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The export of capital theory
Journal of Int,ernational Economics
11 (1981) 279-294. North-Holland
THE EXPORT
OF CAPITAL
Publishing Company
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Avinash DIXIT Princeton U’niversiry, Princeton, NJ 08540, USA Received August 1979, revised version received November
1980
1. Introduction
International trade theory is accustomed to the export and import of ideas with other branches of economics. General equilibrium theory has always been closely associated with trade theory in this way. Monetary economics, welfare economics, and two-sector growth theory have all had a look-in. Industrial economics is a newcomer to this trade in ideas. So is neoRicardian capital theory. Two recent books have given us a very valuable comprehensive statement of the neo-Ricardian contribution. One (FITT) is a collection of articles by Steedman, Metcalfe, Mainwaring and Parrinello, some not previously published, edited by Ian Steedman. The other book (TAGE) by Steedman gives an admirable exposition of the approach using a simplified illustrative model. The time now seems ripe for a detailed evaluation. In TAGE, and in his introductory essay in FITT, Steedman provides a clear statement of their aims. He begins by criticising the usual static two-bytwo model for treating capital as a scalar input made exogenously available in fixed quantity. According to Steedman, a proper treatment must recognise three features: the heterogeneity of capital goods, the fact of their being produced means of production, and the time needed for such production. It is clear that on all three counts the Heckscher-Ohlin-Samuelson model of elementary textbooks must plead guilty. However, few readers would wish to leave this criticism as an item in the pure history of thought. For most, it is the attempt of Steedman et al, to provide a constructive alternative approach that will be the focus of interest. Most of my discussion is8also motivated by that concern. *This article reviews two books: Fundamental Issues in Trade Theory, ed. Ian Steedman, Macmillan, London, 1979, E15, and Trade Amongst Growing Economies, by Ian Steedman, Cambridge University Press, Cambridge and New York, 1979, $21.50. The respective titles will be abbreviated as FITT and TAGE. I am grateful to Ian Steedman for detailed comments that cleared up some misunderstandings, but substantial differences of judgement remain. I am also grateful to John Williamson for encouragement and comments.
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For this purpose, we must compare the work under review, not so much with the static model, but with others that have tried to incorporate capital and growth into trade theory. The obvious candidate for comparison is the :;pproach based on neo-classical two-sector growth theory. This originated in articles by Bardhan, Inada, Oniki and Uzawa;’ textbook expositions can be found in Kemp (1969, chs. 10, 11) and Takayama (1932, ch. 14). These models clearly reccgnise the aspects of production and time, building them into the stock-flow and price-rental relations. What is not allowed is the heterogeneity of capital goods. We must therefore think of that as the major distinctive point of the neo-Ricardian contribution. This view is also consistent with the central claim of neo-Ricardians in the capital-theoretic debates of the sixties. The framework !‘avoured by Steedman and associates is the ‘Cambridge’ model of ,steady-stat<.. growth. All quantities grow at the same rate which is constant over time, thus enabling us to speak of the rate of growth, and all own rates of retur!n are equal across commodities and constant over time, thus enabling us to speak of rhe rate of interest or profit. This is recognised to be a restriction, but claimed to be justified as a benchmark (FITT. p. 11). as a state to which all growth paths will converge (TAGE, p. 9; FITT, p. 164), and as the best available method that avoids the intractability of disequilibrium analysis (TAGE, p. 36; FITT, p. 204). The usual trade-theoretic sequence of models is then set up: a closed economy, a small open economy, and a pair of trading economies. Various comparisons are made, both between regimes (e.g. autarky vs. trade), and ?vithin a regime when some exogenous parameters change (e.g. effects of changing tariffs). The questions posed are also the standard ones: What Mermines the pattern of trade? How do prices of non-tradeables relate to those of tradeables? What are the welfare consequences of trade and of trade policy? Some answers differ from those of the two-by-two static model and tlle two-sector growth models; notable examples are the question of possible losses from trade, and that of equalisation of interest rates by balanced trade in goods. My discussion of these issues will be organised as follows. In the next section I shall comment on the limitations of steady-state models. Then I shall turn to the specific points of gains from trade, the pattern of trade, and factor price equalisation. A brief concluding section follows these three L sections. Before turning to matters of substance, let me say something about the .~yle. Steedman ,Jeserves high praise for his exposition in TAGE; it is simple, clear, excellently organised, and integrates geometric and algebraic methods really well. Perhaps its very quality makes a warning to the reader necessary. Tihe model is very special. While it serves to il!, strate some general features of the approach, some of the techniques of unalysis, as well as some of the
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detailed results, will not survive generalisation After all, much of the seductive quality of the static two-by-two model lies in its neat expository nature. Some of the general models in FI’TT are well-expounded, others are not. Again Steedman must be singled out for praise for his formulation of the general von Neumann model of an open economy (Essay 13 in FITT). He shows a good appreciation of the economic subtleties of general equilibrium as well as the technicalities of mathematical programming in deriving his results. Some other papers, however, spend an inordinate amount of time deriving and discussing the wage-interest frontier, first without input substitution, then with a choice of activities. etc. Surely most of this is standard stulJ by now. The collection would hdve been much more readable if the papers had been revised to give a streamlined exposition, and that could have been done much more simply using unit cost functions. 2. Limitations of steady-state models When we judge whether the restrictions entailed by steady-state analy4s should be accepted. we must consider three things: what are the ahernatives. what kinds of questions cannot bc answered in the framework. and how they could be answered using the more general modes of analysis. On each point. I wish to fill some gaps left in the discussion of Steedman et al. First the alternatives. Steedman et al. give the impression that an intractable disequilibrium analysis is the only one available. This is not so. There are several halfway houses of greater generality and less tractability. offering an almost continuous trade-off. The simplest general&Con is equilibrium over time 4 la Hicks, Malinvaud, Arrow and Debreu. All that is relaxed is the constancy of relative prices and quantities. Expectations of the future are assumed to be correct. The next stage relaxes this requirement. There are in fact two avenues. In Hicksian temporary equilibrium, expectations are single-valued, but may be wrong. In the rational expectations approach, they are stochastic but must be right on the average. Each variant can be developed with flexible or fixed prices. The price of each generalisation is that only simpler models can be solved analytically. Models of equilibrium over time do yield some general results such as turnpike theorems, but details of solution paths can be found only in simple models with few sectors. In tempor:uy equilibrium or rational expectations models it is often necessary to assume special functional forms, such as the log-linear, to allow the computation of a solution. The particular trade-off in the available literature is that of a multi-sector model in a steady state against a tvro-sector model not confined in this way. However, steady states are clearly a special instance of general equilibrium o\cr time. Therefore 1 cannot agree with Steedcan’s assertion (FITT, p 7)
