INTERMEDIATE GOODS, THE PRODUCTION POSSIBILITY CURVE, AND GAINS FROM TRADE * JAMES R. MELVIN

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1 INTERMEDIATE GOODS, THE PRODUCTION POSSIBILITY CURVE, AND GAINS FROM TRADE * JAMES R. MELVIN I. Introduction, 141. II. The production possibility curve, Intermediate goods and the gains from trade, 143. I. INTRODUCTION In a recent article McKinnon has considered the nature of the production possibility curve in the context of an intermediate good model which allows substitution in production.' This paper briefly considers some difficulties which may be encountered in defining the production possibility curve in such models for the case where there is a single primary input: one of the cases considered by McKinnon.2 The question of the gains from trade is then considered and it is shown that while the intermediate good model may allow larger gains than the model which ignores intermediate goods, a point made by McKinnon, we cannot be sure that everyone will share equally in such "extra" gains. In fact a country may be worse off when trade in intermediate goods is allowed than it would be if only final consumer goods were traded. II. THE PRODUCTION POSSIBILITY CURVE Production possibility curves of the kind used by McKinnon were first derived by Georgescu-Roegen,3 and in the simple twoproduct, single-fixed-factor case can be constructed by drawing the common tangent to the two total product curves as shown in Figure I. Each good is assumed to use labor and the output of the other industry as inputs and in Figure I fi. and 12 represent the total product curves for commodities 1 and 2 respectively. Both 11 and *The main points of this paper were made in a Ph.D. thesis submitted to the University of Minnesota in August I would like to thank Dr. John Chipman, my major advisor, for his many helpful comments. The thesis was also much improved by the comments of Professors Richter and Sonnenschein, my two thesis readers. 1. Ronald I. McKinnon, "Intermediate Products and Differential Tariffs: A Generalization of Lerner's Symmetry Theorem," this Journal, LXXX (Nov. 1966). 2. Ibid., pp Nicholas Georgescu-Roegen, "Leontiers System in the Light of Recent Results," Review of Economics and Statistics, XXXII (Aug. 1950).

2 142 QUARTERLY JOURNAL OF ECONOMICS 12 assume the use of the total available labor supply, and consequently all possible production points must be convex combinations of points on 1 1 and 12. In Figure I inputs are measured in a X2 x21 f, FIGURE I negative direction and output in a positive direction. If we assume that 12 and h. reach maxima at A and B respectively, then ABCDEF is the production possibility curve. In autarky only the segment CD is possible since all other points imply imports of one of the goods for use in production. This kind of production possibility curve is presented by McKinnon in his Figure Before proceeding to the discussion of the gains from trade it seems worthwhile pointing out some difficulties which may arise in the present model. First, an examination of Figure I makes it clear that, like the Leontief model, it may be that no output is possible. We can imagine rotating h. clockwise and 1 2 counterclockwise around the origin until BE passes through the origin, in which case positive net output of both goods is impossible. Another kind 4. McKinnon, op. cit., p Note that McKinnon's argument that the total product curves will approach (finite) horizontal and vertical asymptotes if the production functions are Cobb-Douglas, is incorrect. While it is true that the slope of the total product curve approaches zero as the quantity of the intermediate good approaches infinity, output also approaches infinity. In other words, the output of either good, taken individually, is not bounded from above.

3 THE PRODUCTION POSSIBILITY CURVE 143 of difficulty may arise if the total product curves of Figure I become asymptotic to lines which have positive slopes. In such cases, if the product of the slopes of the asymptotes is greater than unity, then infinite amounts of both goods are possible. Here the closed economy production set is not bounded from above. 5 Throughout the remainder of our analysis we shall assume that neither of these cases occurs. III. INTERMEDIATE GOODS AND THE GAINS FROM TRADE We now want to extend our analysis to include the possibility of international trade. Again we assume that there are only two countries and that in autarky both produce positive amounts of the same two goods. Since we want to retain the assumption of a single fixed factor we must assume that production functions differ between countries, for if they do not the two production possibility curves would have the same slope, and trade could never be profitable to either country. We want to examine how taking explicit account of the possibility of trade in intermediate goods will affect the gains from trade. To do so we will consider two worlds. In one we will assume that intermediate goods are used in production and that they can be traded. The production possibility curves will be similar to the one shown in Figure I. In the other world we will assume that intermediate goods cannot be traded, or in other words, that production cannot take place outside the positive quadrant. To be able to compare these two worlds we assume that the closed-economy production sets are identical for both. Our approach will be to construct Edgeworth production boxes in the manner first employed by Matthews, 7 and then to compare the total world consumption sets for the two situations. While it is easily established that total 5. For a further discussion of these and related problems see Nicholas Georgescu-Roegen, Analytical Economics: Issues and Problems (Cambridge: Harvard University Press, 1966), Chap. 9, James R. Melvin, "The Production Set When Labour Is Indispensable," International Economic Review (forthcoming), and "Intermediate Goods in Production Theory: The Differentiable Case," Review of Economic Studies, XXXVI (Jan. 1969). 6. Thus we are assuming that only final consumer goods can be traded. This assumption is admittedly a bit forced when we consider that our two goods serve as both final consumer goods and intermediate goods. 7. R. C. 0. Matthews, "Reciprocal Demand and Increasing Returns," Review of Economic Studies, XVII ( ). For more recent use of this technique see Peter B. Kenen, International Economics (Foundations of Modern Economic Series; Englewood Cliffs, N.J.: Prentice-Hall, 1964), p. 12, W. P. Travis, The Theory of Trade and Protection (Cambridge: Harvard University Press, 1964), pp. 117 and 146.

