FH are proportional to the markups p∗FH − t. Using (12) and (10), it can be shown that those quantities fall with the number of firms in the larger market nH as competition intensifies there.20 So, bilateral trade occurs if and only if q∗FH N 0, or equivalently, if nH remains lower than the threshold

2b nH ðϑÞ ≡ τ

α−τ þ

2b ðα−τθH Þ ϑð2b þ cÞ−2b

c þ ðθH −θ F Þ

!; 2 2b þ c 4b − ϑ ð2b þ cÞ−2b ϑ−1

ð17Þ

where the second term in the denominator is positive because ϑ N 1. It is apparent that the threshold nH ðϑÞ falls with θH and τ. Therefore, bilateral trade is more likely to be supported for smaller region size asymmetries and trade costs. The role of investments in product quality is however ambiguous. Consider firstly the case where decreasing returns to quality investments are small enough (e.g., ϑ → 1). Then we get nH ð1Þ ¼ 0 and we conclude that bilateral trade is never feasible. In this case, firms have very strong incentives to invest in quality in the larger region because they benefit from a better access to the larger market and because the cost of quality investment does not increase that much as quality rises. Regional quality and markups diverge dramatically and create large price discrepancies and large export differences. As a consequence, exports from the smaller region fall to zero for any trade cost and any regional size asymmetries. Consider secondly the case where decreasing returns to quality investment are very large (e.g., ϑ → ∞). In this case, firms choose a quality level close to the costless quality α and the markups for quality (α∗i − α∗)/2 tend to zero. We therefore return to a model with a homogenous quality α where, as explained in the previous sub-section, a higher quality increases the willingness to pay for each product and reduces the impact of trade costs on firms' competition and therefore on prices. Firms' location will then have a smaller impact on the existence of exports from region F if trade barriers are low. Using the previous formula, we get that bilateral trade is feasible if nH b nH ð∞Þ≡2bðα−τÞ=ðτcÞ. One can check that bilateral trade is always feasible if τ b τ ∞ ≡2bα=ð2b þ cÞ because nH ð∞Þ lies above one, while it is never feasible if τ Nα because nH ð∞Þ is smaller than zero. For trade costs between τ∞ and α, bilateral trade is feasible only if the larger region does not host too many manufacturing competitors. For intermediate values of returns ϑ, the impact of firms' location on exports from region F depends on how average quality and quality differences move. Assuming again τ b α, one can check that the function nH ðϑÞ is a bell-shaped function of ϑ for low enough θH and otherwise it is an increasing function of ϑ. Those patterns are presented in Fig. 1. On the one hand, when returns to quality investment are strong (small ϑ) or region sizes differ a lot (high θH), nH ðϑÞ is an increasing function. A rise in the number of firms in market H mainly accentuates product quality differences between regions, intensifies competition and impedes firms to export to the larger market. Weaker returns to quality investment (larger ϑ) diminish quality differences and therefore reduce competition in H. As a result foreigners are enticed to export in market H. On the other hand, when region sizes do not differ too much (low θH), nH ðϑÞ is a non-monotone function. In this case, regional 19 Behrens (2005a,b) and Okubo et al. (2014) provide a full study of bilateral and unilateral trade flows in a homogenous quality model. dq ϑð4bþcÞ−2b 20 cτ Indeed, dnFH ¼ − 12 2bþc ½1 þ ðϑ−1Þðϑð2bþcÞ−2bÞ ðθH −θ F Þ b 0: H

24

P.M. Picard / Regional Science and Urban Economics 54 (2015) 18–27

we know that quality investments depend on firms' locations. The rent differential writes as n h h 2 i 2 io 2  2  Δr ðnH Þ ¼ L θH pHH − pFH −τ −θ F pF F − pH F −τ   2   2 o 1 n ; − θH pHH þ θ F pH F −τ − θ F pF F þ θH pFH −τ ϑ where optimal prices are functions of the optimal individual quality α∗i and equilibrium average quality α∗ that depend on the location of firms. Bilateral trade imposes that the spatial equilibrium nH satisfies condition (17). 6.1. Spatial equilibrium Fig. 1. Maximum mass of firms supporting exports to H.