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that the former have potential for improving our understanding of real-world trade which the latte:r could ilever hope to match. It appears to be linked to a belief that comparative advantage is essentially a long-run property (PITT, p. 7. p. 74 $ri. 3). Although shared by some eminent earlier workers, this idea is suxzly b90 restrictive. More generally, comparative advantage consists of differences in relative pre-trade marginal costs; this can arise in any short run a.s well as in a long run. The more general models in fact pose a dilemma. In multiple-asset models, gelera non-steady growth paths often have a saddle-point structure. Perfect foresight over an infinite horizon is needed for the selection of a path that wiJr lead to a steady state. I suspect most neo-Ricardians would find it difhcult to accept this assumption, even though it can justify their use of steady states as an asymptotic approximation. Let us next consider what issues cannot be analysed using steady states, and how other models, especially two-sector growth models, treat them. The problems for steady-state analysis arise from the fact that such a state is, in modern parlance, ‘an ongoing situation’. There are no historically determined initial conditions. For given values of the growth rate and the profit rate, only one pattern of relative quantities and prices is compatible with the steady-state conliguration. Any actual economy has several stock ma.gnitudes fixed by its history, and they are typically not in a steady-state configuration. Models which confine themselves to steady states are therefore simply inap’propriate for answering real-world policy questions. Two-sector growth models can, on the other hand. offer such answers. They have initial conditions that are determined historically [not, as Steedman says (FITT, p. 6). arbitrarily]. This barretiness of steady-state models with regard to applicable pclicy prescription:; is surely a very high price to pay for the ;accommodation of capitai heterogeneity. My second point is that steady-state models have grave and inherent weaknesses in treating unbalanced trade and international investment. Consider the simple accounting relationships as derived by Metcalfe and Steedman (FITT, p. 213). Consider one country, and let Z denote its net holdings of foreign bonds, and I3 its balance of trade. Let g be its growth rate of all quantities, and i the rate of interest available on foreign Ibonds. In the steady state, Z increases in a period by gZ, and the increase comes from the interest flow on the existing stock of foreign bonds, and the flow trade balance. Therefore gZ = iZ+ B, or B= Ig- i)Z. Now g and i are constants, while Z changes exponentially at rate g and therefore has the same sign at #all times. Therefore B has the same sign at all times. in other words, in a :;teady state it must be the case that a country has exports of goods in excess of imports, or vice versa, at all times. Even in the exceptional case of g = i and B=O, Z is maintained on an exponential path by reinvesting abroad the interest on existing assets, for ever. This is surely a very undesirable
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restriction. Probably the most important purpose of international investment, like that of any investment, is to secure an advantageous inter-temporal reallocation of consumption. In this context, that means having B negative at some times and positive at others. But that is inherently outside the scope of steady-state models. For two-sector models this of course is no problem. The appropriate intertemporal trade balance constraint can be expressed in integral form, and the integrand, the discounted flow trade balance, can change sign as often as the conditions of equilibrium require. Several twosector models do assume constantly-balanced trade, but they are not compelled to do so by the logic of the method. The next problem arises in the treatment of growth at different rates in the trading countries. Some of the contributors do seem to have a sense of unease about this (TAGE, p. 110; FITT, p. 165). But they go ahead in the following way. In the long run, the country with the higher growth rate will dominate the other. Therefore the trading prices will coincide with the autarky prices of the large cormtry, and the other one can be analysed like a small country facing parametric prices. But this forgets the
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surpluses or deficits. Cumulative reserve losses are not calculated; in fact there is no money at all. To sum up, the costs of using steady states, measured in terms of the loss of analytical power, seem to me quite substantial. No doubt there are other dficulties which will occur to the readers. We must set against these costs the advantages that derive from our being able to consider in greater detail the features associated with the heterogeneity af capita1 goods. The next three sections examine the gains of this kind that are claimed by Steedman et al.
3. The gains from triide Steedman begns his treatment of the subject with a commendable
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All of the following discussion of gains from trade will assume that some such redistributive policies are used. The standard argument for these gains can then be illustrated very simply. Let the country start at an autarkic aggregate production-cum-consumption point, shown as A in fig. 1. Let PP be the frontier of production possibilities open to it in view of its resources, technology, and any irreversible commitments made in setting up its initial state. Let trade open up, and suppose the trade equilibrium prices differ from the autarky prices in a non-trivial way. If the frontier PP admits any transformation possibilities, a new point T for production will be chosen.
good
1
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Since producers seek to maximise the value of net output, and since A remains feasible, at trade prices T must have a higher value of net output. The trade consumption point can lie anywhere on the budget line BB corresponding to the trade prices and the aggregate national income or product under trade. The autarky consumption point, on the other hand, must coincide with the autarky production point. Thus, the autarky consumption point lies inside the budget line that is possible under free trade. The redistributive tools can now be wielded in such a way as to achieve an aggregate consumption point C which dominates that under autarky, and is distributed in such a way as to benefit all consumers. It is clear that the argument is valid for any number of goods, and in no way depends upon the two-dimensional geometry used for illustration. Therefore it can be interpreted in the context of equilibrium over time. The multi-d@ensional production possibility frontier shows intertemporal tradeoffs in production, the goods on the axes are distinguished by date of availability, and the prices are discounted present values. A detailed account of this can be found in Smith (1979).
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at A, while the consumption under trade can move away from T. It is this possibility that is correctly captured by evaluation at trade prices. And the whole argument is quite independent of how small the difference between autarky and trade prices might be, contrary to Mainwaring’s belief. Each point continues to have the higher value at its own prices, and it is the comparison of values at trade prices that yields information concerning consumption possibilities. It seems worth stating a few other aspects of the general argument for &IS from trade to avoid other misunderstandings. Any number of nont$ldeable goods are allowed; their prices should adjust to clear the domestic markets. There is no need for the country to be small. The argument goes through in terms of whatever trade prices emerge in equilibrium, and these may depend on this country’s pattern and extent of trade. [Of course. comparison of free trade vs. restricted trade is affected by this; see Dixit and Norman (1980b).] One point that is crucial to the argument is that t!:cre should be a single budget constraint as shown by the line BB in fig. 1. In the intertemporal context, this means that trade should be balanced over time in the sense that the discounted present value of net exports should be zero. Requiring trade to be balanced at each date imposes further constraints on the way in which the trade consumption plan can differ from the trade production plan. and this restricts the potential for achieving gains from trade. However, the requirement of trade balance at each instant is an arbitrary assumption without empirical justification. (Steedman et al. are not the only ones who make it, of course.) Let us turn to examine the most heavily emphasised welfare result of Steedman et al. (TAGE, ch. 5; FITT, Essays 4, 11 and in passing others), namely the possibility that for a given country, a trading steady state may have a lower level of consumption than an autarkic steady state. Such a result was obtained in a two-sector growth model by Stiglitz (1970); thus there is nothing inherent in the heterogeneity of capital goods that causes it. Also, it must be remembered that the models assume that trade is balanced at each date (and we have seen that it is in the nature of steady-state analysis that such a restriction be imposed). Therefore important and realistic possibilities for gain from intertemporal reallocation through trade are neglected. However, the most serious difficulty lies in determining what the result implies. Steedman in particular is careful not to draw any policy implications from it. However, several readers will fall into the error of inferring that autarky may be a better policy than free trade. Some non-economists may be glad to think that here they have an economic argument to justify their politi.cai beliefs. Hence a more detailed explanation of the limitations of the result is necessary. It is here that the barrenness of steady-state models with regard to policy prescriptions is crucial. To understa!ld the earlier general
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point in a similar, simpler context, consider capital accumulation in a closed economy. Among all the steady states in which such an econadny could be, the Golden Rule state has the highest level of consumption per head. Does this mean that an economy should try to be in the Golden Rule? We all spend a few minuses warning undergraduates against drawing such an iderence. The point is that each steady state dictates the level of capital stocks it will require. The economy contemplating its accumulation policy is typically not endowed with them, and cannot acquire them for free. If their acquisition entails some sacrifice of current consumption, this is a trade-off that has to be judged in the light of intertemporal objectives. Secondly, even if an economy has just the right amount of initial capital stocks for the Golden Rule, there is no compulsion other than the steady-state analyst’s dictat for maintaining them. If the intertemporal objectives work against the sacrifice of current consumption to acquire the Golden Rule capital stocks, they will equally make it desirable to decumulate stocks away from an initial position at the Golden Rule in order to enjoy more current consumption. The corresponding implications for trade and growth are obvious. The general result on gains from trade shows that, given the necessary redistributive tools. an autarkic economy skould move to free trade, and a free-trading economy should not move to autarky. This is so irrespective of the comparison of the two steady-state consumption levels. Economies in the real world are clearly constrained by their historically determined initial conditions. The kind of ahistoric comparison made in :-he Golden Rule result or the result of ‘Steedman et a!. is clear1.y of no practical relevance for accumulation or trade policy. Is there any guide to action it can give? I have been able to think of only one. Suppose that among all the economies in the universe there are two, otherwise identical, and each determined to remain in a steady state. One is to be in autarky, the other in free trade with the remaining o&s. An outsider, whose arrival will make only a negligible difference to each, is considering which economy he should join. His choice will then be governed by the comparison of the rival levels of consumption per head. As Steedman et a!. point out, there are circumstances in ;Nhich he may prefer to join the autarkic economy. However, even that is not the end of the story. What he should really do in these circumstances is to move to the autarkic economy and try to persuade it to adopt a policy of free trade accompanied by suitable redistributive policies. When Steedman comes to the effects of tariffs, he finds that the wageprofit frontier with taritfs lies uniformly below that under free trade, Here (TAGE, p. 72), he emphasises the importance of looking at transitions from one steady state to another. Surely the same arguments apply in the comparison of autarky and free trade, which is after all the special case of Steedman’s analysis where prohibitive tariffs are being compared with zero tariffs.
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4. Factor-price equalisation Several essays in FITT consider the question of whether constantlybalanced trade in all or some goods can equalise the wage rate and the interest rate across countries with identical technologies. I shall discuss the contributions of Mainwaring (Essays 6, 7), since they are the ones most directly addressed to the issue. Consider first the case where all goods are traded, and can all enter the production process as inputs of circulating capital. Let pi denote the world market price of good j, p the vector of these prices, w the wage rate, r the interest rate, and u (1 + r). Let fj be the unit cost function for good j. With constant returns to scale, competitive pricing will eliminate any pure profit, yielding for all j PjS
fj(~7p9 w)*
If good j is being produced in the country in question, (2)
Pj=fj(vPvw)*
Mainwaring assumes that the equality holds for all j, and asks whether different values of w and r are compatible with a given p. He constructs numerical examples of activity-analysis technologies where this may be so. From these examples it is difficult to judge whether the phenomenon is likely or exceptional. There is a more serious problem: the assumption that all goods are produced is generally not valid. We see this by constructing the wage-interest frontier at given world prices. Fig. 2 shows the region in (w, O) space that satisfies (1). For each i we find a convex region bounded to the south-west by the corresponding contour (2). The overall permissible region is the intersection of all these, and is bounded by the upper envelope of all the contours. Since at least one good must be produced, the actual (w,t’)
V
Fig. 2
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combination must lie on this frontier. If it lies at a corner, two goods corresponding to the two intersecting contour:; can be produced; if on a face, r-qly OI?C. Thus, for arbitrarily given world prices p, such as a small country might find itself facing, the kind of complete non-specialisation considered by Mainwering is exceptional, occurring only when all the goods’ contours haippen to pass through one point. This has static analogues; see Dixit and Norman (l%Oa, p. 48). Whether one good will be produced or two will depend in the static case on the factor endowments; corresponding steadysrate determinants remain to be found. In any event, it appears that the neoRicardian procedure of fixing the interest rate could be imposed independently in each country, and there is no reason here why the two should be equal. Plowever, let us follow the usual approach, and simply assume sufficiently diversified production, i.e. that two guods (say j= 1 and 2) are being produced. Then (2) is satisfied for these goods. Does this uniquely determine \V and r? That depends on whether the contours can intersect more than once, as happens in iig. 3.The simplest condition sufficient to rule this out is
V
Fig. 3
that at any point of intersection, one particular contour should alway; be the steeper. We can easily find the elasticity of ~7 with respect to u alung one such contour. Taking total logarithmic differentials of (2) for j= 1, and letting I;*denote dw/ltt, etc. we have
where Biir is the elasticity of f ’ with respect to the kth component of vp, i.e. the distribt.tive share of the rental of the kth good in the cost of good 1, and OIL is the share of labour in the cost of good 1. But all these shares add up
‘91
to unity; therefore (1 -(I,L)i:+o*,.~i.=o. yielding the elasticity d log rv/d log r = r;.,/l”l= -
( 1 - 0, ,_)!‘I), ,..