product quality differences do not constitute the dominant channel when returns to quality investment are weak (high ϑ). Rather, weaker returns to quality investment (larger ϑ) diminish the average quality, consumers' willingness to pay and the average product prices. Trade costs become a larger component of product prices so that exporting becomes more difficult, in particular from the smaller market F. We summarize this discussion in the following proposition: Proposition 2. Bilateral trade is more likely to be supported for smaller trade costs and/or lower dispersion of consumers and/or smaller number of firms in the larger market. Bilateral trade is more likely to be supported for weaker returns to quality investments (larger ϑ) if region sizes are sufficiently different. Otherwise this latter relationship is non-monotone. We now turn to the discussion of the firms' location choice. 6. Product quality and location of firms In this section we study how firms' choices of location and quality shape the economic geography. It is well-known that firm or capital mobility fosters spatial polarization of economic activity. It is however less clear how differences in region sizes affect the quality produced in each region and the number of firms locating in each region. We here show that, compared to the case with exogenous quality levels, the home market effect can be stronger or weaker under endogenous quality. We now allow capital owners to choose the location of their capital investments, so that nH and nF are now endogenous. Capital owners allocate their capital to the firms that offer the highest return across regions. To obtain a unit of capital, each firm chooses the location that maximizes its profit and bids for capital up to the value that cancels its profit. As a result, we get two possible configurations. On the one hand, the whole capital flows in region H (resp. F) so that nH = 1 (resp. nF = 1) because firms producing in this region always offers a better return: r∗ = rH N rF (resp rF N rH). On the other hand, the capital spreads across regions so that nH ∈ [0, 1] because firms offer the same return in both regions: r∗ = rH = rF. Therefore, the location of firms is given by the rent differential Δr∗(nH) = rH − rF. For the sake of simplicity, we focus on the case of bilateral trade. We study the equilibrium where firms simultaneously choose their location and quality investment. This means that firms see the two decisions with the same degree of irreversibility.21 From the previous section

21

Note that the present model also applies to the sequential model where firms choose their locations before their quality investments. The present model can be loosely interpreted as a dynamic model where, in each period, some firms die because their varieties become obsolete and are replaced by new firms that choose their location and quality.

After some simplifications, we get that the rent differential Δr∗(nH) is proportional to the function Δ(θH, ϑ) − (nH − 1/2) where ΔðθH ; ϑÞ ¼

2bð2α−τ Þ ðθH −1=2ÞM ðθH −1=2; ϑÞ cτ

ð18Þ

and Mðx; ϑ Þ ¼

ð2b þ cÞϑ ðϑ−1Þ : ðϑ−1Þðð2b þ cÞϑ−2bÞ þ ðð4b þ cÞϑ−2bÞ4x2

The numerator and denominator of the function M are positive because ϑ N 1. Because Δr∗ decreases in nH, the location equilibrium exists and is unique. Therefore the location equilibrium is given by  1 þ ΔðθH ; ϑ Þ; 1 : nH ¼ min 2 We first highlight the effects of trade costs. It is trivial to check that Δ(θH) and thus n∗H decrease with larger τ. Furthermore, using (11) and (12), it can readily be shown that   d α H −α H 2θH −1 ¼ N0 dτ ϑ−1

and

dn dα  τ ∝−ðθH n F þ θ F nH Þ þ ð2θH −1Þ H b 0: dτ dτ 2

Therefore, whereas the quality gap falls when trade cost falls, average quality rises. The directions of those effects are the same as in the model with exogenous firm locations that we discussed in the previous section. The following proposition summarizes those results. Proposition 3. Under bilateral trade, the location equilibrium exists and is unique. In this equilibrium, high quality varieties are produced in the larger region. As trade costs fall, more firms locate in the larger region, the average quality rises and the quality gap between regions decreases. The proposition is supported by empirical evidence. For instance, it confirms Hummels and Klenow's (2005) view that larger countries export higher quality and more numerous varieties. The important point is that differences in product quality and diversity are here determined by the endogenous choice of capital investments across regions. 6.2. Home market effect We can now discuss how the spatial distribution of firms changes as region size asymmetries rise. In particular we study the home market effect (HME) according to which the market equilibrium may involve