(3)
The required condition is that the distributive share of Mbour for one particular good shoulc always be higher than that for the other. This is simple, has natural static analogues, and is operational in a way that Samuelson’s condition of ‘uniform differences in factor intensities’ is not. This is not all that can be said, however. We have NOfar taken the prices of goods as arbitrarily fixed. Implicitly, they arc supposed to be determined by the market-clearing conditions for the world. Consider the realistic case of a world in which there are many times more goods than countries. In an equilibrium, all goods must be produced somewhere, and each country producing one or two goods is not enough to ensure this. Therefore output prices must adjust to make it possible for one country to produce more goods ,Athout loss, i.e. changes in the pj must shift contours like (2) until more than two of them pass through one point in (M..I*) space. One suspects that this reduces the likelihood of the same three or more contours passing through another common point, i.e. strengthens the cast for diversification ensuring factor-price equalisation. However. even in the static case, the actual pattern of diversification or specialisation that emerges in equilibrium depends in compl&ted ways on demand, technology. and factor endowments; see Dixit and Norman (1980a. pp. 110 13). The corresponding analysis for steady-state equilibria remains to be done. Non-trrdeables cause problems in the usual way. Let irs consider the case where they are circulating capital inputs as well, and let 11~be their prices and gi the unit cost functions. For the traded goods we have the obvious generalisation of (1) and (2): (4) with equality if good 1 is produced. Since the non-traded produced at home, we have for all i an equation
goods must all bo
We can use (5) to determine y in terms of p, I*and M’,although there may be further problems of univalence in this sub-problem. Substituting in (4), WC have a reduced-form relation involving only p, 1’and 1~. We can use this to
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draw contours as before. However. the expression for the elasticity of a contour now involves indirect effects working through induced changes in q, and it is not possible to derive a simple condition ensuring univalence of w and r when two goods are being produced. Readers can now easily consider cases, e.g. where some of the goods are purely consumer goods, or where there are other primary factors, and see how the models of Mainwaring (FITT, Essay 7) and Metcalfe and Steedman (FITT, Essays 2, 3 and 5) tit into this general framework. My conclusion is that there are issues in the area of factor-price equalisation in steady-state models that remain to be investigated. I believe they can be much better handled using unit cost functions, and should pay heed to the generalequilibrium implications of the market-clearing conditions for tradeables and non-tradeables, i.e. to demand and factor endowments. However,. in view of the purely academic nature of the whole question, I doubt whether such furthlsr research is worth the effort. If ;my more argument is needed in support of this contention, I should point out that the whole discussion assumes constantly-balanced trade. This ‘is empirically unrealistic and theoretically undesirable since it rules out any action in response to the mutual desire for international borrowing and lending that exists in this situation. Once that is allowed, the question of interest-rate equalisation moves to an entirely different arena.
5. The pattern of trade
In the static two-by-two model, where capital is treated just like a primary input, and factor-intensity reversals are assumed away, the relatively capitalabundant country exports the relatively capital-intensive good. This is so whether capital-abundance is interpreted in terms of the physical quantity of capital relative to the other primary input, labour, or their relative prices, the wage-rental ratio. This result, the Heckscher-Ohlin theorem, is established through the following steps: (1) the relation between the wage-rental ratio and the commodity price ratio is governed by relative factor intensities; (2) the country with the lower pre-trade relative price of a commodity will export that commodity when trade opens up; and (3) there is a negative relation between the relative quantities and prices of factors in autarky when certain demand ‘perversities’ are assumed away, It being sufftcient to assume homothetic tastes. Steedman et al. rightly criticise this model for its neglect of the endogeneity of capital as well as its heterogeneity. Consider the former first. In balanced trade at an instant of time, where capital stocks are historically fixed, we could define capital intensity in terms of the relative quantities or the wage--rental ratio, and the standard theorem would apply, so long as there was a single capital good. However, in any run longer than an instant,
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we must face up to the question of how the relatively capital-intensive country came to be so. One possible answer is in terms of the aggregate propensity to save. This works: Dixit (1978) shows that, in steady states in a one-capital-good model, the country with the higher saving propensity exports the relatively capital-intensive good. Another approach is in terms of the interest rate. This can be criticised on the grounds that the interest rate is itself endogenous, but it is in the tradition of the price form of the Heckscher-Ohlin theorem. Again, in a one-capital-good model in steady states, this works. Let good 1 be the consumer good and good 2 the capital good, and use the same notation i:s in the previous section. The price-cost relations are I p1 =f’
(vpz, w)
and
p2 =Jf2 (opt, w).
(6)
Total logarithmic differentiation of (is) immediately gives us a relation between pl/pr and V, and it is governed by the relative factor intensities. Then the country with the lower autarky interest rate has the lower relative price of the m6re capital-intensive good in autarky, and therefore exports it in constantly-balanced trade. See Ethier (1979) for a more general treatment. Heterogeneity of capital can bring in additional problems (FITT, Essay 5). However, so can multiplicity of goods znd factors in general. In the context of steady-state models, there are examples in FITT, Essays 2 and 3. But even static models run into similar problems as soon as we leave the two-by-two framework. None of the steps in the proof of the Heckscher-Ohlin theorem remains, valid. More precisely, we can only establish correlation: between various quantity or price differences, and cannot unambiguously derive general comparisons commodity by commodity. Even at the most basic level, we cannot be sure that a country will export each good for which it has a lower pre-trade relative price; we can only say that export quantities are positively correlated with the excess of foreign pre-trade relative prices over domestic ones. It is similarly only ‘on the average’ that we can say that a country will have lower pre-trade relative prices of goods which are intensive in using the factors with which it is more abundantly endowed. These matters are discussed in static models by Dixit and Norman (1980a, pp. 94100) and Woodland (1980). In the general von Neumann model of steadystate growth (FITT, Essay 13), Steedman obtains very similar correlations. ln this respect, I conclude that the mure serious defect of the elementary textbook model is its two-ness rather than its neglect of the particular features of capital. 6. Concluding comments Steedman and associates have performed a most valuable service to the community of international trade theorists by alerting them to serious defects
of the static two-by-two model that need to be remedied if it is to be useful in important dynamic contexts. The questions they have posed, and their amdyses, have opened up usefu! avenues for further research. But I do not think success lies in the neo-Ricardian direction. In particular, confining the theory to the ahistoric straitjacket of steady states would be a serious mistake. In the trade-off where one can handle either heterogeneous capital goods or non-steady-state paths, for me the latter facility seems vastly more impor!ant. Finally, it should be said for the record that the limitations of the static two-by-two textbook model do not arise solely from its neglect of capital. There are other purposes for which it has been augmented or altered, while preserving its static character. The specific factor model is perhaps the most eminent example, but there are several others. The criticis,,ns of Steedman et al. do not destroy the usefulness of such models in the appropriate contexts.
References Dixit. A.. 1978. 0 I Rybczynski’s theorem in a setting of growth, Journal of International Economics 8, 127- 129. Dixit. A. and Norman, V.. 1980a, Theory of international trade (Nisbets and Cambridge University Press, Welwyn, Herts., U.K.). Dixit. A. and Norman, V., 198Ob. The gain from free trade, Warwick Ecc nomic Research Paper no. 173. August, 1980 Ethier. W., 1979, The tileorems of international trade in time-pllascd economies, Journal of International Economics 9, 225 238. Kemp, M.C.. 1969. The pure theory of international trade and investment (Prentice-Hall, Englewood Cliffs, NJ). Smith, M.A.M., 1979, Intertemporal gains from trade, Journal of International Economics 9. 239-248. Stiglitz J.E., 1970, Factor price equalisation in a dynam;c economy. Journal of Political Economy 78,456488. Takayama, A., 1972. International trade (Holt, Rinehart and Winston, New York). Wood!aiid, AD., 19x0, The relationship between factor endowments and commodity trade, manuscript, University of British Cohrmbrd.
11 (1981) 279-294. North-Holland
THE EXPORT
OF CAPITAL
Publishing Company
THEORY*
Avinash DIXIT Princeton U’niversiry, Princeton, NJ 08540, USA Received August 1979, revised version received November
1980
1. Introduction
International trade theory is accustomed to the export and import of ideas with other branches of economics. General equilibrium theory has always been closely associated with trade theory in this way. Monetary economics, welfare economics, and two-sector growth theory have all had a look-in. Industrial economics is a newcomer to this trade in ideas. So is neoRicardian capital theory. Two recent books have given us a very valuable comprehensive statement of the neo-Ricardian contribution. One (FITT) is a collection of articles by Steedman, Metcalfe, Mainwaring and Parrinello, some not previously published, edited by Ian Steedman. The other book (TAGE) by Steedman gives an admirable exposition of the approach using a simplified illustrative model. The time now seems ripe for a detailed evaluation. In TAGE, and in his introductory essay in FITT, Steedman provides a clear statement of their aims. He begins by criticising the usual static two-bytwo model for treating capital as a scalar input made exogenously available in fixed quantity. According to Steedman, a proper treatment must recognise three features: the heterogeneity of capital goods, the fact of their being produced means of production, and the time needed for such production. It is clear that on all three counts the Heckscher-Ohlin-Samuelson model of elementary textbooks must plead guilty. However, few readers would wish to leave this criticism as an item in the pure history of thought. For most, it is the attempt of Steedman et al, to provide a constructive alternative approach that will be the focus of interest. Most of my discussion is8also motivated by that concern. *This article reviews two books: Fundamental Issues in Trade Theory, ed. Ian Steedman, Macmillan, London, 1979, E15, and Trade Amongst Growing Economies, by Ian Steedman, Cambridge University Press, Cambridge and New York, 1979, $21.50. The respective titles will be abbreviated as FITT and TAGE. I am grateful to Ian Steedman for detailed comments that cleared up some misunderstandings, but substantial differences of judgement remain. I am also grateful to John Williamson for encouragement and comments.
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For this purpose, we must compare the work under review, not so much with the static model, but with others that have tried to incorporate capital and growth into trade theory. The obvious candidate for comparison is the :;pproach based on neo-classical two-sector growth theory. This originated in articles by Bardhan, Inada, Oniki and Uzawa;’ textbook expositions can be found in Kemp (1969, chs. 10, 11) and Takayama (1932, ch. 14). These models clearly reccgnise the aspects of production and time, building them into the stock-flow and price-rental relations. What is not allowed is the heterogeneity of capital goods. We must therefore think of that as the major distinctive point of the neo-Ricardian contribution. This view is also consistent with the central claim of neo-Ricardians in the capital-theoretic debates of the sixties. The framework !‘avoured by Steedman and associates is the ‘Cambridge’ model of ,steady-stat<.. growth. All quantities grow at the same rate which is constant over time, thus enabling us to speak of the rate of growth, and all own rates of retur!n are equal across commodities and constant over time, thus enabling us to speak of rhe rate of interest or profit. This is recognised to be a restriction, but claimed to be justified as a benchmark (FITT. p. 11). as a state to which all growth paths will converge (TAGE, p. 9; FITT, p. 164), and as the best available method that avoids the intractability of disequilibrium analysis (TAGE, p. 36; FITT, p. 204). The usual trade-theoretic sequence of models is then set up: a closed economy, a small open economy, and a pair of trading economies. Various comparisons are made, both between regimes (e.g. autarky vs. trade), and ?vithin a regime when some exogenous parameters change (e.g. effects of changing tariffs). The questions posed are also the standard ones: What Mermines the pattern of trade? How do prices of non-tradeables relate to those of tradeables? What are the welfare consequences of trade and of trade policy? Some answers differ from those of the two-by-two static model and tlle two-sector growth models; notable examples are the question of possible losses from trade, and that of equalisation of interest rates by balanced trade in goods. My discussion of these issues will be organised as follows. In the next section I shall comment on the limitations of steady-state models. Then I shall turn to the specific points of gains from trade, the pattern of trade, and factor price equalisation. A brief concluding section follows these three L sections. Before turning to matters of substance, let me say something about the .~yle. Steedman ,Jeserves high praise for his exposition in TAGE; it is simple, clear, excellently organised, and integrates geometric and algebraic methods really well. Perhaps its very quality makes a warning to the reader necessary. Tihe model is very special. While it serves to il!, strate some general features of the approach, some of the techniques of unalysis, as well as some of the
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detailed results, will not survive generalisation After all, much of the seductive quality of the static two-by-two model lies in its neat expository nature. Some of the general models in FI’TT are well-expounded, others are not. Again Steedman must be singled out for praise for his formulation of the general von Neumann model of an open economy (Essay 13 in FITT). He shows a good appreciation of the economic subtleties of general equilibrium as well as the technicalities of mathematical programming in deriving his results. Some other papers, however, spend an inordinate amount of time deriving and discussing the wage-interest frontier, first without input substitution, then with a choice of activities. etc. Surely most of this is standard stulJ by now. The collection would hdve been much more readable if the papers had been revised to give a streamlined exposition, and that could have been done much more simply using unit cost functions. 2. Limitations of steady-state models When we judge whether the restrictions entailed by steady-state analy4s should be accepted. we must consider three things: what are the ahernatives. what kinds of questions cannot bc answered in the framework. and how they could be answered using the more general modes of analysis. On each point. I wish to fill some gaps left in the discussion of Steedman et al. First the alternatives. Steedman et al. give the impression that an intractable disequilibrium analysis is the only one available. This is not so. There are several halfway houses of greater generality and less tractability. offering an almost continuous trade-off. The simplest general&Con is equilibrium over time 4 la Hicks, Malinvaud, Arrow and Debreu. All that is relaxed is the constancy of relative prices and quantities. Expectations of the future are assumed to be correct. The next stage relaxes this requirement. There are in fact two avenues. In Hicksian temporary equilibrium, expectations are single-valued, but may be wrong. In the rational expectations approach, they are stochastic but must be right on the average. Each variant can be developed with flexible or fixed prices. The price of each generalisation is that only simpler models can be solved analytically. Models of equilibrium over time do yield some general results such as turnpike theorems, but details of solution paths can be found only in simple models with few sectors. In tempor:uy equilibrium or rational expectations models it is often necessary to assume special functional forms, such as the log-linear, to allow the computation of a solution. The particular trade-off in the available literature is that of a multi-sector model in a steady state against a tvro-sector model not confined in this way. However, steady states are clearly a special instance of general equilibrium o\cr time. Therefore 1 cannot agree with Steedcan’s assertion (FITT, p 7)