P.M. Picard / Regional Science and Urban Economics 54 (2015) 18–27

a more than proportionate share of capital in the region with the larger population. That is, we measure the home market effect as22 HME≡

nH −1=2 : θH −1=2

There exists a home market effect if this measure is larger than one. In our model with endogenous regional product qualities (α∗H, α∗F), we get   2bð2α−τ Þ M ðθH −1=2; ϑ Þ: HME α H ; α F ¼ cτ

ð19Þ

As in the standard footloose capital model, the home market effect increases with smaller trade costs. Furthermore, the function M(x, ϑ) decreases in x for all x ∈ 0, 1/2]: it is larger than one if and only if pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x b ^x≡ bðϑ−1Þ=½2ð4b þ cÞϑ−4b. Hence, the home market effect falls with stronger region size asymmetries. This analysis allows us to answer to two additional questions. First, what is the effect of the possibility to invest in product quality on the home market effect? To investigate this question, consider the situation where quality investment costs are prohibitive (ϑ → ∞) so that firms only implement the costless quality α . Since limϑ → ∞ M(x, ∞) = 1, (19) becomes HMEðα; α Þ ¼

2bð2α−τÞ ; cτ

which is the measure presented in the homogenous quality model discussed by Ottaviano and Thisse (2004). These authors show that it is larger than one under the condition that bilateral trade is always feasible for all spatial distribution of firms (τ b τ∞).23 So, when quality investments are prohibitive, there always exists a home market effect that is independent of region sizes. It is also apparent that HMEðα; αÞ is smaller than HME(α∗H, α∗F) if and only if 1 b M(θH − 1/2, ϑ), or equivalently, θH b 1=2 þ ^x.24 When regions are not too dissimilar, the home market effect is lower than in the absence of investment. Indeed, when investment costs are not prohibitive, firms invest more in the larger region because of its better market access. Product quality and consumers' willingness to pay increase there so that firms can set higher prices. As a result, trade costs offer a smaller protection against competition, which weakens the dispersion forces and strengthens the home market effect. This mechanism reflects the impact of quality investments on ‘average quality’. Second, what is the impact of quality differences across regions on the home market effect? To get some light on this issue, let us sterilize regional quality differences by imposing to all firms the same ‘average quality’ α∗ (obtained under endogenous quality). We get HMEðα  ; α  Þ ¼

2bð2α  −τÞ : cτ

In the absence of region size asymmetries (θH = 1/2), there is no quality differences across regions so that α∗H = α∗F = α∗ and therefore HME(α∗, α∗) = HME(α∗H, α∗F). However, HME(α∗H, α∗F) falls with stronger size asymmetry (higher θH). As a result, we have HME(α∗H, α∗F) b HME(α∗,α∗) if θH N 1/2. The home market effect is smaller when firms set their own product quality than when they produce the average quality. This

is because the co-agglomeration of firms and consumers is bad for the firms producing in the larger market. It reduces their profits and diminishes the incentives to relocate there. This mechanism reflects the procompetitive effects of product quality and quality investments. This yields the following proposition. Proposition 4. Under bilateral trade, the home market effect decreases with stronger region size asymmetries. It is stronger than the home market effect prevailing without investment possibilities if regions are not too dissimilar. It is weaker than the home market effect existing in the absence of quality differences across markets. 6.3. Exports We can now come back the effects of trade costs on exports and discuss the impact of firms' location choice. Since export quantities prices are proportional the markups, it suffices to study the impact of trade costs on markups. Repeating the exercise of Section 5.3, we get that the marginal change in markup, d(p∗ij − τ)/dτ, is equal to expression (16) plus the following term: 3    61 τc  7  b dα 1 d α i −α 7 dni 6 þ þ : 7 6 5 |{z} 42 2b þ c 2b þ c dni dni dτ |fflfflfflfflffl{zfflfflfflfflffl} |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} 2 |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} 2