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that the former have potential for improving our understanding of real-world trade which the latte:r could ilever hope to match. It appears to be linked to a belief that comparative advantage is essentially a long-run property (PITT, p. 7. p. 74 $ri. 3). Although shared by some eminent earlier workers, this idea is suxzly b90 restrictive. More generally, comparative advantage consists of differences in relative pre-trade marginal costs; this can arise in any short run a.s well as in a long run. The more general models in fact pose a dilemma. In multiple-asset models, gelera non-steady growth paths often have a saddle-point structure. Perfect foresight over an infinite horizon is needed for the selection of a path that wiJr lead to a steady state. I suspect most neo-Ricardians would find it difhcult to accept this assumption, even though it can justify their use of steady states as an asymptotic approximation. Let us next consider what issues cannot be analysed using steady states, and how other models, especially two-sector growth models, treat them. The problems for steady-state analysis arise from the fact that such a state is, in modern parlance, ‘an ongoing situation’. There are no historically determined initial conditions. For given values of the growth rate and the profit rate, only one pattern of relative quantities and prices is compatible with the steady-state conliguration. Any actual economy has several stock ma.gnitudes fixed by its history, and they are typically not in a steady-state configuration. Models which confine themselves to steady states are therefore simply inap’propriate for answering real-world policy questions. Two-sector growth models can, on the other hand. offer such answers. They have initial conditions that are determined historically [not, as Steedman says (FITT, p. 6). arbitrarily]. This barretiness of steady-state models with regard to applicable pclicy prescription:; is surely a very high price to pay for the ;accommodation of capitai heterogeneity. My second point is that steady-state models have grave and inherent weaknesses in treating unbalanced trade and international investment. Consider the simple accounting relationships as derived by Metcalfe and Steedman (FITT, p. 213). Consider one country, and let Z denote its net holdings of foreign bonds, and I3 its balance of trade. Let g be its growth rate of all quantities, and i the rate of interest available on foreign Ibonds. In the steady state, Z increases in a period by gZ, and the increase comes from the interest flow on the existing stock of foreign bonds, and the flow trade balance. Therefore gZ = iZ+ B, or B= Ig- i)Z. Now g and i are constants, while Z changes exponentially at rate g and therefore has the same sign at #all times. Therefore B has the same sign at all times. in other words, in a :;teady state it must be the case that a country has exports of goods in excess of imports, or vice versa, at all times. Even in the exceptional case of g = i and B=O, Z is maintained on an exponential path by reinvesting abroad the interest on existing assets, for ever. This is surely a very undesirable
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restriction. Probably the most important purpose of international investment, like that of any investment, is to secure an advantageous inter-temporal reallocation of consumption. In this context, that means having B negative at some times and positive at others. But that is inherently outside the scope of steady-state models. For two-sector models this of course is no problem. The appropriate intertemporal trade balance constraint can be expressed in integral form, and the integrand, the discounted flow trade balance, can change sign as often as the conditions of equilibrium require. Several twosector models do assume constantly-balanced trade, but they are not compelled to do so by the logic of the method. The next problem arises in the treatment of growth at different rates in the trading countries. Some of the contributors do seem to have a sense of unease about this (TAGE, p. 110; FITT, p. 165). But they go ahead in the following way. In the long run, the country with the higher growth rate will dominate the other. Therefore the trading prices will coincide with the autarky prices of the large cormtry, and the other one can be analysed like a small country facing parametric prices. But this forgets the
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surpluses or deficits. Cumulative reserve losses are not calculated; in fact there is no money at all. To sum up, the costs of using steady states, measured in terms of the loss of analytical power, seem to me quite substantial. No doubt there are other dficulties which will occur to the readers. We must set against these costs the advantages that derive from our being able to consider in greater detail the features associated with the heterogeneity af capita1 goods. The next three sections examine the gains of this kind that are claimed by Steedman et al.
3. The gains from triide Steedman begns his treatment of the subject with a commendable
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All of the following discussion of gains from trade will assume that some such redistributive policies are used. The standard argument for these gains can then be illustrated very simply. Let the country start at an autarkic aggregate production-cum-consumption point, shown as A in fig. 1. Let PP be the frontier of production possibilities open to it in view of its resources, technology, and any irreversible commitments made in setting up its initial state. Let trade open up, and suppose the trade equilibrium prices differ from the autarky prices in a non-trivial way. If the frontier PP admits any transformation possibilities, a new point T for production will be chosen.
good
1
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Since producers seek to maximise the value of net output, and since A remains feasible, at trade prices T must have a higher value of net output. The trade consumption point can lie anywhere on the budget line BB corresponding to the trade prices and the aggregate national income or product under trade. The autarky consumption point, on the other hand, must coincide with the autarky production point. Thus, the autarky consumption point lies inside the budget line that is possible under free trade. The redistributive tools can now be wielded in such a way as to achieve an aggregate consumption point C which dominates that under autarky, and is distributed in such a way as to benefit all consumers. It is clear that the argument is valid for any number of goods, and in no way depends upon the two-dimensional geometry used for illustration. Therefore it can be interpreted in the context of equilibrium over time. The multi-d@ensional production possibility frontier shows intertemporal tradeoffs in production, the goods on the axes are distinguished by date of availability, and the prices are discounted present values. A detailed account of this can be found in Smith (1979).
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at A, while the consumption under trade can move away from T. It is this possibility that is correctly captured by evaluation at trade prices. And the whole argument is quite independent of how small the difference between autarky and trade prices might be, contrary to Mainwaring’s belief. Each point continues to have the higher value at its own prices, and it is the comparison of values at trade prices that yields information concerning consumption possibilities. It seems worth stating a few other aspects of the general argument for &IS from trade to avoid other misunderstandings. Any number of nont$ldeable goods are allowed; their prices should adjust to clear the domestic markets. There is no need for the country to be small. The argument goes through in terms of whatever trade prices emerge in equilibrium, and these may depend on this country’s pattern and extent of trade. [Of course. comparison of free trade vs. restricted trade is affected by this; see Dixit and Norman (1980b).] One point that is crucial to the argument is that t!:cre should be a single budget constraint as shown by the line BB in fig. 1. In the intertemporal context, this means that trade should be balanced over time in the sense that the discounted present value of net exports should be zero. Requiring trade to be balanced at each date imposes further constraints on the way in which the trade consumption plan can differ from the trade production plan. and this restricts the potential for achieving gains from trade. However, the requirement of trade balance at each instant is an arbitrary assumption without empirical justification. (Steedman et al. are not the only ones who make it, of course.) Let us turn to examine the most heavily emphasised welfare result of Steedman et al. (TAGE, ch. 5; FITT, Essays 4, 11 and in passing others), namely the possibility that for a given country, a trading steady state may have a lower level of consumption than an autarkic steady state. Such a result was obtained in a two-sector growth model by Stiglitz (1970); thus there is nothing inherent in the heterogeneity of capital goods that causes it. Also, it must be remembered that the models assume that trade is balanced at each date (and we have seen that it is in the nature of steady-state analysis that such a restriction be imposed). Therefore important and realistic possibilities for gain from intertemporal reallocation through trade are neglected. However, the most serious difficulty lies in determining what the result implies. Steedman in particular is careful not to draw any policy implications from it. However, several readers will fall into the error of inferring that autarky may be a better policy than free trade. Some non-economists may be glad to think that here they have an economic argument to justify their politi.cai beliefs. Hence a more detailed explanation of the limitations of the result is necessary. It is here that the barrenness of steady-state models with regard to policy prescriptions is crucial. To understa!ld the earlier general
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point in a similar, simpler context, consider capital accumulation in a closed economy. Among all the steady states in which such an econadny could be, the Golden Rule state has the highest level of consumption per head. Does this mean that an economy should try to be in the Golden Rule? We all spend a few minuses warning undergraduates against drawing such an iderence. The point is that each steady state dictates the level of capital stocks it will require. The economy contemplating its accumulation policy is typically not endowed with them, and cannot acquire them for free. If their acquisition entails some sacrifice of current consumption, this is a trade-off that has to be judged in the light of intertemporal objectives. Secondly, even if an economy has just the right amount of initial capital stocks for the Golden Rule, there is no compulsion other than the steady-state analyst’s dictat for maintaining them. If the intertemporal objectives work against the sacrifice of current consumption to acquire the Golden Rule capital stocks, they will equally make it desirable to decumulate stocks away from an initial position at the Golden Rule in order to enjoy more current consumption. The corresponding implications for trade and growth are obvious. The general result on gains from trade shows that, given the necessary redistributive tools. an autarkic economy skould move to free trade, and a free-trading economy should not move to autarky. This is so irrespective of the comparison of the two steady-state consumption levels. Economies in the real world are clearly constrained by their historically determined initial conditions. The kind of ahistoric comparison made in :-he Golden Rule result or the result of ‘Steedman et a!. is clear1.y of no practical relevance for accumulation or trade policy. Is there any guide to action it can give? I have been able to think of only one. Suppose that among all the economies in the universe there are two, otherwise identical, and each determined to remain in a steady state. One is to be in autarky, the other in free trade with the remaining o&s. An outsider, whose arrival will make only a negligible difference to each, is considering which economy he should join. His choice will then be governed by the comparison of the rival levels of consumption per head. As Steedman et a!. point out, there are circumstances in ;Nhich he may prefer to join the autarkic economy. However, even that is not the end of the story. What he should really do in these circumstances is to move to the autarkic economy and try to persuade it to adopt a policy of free trade accompanied by suitable redistributive policies. When Steedman comes to the effects of tariffs, he finds that the wageprofit frontier with taritfs lies uniformly below that under free trade, Here (TAGE, p. 72), he emphasises the importance of looking at transitions from one steady state to another. Surely the same arguments apply in the comparison of autarky and free trade, which is after all the special case of Steedman’s analysis where prohibitive tariffs are being compared with zero tariffs.
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4. Factor-price equalisation Several essays in FITT consider the question of whether constantlybalanced trade in all or some goods can equalise the wage rate and the interest rate across countries with identical technologies. I shall discuss the contributions of Mainwaring (Essays 6, 7), since they are the ones most directly addressed to the issue. Consider first the case where all goods are traded, and can all enter the production process as inputs of circulating capital. Let pi denote the world market price of good j, p the vector of these prices, w the wage rate, r the interest rate, and u (1 + r). Let fj be the unit cost function for good j. With constant returns to scale, competitive pricing will eliminate any pure profit, yielding for all j PjS
fj(~7p9 w)*
If good j is being produced in the country in question, (2)
Pj=fj(vPvw)*
Mainwaring assumes that the equality holds for all j, and asks whether different values of w and r are compatible with a given p. He constructs numerical examples of activity-analysis technologies where this may be so. From these examples it is difficult to judge whether the phenomenon is likely or exceptional. There is a more serious problem: the assumption that all goods are produced is generally not valid. We see this by constructing the wage-interest frontier at given world prices. Fig. 2 shows the region in (w, O) space that satisfies (1). For each i we find a convex region bounded to the south-west by the corresponding contour (2). The overall permissible region is the intersection of all these, and is bounded by the upper envelope of all the contours. Since at least one good must be produced, the actual (w,t’)
V
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combination must lie on this frontier. If it lies at a corner, two goods corresponding to the two intersecting contour:; can be produced; if on a face, r-qly OI?C. Thus, for arbitrarily given world prices p, such as a small country might find itself facing, the kind of complete non-specialisation considered by Mainwering is exceptional, occurring only when all the goods’ contours haippen to pass through one point. This has static analogues; see Dixit and Norman (l%Oa, p. 48). Whether one good will be produced or two will depend in the static case on the factor endowments; corresponding steadysrate determinants remain to be found. In any event, it appears that the neoRicardian procedure of fixing the interest rate could be imposed independently in each country, and there is no reason here why the two should be equal. Plowever, let us follow the usual approach, and simply assume sufficiently diversified production, i.e. that two guods (say j= 1 and 2) are being produced. Then (2) is satisfied for these goods. Does this uniquely determine \V and r? That depends on whether the contours can intersect more than once, as happens in iig. 3.The simplest condition sufficient to rule this out is
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that at any point of intersection, one particular contour should alway; be the steeper. We can easily find the elasticity of ~7 with respect to u alung one such contour. Taking total logarithmic differentials of (2) for j= 1, and letting I;*denote dw/ltt, etc. we have
where Biir is the elasticity of f ’ with respect to the kth component of vp, i.e. the distribt.tive share of the rental of the kth good in the cost of good 1, and OIL is the share of labour in the cost of good 1. But all these shares add up
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to unity; therefore (1 -(I,L)i:+o*,.~i.=o. yielding the elasticity d log rv/d log r = r;.,/l”l= -
( 1 - 0, ,_)!‘I), ,..