þ

þ

−=þ

−=þ

Consider a fall in trade costs and the firms producing in the larger region (i = H). By Proposition 3, capital and firms move from F to H (dni/dτ = dnH/dτ b 0). This movement has three additional effects on export quantities and markups. First, those firms export in a market that is served by fewer local firms and is thus less competitive so that they have an incentive to set higher export markups (first positive term in the squared bracket). Second, the movement of firms results in a stronger co-agglomeration of firms and consumers. This raises average product quality and also entices those firms to increase their export markups (second positive term in the squared bracket). Finally, the movement of firms also alters the markup for quality in region H (last term in the squared bracket). However, when regions have similar sizes (θH ≃ θF), markups for quality are small and this effect is dominated by the two previous effects. In this case, smaller trade costs lead to higher export markups and quantities. By contrast, when regions have different sizes, the larger region offers a market access advantage. This advantage however diminishes because the relocation of firms induces stronger competition, which restrains or even reverts the rise of export prices and output from the larger region. The important point is that, for sufficient large regional asymmetries and returns to quality investment, lower trade costs may even reduce the export markups and quantities of each firm producing in the larger region.25 However, since more firms locate there, the total export rises. In other words, their intensive margins fall while their extensive margins rise. 6.4. Quality investments We finally study the impact of a fall in the decreasing returns of quality investment ϑ on the location of firms. One can show that M(x, 1) = 0 and M(x, ∞) = 1 and that M(x, ϑ) increases in ϑ for any

22

This definition of the home market effect is commonly used in footloose capital models including and following Martin and Rogers (1995) and Ottaviano and Thisse (2004). It is also related to the measure used in other models based on linear quadratic preference models like Ottaviano et al. (2002 IER) and followers. 23 Okubo et al. (2010b, p. 15) show that it is larger than one under the condition that bilateral trade exits at the equilibrium spatial distribution of firms. 24 Note that we have been unable to find analytical or numerical examples of this reverse condition under the bilateral trade condition. See Behrens (2005a) and Okubo et al. (2014) for further discussions of reverse home market effects.

25

ϑ b ϑ ð xÞ ≡

8 < :

1þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2x2 ð2b þ cÞ þ 2bð2b þ cÞð1−4x2 Þx2 if b−ð8b þ 2cÞx2 ∞ if

x2 b b=½2ð4b þ cÞ

:

x2 ≥ b=½2ð4b þ cÞ

25 For instance, a lower trade cost reduces region H's export markups and quantities for the following parameters: α ¼ 1; β ¼ 1; γ ¼ :9; τ ¼ :06; ξ ¼ 2:6; ϑ ¼ 1:04; θH ¼ 0:55 and the endogenous value nH = 0.83 satisfying (17) and (18).

26

P.M. Picard / Regional Science and Urban Economics 54 (2015) 18–27

A fall in the decreasing returns of quality investment has a non-monotone effect on firms location asymmetries n H and home market effect if region size asymmetries are small enough (i.e., (θ H − 1/2) 2 b b/[2(4b + c)]). As ϑ falls to one, location asymmetries n H and home market effect first increase and then decrease. Otherwise, if region size asymmetries are large enough, location asymmetries and home market effect always diminish as ϑ falls. This result must be related to Proposition 2 and stems from the agglomeration and dispersion forces of the choice of quality on firms' location. For large ϑ, the agglomeration effect dominates as a fall in ϑ increases ‘average quality’ more than it decreases the quality markups. For small enough ϑ, the dispersion effect dominates as a fall in ϑ affects more negatively the quality markups than it affects ‘average quality’. Hence, firms tend to agglomerate more for larger ϑ and disperse more for smaller ϑ. To sum up, weaker decreasing returns to quality investment monotonically increase the number of firms in the larger region only if region size asymmetries are strong enough. Otherwise, they can have non-monotone effects. This is summarized in our last proposition. Proposition 5. Under bilateral trade, if region size asymmetries are large enough, the asymmetries in economic activity and the home market effect always diminish as the decreasing returns of quality investment falls. Otherwise, they first rise and then fall. From a policy viewpoint, one observes that technological progress may foster the dispersion of economic activities and reduce discrepancies in quality only if regions are rather dissimilar. Otherwise, it may lead to more agglomeration and spread in product quality. Since one or another pattern highly depends on many parameters, it is hard to predict whether governmental policies in favor of technological progress will help agglomeration or dispersion of economic activities.

7. Conclusion The present paper studies the effect of the choice of product quality on trade and location of firms. Consumers have preferences for the quality of a set of manufacturing varieties. Firms do not only develop and sell manufacturing varieties in a monopolistic competitive market but also determine the quality level of their varieties by investing in research and development. We show that the larger region produces varieties of higher quality and that the quality gap increases with larger asymmetries in region sizes and with larger trade costs. In a footloose capital model we find that the home market effect is qualified. This paper sets the stage for further investigations. A traditional research direction is the study of workers' mobility in a core-periphery model. As discussed in our analysis, we expect that the investments in product quality exacerbate the agglomeration forces and give more prevalence to the central places. This might fit the difference in product quality between rural and urban areas and between large and small cities. It would be interesting to highlight the effect of investments on the average quality and quality markups and therefore to outline the procompetitive effects resulting from quality choices. A more challenging study would be to extend the model to income heterogeneity, as the patterns of trade depend on product quality and therefore on the subtle interplay of the income distribution and non-homothetic preferences. Also, because they depend on exogenous regional differences and quality markups, income distribution might reinforce the tendency of firms producing high quality to agglomerate in the high income region. Such a study should discuss a model with non-homothetic preferences and income effects on the consumption of the differentiated varieties (e.g., Fajgelbaum et al. (2011)).

Appendix A A.1. Consumer demand Consumer demands are obtained as follows. Assuming that all varieties are consumed, consumers maximize their utility (1) subject to their budget constraint (2). We can write the following first order condition: ^ i ðvÞ−ðβ−γ Þqi j ðvÞ−γ α

XZ Vi

i

qi j ðξÞdξ−pi j ðvÞ ¼ 0:

ð20Þ

Integrating the left hand side of this equality on all varieties yields the average quality α¼β

XZ i

Vi

qi j ðvÞdv þ

XZ i

Vi

pi j ðvÞdv:

The last two expressions allow us to derive the individual demand for variety v as (4). A.2. Product market equilibrium Under monopolistic competition, firms are too small to affect the aggregate variables. The product market equilibrium is defined as the set of prices {pii(v), pij(v)}, such that (a) the demands satisfy (4) and (b) the prices pii(v) and pij(v) maximize the profit Πi(v) of each firm v ^H in region i taking the price indices (ℙH, ℙF) and the quality profiles ðα ^ F ðÞÞ as givens. For given ℙi and α ^ i ðÞ, i = H, F, the profit maximizing ðÞ; α prices are computed as pii ðvÞ ¼

  ^ i ðvÞ þ c ℙ j −α ^ i ðvÞ þ cðℙi −α Þ ðb þ cÞα ðb þ cÞα τ þ ; and pi j ðvÞ ¼ 2ðb þ cÞ 2ðb þ cÞ 2