(3)
The required condition is that the distributive share of Mbour for one particular good shoulc always be higher than that for the other. This is simple, has natural static analogues, and is operational in a way that Samuelson’s condition of ‘uniform differences in factor intensities’ is not. This is not all that can be said, however. We have NOfar taken the prices of goods as arbitrarily fixed. Implicitly, they arc supposed to be determined by the market-clearing conditions for the world. Consider the realistic case of a world in which there are many times more goods than countries. In an equilibrium, all goods must be produced somewhere, and each country producing one or two goods is not enough to ensure this. Therefore output prices must adjust to make it possible for one country to produce more goods ,Athout loss, i.e. changes in the pj must shift contours like (2) until more than two of them pass through one point in (M..I*) space. One suspects that this reduces the likelihood of the same three or more contours passing through another common point, i.e. strengthens the cast for diversification ensuring factor-price equalisation. However. even in the static case, the actual pattern of diversification or specialisation that emerges in equilibrium depends in compl&ted ways on demand, technology. and factor endowments; see Dixit and Norman (1980a. pp. 110 13). The corresponding analysis for steady-state equilibria remains to be done. Non-trrdeables cause problems in the usual way. Let irs consider the case where they are circulating capital inputs as well, and let 11~be their prices and gi the unit cost functions. For the traded goods we have the obvious generalisation of (1) and (2): (4) with equality if good 1 is produced. Since the non-traded produced at home, we have for all i an equation
goods must all bo
We can use (5) to determine y in terms of p, I*and M’,although there may be further problems of univalence in this sub-problem. Substituting in (4), WC have a reduced-form relation involving only p, 1’and 1~. We can use this to
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draw contours as before. However. the expression for the elasticity of a contour now involves indirect effects working through induced changes in q, and it is not possible to derive a simple condition ensuring univalence of w and r when two goods are being produced. Readers can now easily consider cases, e.g. where some of the goods are purely consumer goods, or where there are other primary factors, and see how the models of Mainwaring (FITT, Essay 7) and Metcalfe and Steedman (FITT, Essays 2, 3 and 5) tit into this general framework. My conclusion is that there are issues in the area of factor-price equalisation in steady-state models that remain to be investigated. I believe they can be much better handled using unit cost functions, and should pay heed to the generalequilibrium implications of the market-clearing conditions for tradeables and non-tradeables, i.e. to demand and factor endowments. However,. in view of the purely academic nature of the whole question, I doubt whether such furthlsr research is worth the effort. If ;my more argument is needed in support of this contention, I should point out that the whole discussion assumes constantly-balanced trade. This ‘is empirically unrealistic and theoretically undesirable since it rules out any action in response to the mutual desire for international borrowing and lending that exists in this situation. Once that is allowed, the question of interest-rate equalisation moves to an entirely different arena.
5. The pattern of trade
In the static two-by-two model, where capital is treated just like a primary input, and factor-intensity reversals are assumed away, the relatively capitalabundant country exports the relatively capital-intensive good. This is so whether capital-abundance is interpreted in terms of the physical quantity of capital relative to the other primary input, labour, or their relative prices, the wage-rental ratio. This result, the Heckscher-Ohlin theorem, is established through the following steps: (1) the relation between the wage-rental ratio and the commodity price ratio is governed by relative factor intensities; (2) the country with the lower pre-trade relative price of a commodity will export that commodity when trade opens up; and (3) there is a negative relation between the relative quantities and prices of factors in autarky when certain demand ‘perversities’ are assumed away, It being sufftcient to assume homothetic tastes. Steedman et al. rightly criticise this model for its neglect of the endogeneity of capital as well as its heterogeneity. Consider the former first. In balanced trade at an instant of time, where capital stocks are historically fixed, we could define capital intensity in terms of the relative quantities or the wage--rental ratio, and the standard theorem would apply, so long as there was a single capital good. However, in any run longer than an instant,
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we must face up to the question of how the relatively capital-intensive country came to be so. One possible answer is in terms of the aggregate propensity to save. This works: Dixit (1978) shows that, in steady states in a one-capital-good model, the country with the higher saving propensity exports the relatively capital-intensive good. Another approach is in terms of the interest rate. This can be criticised on the grounds that the interest rate is itself endogenous, but it is in the tradition of the price form of the Heckscher-Ohlin theorem. Again, in a one-capital-good model in steady states, this works. Let good 1 be the consumer good and good 2 the capital good, and use the same notation i:s in the previous section. The price-cost relations are I p1 =f’
(vpz, w)
and
p2 =Jf2 (opt, w).
(6)
Total logarithmic differentiation of (is) immediately gives us a relation between pl/pr and V, and it is governed by the relative factor intensities. Then the country with the lower autarky interest rate has the lower relative price of the m6re capital-intensive good in autarky, and therefore exports it in constantly-balanced trade. See Ethier (1979) for a more general treatment. Heterogeneity of capital can bring in additional problems (FITT, Essay 5). However, so can multiplicity of goods znd factors in general. In the context of steady-state models, there are examples in FITT, Essays 2 and 3. But even static models run into similar problems as soon as we leave the two-by-two framework. None of the steps in the proof of the Heckscher-Ohlin theorem remains, valid. More precisely, we can only establish correlation: between various quantity or price differences, and cannot unambiguously derive general comparisons commodity by commodity. Even at the most basic level, we cannot be sure that a country will export each good for which it has a lower pre-trade relative price; we can only say that export quantities are positively correlated with the excess of foreign pre-trade relative prices over domestic ones. It is similarly only ‘on the average’ that we can say that a country will have lower pre-trade relative prices of goods which are intensive in using the factors with which it is more abundantly endowed. These matters are discussed in static models by Dixit and Norman (1980a, pp. 94100) and Woodland (1980). In the general von Neumann model of steadystate growth (FITT, Essay 13), Steedman obtains very similar correlations. ln this respect, I conclude that the mure serious defect of the elementary textbook model is its two-ness rather than its neglect of the particular features of capital. 6. Concluding comments Steedman and associates have performed a most valuable service to the community of international trade theorists by alerting them to serious defects
of the static two-by-two model that need to be remedied if it is to be useful in important dynamic contexts. The questions they have posed, and their amdyses, have opened up usefu! avenues for further research. But I do not think success lies in the neo-Ricardian direction. In particular, confining the theory to the ahistoric straitjacket of steady states would be a serious mistake. In the trade-off where one can handle either heterogeneous capital goods or non-steady-state paths, for me the latter facility seems vastly more impor!ant. Finally, it should be said for the record that the limitations of the static two-by-two textbook model do not arise solely from its neglect of capital. There are other purposes for which it has been augmented or altered, while preserving its static character. The specific factor model is perhaps the most eminent example, but there are several others. The criticis,,ns of Steedman et al. do not destroy the usefulness of such models in the appropriate contexts.
References Dixit. A.. 1978. 0 I Rybczynski’s theorem in a setting of growth, Journal of International Economics 8, 127- 129. Dixit. A. and Norman, V.. 1980a, Theory of international trade (Nisbets and Cambridge University Press, Welwyn, Herts., U.K.). Dixit. A. and Norman, V., 198Ob. The gain from free trade, Warwick Ecc nomic Research Paper no. 173. August, 1980 Ethier. W., 1979, The tileorems of international trade in time-pllascd economies, Journal of International Economics 9, 225 238. Kemp, M.C.. 1969. The pure theory of international trade and investment (Prentice-Hall, Englewood Cliffs, NJ). Smith, M.A.M., 1979, Intertemporal gains from trade, Journal of International Economics 9. 239-248. Stiglitz J.E., 1970, Factor price equalisation in a dynam;c economy. Journal of Political Economy 78,456488. Takayama, A., 1972. International trade (Holt, Rinehart and Winston, New York). Wood!aiid, AD., 19x0, The relationship between factor endowments and commodity trade, manuscript, University of British Cohrmbrd.