ð21Þ which depend on the quality of the variety offered. At the equilibrium in the product market, the firm's prices (pii(v), pij(v)) are consistent with demand (4). For this to happen, the price indices (ℙH, ℙF) should result from individual prices (21). We successively have   Z ^ j ðvÞ þ c ℙ j −α ðb þ cÞα dv pi j ðvÞdv ¼ 2ðb þ cÞ Vj Vi V   j   Z ^ i ðvÞ þ c ℙ j −α ðb þ cÞα τ α ðb þ cÞ c ℙ j −α þ dv ¼ þ þ 2ðb þ cÞ 2ðb þ cÞ 2 2ðb þ cÞ Vi Z

ℙj ¼

Z

p j j ðvÞdv þ

αb þ cℙ j τ τ þ ni ¼ þ n: 2ðb þ cÞ 2 i 2 Solving for the fixed point in ℙj yields (6). Equilibrium prices are then equal to (5). References Acemoglu, D., Linn, J., 2004. Market size in innovation: theory and evidence from the pharmaceutical industry. Q. J. Econ. 119 (3), 1049–1090. Antoniades, A., 2015. Heterogeneous firms, quality, and trade. J. Int. Econ. 95 (2), 263–273. Baldwin, R.E., 2005. Heterogeneous firms and trade: testable and untestable properties of the Melitz model. NBER Working Paper, p. 11471. Baldwin, R.E., Harrigan, J., 2011. Zeros, quality, and space: trade theory and trade evidence. Am. Econ. J. Microecon. 3 (2), 60–88. Behrens, K., 2005a. How endogenous asymmetries in interregional market access trigger regional divergence. Reg. Sci. Urban Econ. 35, 471–492. Behrens, K., 2005b. Market size and industry location: traded vs non-traded goods. J. Urban Econ. 58, 24–44. Berry, S., Waldfogel, J., 2010. Product quality and market size. J. Ind. Econ. 58 (1), 1–31. Crozet, M., Head, K., Mayer, Th., 2012. Quality Sorting and Trade: Firm-level Evidence for French Wine. Review of Economic Studies, Oxford University Press 79 (2), 609–644. Dasgupta, P., Stiglitz, J.E., 1980. Industrial structure and the nature of innovative activity. Econ. J. 90, 266–293. De Loecker, J., Khandelwal, A., Pavcnik, N., 2012. Prices. Reform, Markups and Trade.

P.M. Picard / Regional Science and Urban Economics 54 (2015) 18–27 Di Comite, F., Thisse, J.-F., Vandenbussche, H., 2014. Verti-zontal differentiation in export markets. Journal of International Economics 93 (1), 50–66. Eckel, C., Iacovone, L., Javorcik, B., Neary, P., 2011. Multi-product firms at home and away: cost- versus quality-based competence. CEPR Discussion Papers 8186, C.E.P.R. Discussion Papers. Ellison, G., Glaeser, E., Kerr, W., 2010. What causes industry agglomeration? Evidence from coagglomeration patterns. Am. Econ. Rev. 100 (3), 1195–1213. Fajgelbaum, P., Grossman, G., Helpman, E., 2011. Income distribution, product quality, and international trade. J. Polit. Econ. 119 (4), 721–765. Falvey, R., 1981. Commercial policy and intra-industry trade. J. Int. Econ. 11, 495–511. Falvey, R., Kierzkowski, H., 1987. Product quality, intra-industry trade and (im)perfect competition. In: Kierzkowski, H. (Ed.), Protection and Competition in International Trade. Basil Blackwell, Oxford, pp. 143–161. Feenstra, R. and J. Romalis (2006). A Model of Trade with Quality Choice, University of California, mimeo. Ferreira, F., Petrin, A., and J. Waldfogel (2012). Trade, endogenous quality, and welfare in motion pictures. Mimeo University of Minnesota Flam, H., Helpman, E., 1987. Vertical product differentiation and north–south trade. Am. Econ. Rev. 77, 810–822. Foster, L., Haltiwanger, J., Syverson, C., 2008. Reallocation, firm turnover and efficiency: selection on productivity or profitability. Am. Econ. Rev. 98 (1), 394–425. Fukao, K., Ishido, H., Ito, K., 2003. Vertical intra-industry trade and foreign direct investment in East Asia. J. Jpn. Int. Econ. 17 (4), 468–506. Gabszewicz, J., Wauthy, X., 2012. Nesting horizontal and vertical differentiation. Reg. Sci. Urban Econ. 42 (6), 998–1002. Greenaway, D., 1995. Vertical and horizontal intra-industry trade: a cross industry analysis for the United Kingdom. Econ. J. 105, 1505–1518. Greenaway, D., Hine, R., Milner, C., 1995. Vertical and horizontal intra-industry trade: a cross industry analysis for the United Kingdom. Econ. J. 105, 1505–1518. Griliches, Z., 1957. Hybrid corn: an exploration in the economics of technological change. Econometrica 25, 501–522. Hummels, D., Klenow, P.J., 2005. The variety and quality of a nation's exports. Am. Econ. Rev. 95 (3), 704–723. Khandelwal, A., 2010. The long and short (of) quality ladders. Rev. Econ. Stud. 77 (4), 1450–1476. Krugman, P., 1991. Increasing returns and economic geography. J. Polit. Econ. 99, 483–499.

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Kugler, M., Verhoogen, E., 2012. Prices, plant size, and product quality. Rev. Econ. Stud. 79 (1). Linder, S., 1961. An Essay on Trade and Transformation. Almqvist and Wiksell, Stockholm. Manova, K., Zhang, Z., 2012. Export prices across firms and destinations. Q. J. Econ. 127, 379–436. Martin, P., Rogers, C.A., 1995. Industrial location and public infrastructure. J. Int. Econ. 39 (3–4), 335–351. Melitz, M., Ottaviano, G., 2008. Market size, trade, and productivity. Rev. Econ. Stud. 75 (1), 295–316. Murphy, K., Shleifer, A., 1997. Quality and trade. J. Dev. Econ. 53, 1–15. Okubo, T., Picard, P.M., Thisse, J., 2010a. The spatial selection of heterogeneous firms. J. Int. Econ. 82 (2), 230–237. Okubo, T., Picard, P.M., Thisse, J., 2010b. On zero and asymmetric trade flows. CREA Discussion Paper Series 10-08. Center for Research in Economic Analysis, University of Luxembourg. Okubo, T., Picard, P.M., Thisse, J.-F., 2014. On the impact of competition on trade and capital mobility. J. Reg. Sci. 54 (5), 731–754. Ottaviano, G.I.P., Thisse, J.-F., 2004. Agglomeration and economic geography. In: Henderson, J.V., Thisse, J.-F. (Eds.), Handbook of Regional and Urban Economics Volume 4. Ottaviano, G.I.P., Tabuchi, T., Thisse, J.-F., 2002. Agglomeration and trade revisited. Int. Econ. Rev. 43 (2), 409–436. Picard, P.M., Okubo, T., 2012. Firms' locations under demand heterogeneity. Reg. Sci. Urban Econ. 42 (6), 961–974. Porter, M., 1990. The Competitive Advantage of Nations. The Free Press, New York. Schmookler, J., 1966. Invention and Economic Growth. Harvard University Press, Cambridge, Mass. Shaked, S., Sutton, J., 1987. Product differentiation and industrial structure. J. Ind. Econ. 36 (2), 131–146. Spence, M., 1975. Monopoly, quality, and regulation. Bell J. Econ. 6 (2), 417–429. Stockey, N.L., 1991. The volume and composition of trade between rich and poor countries. Rev. Econ. Stud. 58, 63–80. Sutton, J., 1991. Sunk Costs and Market Structure. MIT Press.