4 144 QUARTERLY JOURNAL OF ECONOMICS world consumption can be greater when trade in intermediate goods is allowed, it is by no means clear that both countries will share in this extra consumption. In Figure II CDO is the production possibility set for country 1 and C'D'O' is the production possibility set for country 2, for the case where there is no trade in intermediate goods. If we assume that in equilibrium the first country specializes in the first commodity XI v X 2 AS D' 0` 0 FIGURE II so that it produces at D, and that the second country specializes in the second commodity so that it produces at C', then the box with corners 0 and 0' represents the total world production box. The consumption of this output will be allocated between the two countries by demand conditions, and the consumption point could be anywhere in the area bounded by SD'DC. For definiteness we will assume that TD represents the world terms of trade and that T is the world consumption point. Before proceeding we want to stress two points. First, our assumption that both countries will specialize is really just an assumption about demand conditions. The production configuration assumed in Figure II is just one of an infinite number of possibilities, although it is the only one consistent with a world price ratio line which lies strictly between the slope of the two production possibility curves. That is, 0' is the only world production point consistent with gains from trade for both countries. Second, even if both countries specialize it is not necessary that both countries gain from trade, for the world consumption point could lie on CD or on C'D'. All that we are claiming, then, is that the situation depicted in Figure II is possible..

5 THE PRODUCTION POSSIBILITY CURVE 145 Figure III illustrates a possible situation for the case where intermediate goods can be traded. For convenience we have assumed that the total product curves reach maxima at A and F in 01" x2 FIGURE III country 1 and at A' and F' in country and are thus the lower bounds of the sets of efficient production points for countries 1 and 2 respectively. The production point is G, where the two transformation surfaces are tangent, and the consumption point is assumed to be W, where the line WG is the common tangent to the two transformation curves at G. Again, the actual positions of G and W will depend on demand conditions, and we are only suggesting that the situation shown in Figure III is possible. Notice that the production point G is consistent with only one commodity price ratio and that in order to change this price ratio we must change the relative positions of the two production possibility curves, i.e., we must slide one of them along the other.8 We also observe that if the equilibrium price ratio lies strictly between the slopes of the linear portions of the production possibility curves, both countries will specialize and they must therefore import their X A' 8. If the reader likes to think in terms of community indifference curves, then the situation in Figure III is an equilibrium if and only if at W there is a community indifference curve from both countries tangent to the price ratio line WG. Thus the rate of product transformation, the rate of commodity substitution and the output-price ratio are equal and are the same for both countries, and trade is balanced.

6 146 QUARTERLY JOURNAL OF ECONOMICS entire requirement of the intermediate products. Both countries therefore produce outside the positive quadrant. We now want to construct the world consumption possibility sets for the two situations represented in Figures II and III. For Figure II this is done by sliding the point C' up the line CD until C and C' are coincident, and then sliding D'C' in the other direction keeping it always in contact with the point D. 9 This construction is indicated in Figure IV where the world consumption set is MO'N, and is traced out by 0' as the production set for country 2 is moved to all possible positions of contact with the production set of country 1. To construct the world consumption set for the intermediate good case we consider Figure III and proceed in exactly the same way.' The production set for country 2 is slid along that of country FIGURE IV 1 (i.e., the tangency between the two sets is maintained) and 0' traces out the consumption possibility set. We have a further constraint in this case, however, for we are interested only in feasible 9. For the case of no trade in intermediate goods this method of construction is exactly equivalent to that first used by Abba P. Lerner "The Diagrammatical Representation of Cost Conditions in International Trade," Economica, XII (Aug. 1932). For a more recent use of this technique see John S. Chipman, "A Survey of the Theory of International Trade: Part 1, The Classical Theory," Econometrica, XXXIII (July 1965). For the case of intermediate goods our method seems more satisfactory, at least from an expositional point of view. 1. World consumption (or production) sets similar to the ones we will construct here have been constructed by Lionel W. McKenzie, "Specialization and Efficiency in World Production," Review of Economic Studies, XXI (June 1954), P While McKenzie considers intermediate goods, his models do not allow for substitution in production,

7 THE PRODUCTION POSSIBILITY CURVE 147 consumption points and thus the intersection of the positive quadrants for the two countries must always be nonempty. Thus we can slide the production surface for country 2 to the left only to the point where the X2 axes are coincident. At this point both countries will consume only commodity 2. It is interesting to observe that at this point even though both countries consume the same single good, trade takes place and country 2 gains from trade. In a similar way, the limit moving in the other direction occurs when the X1 axes for the two countries are coincident. Here only the first commodity is consumed, and in this case country 1 gains from trade. The locus of all such consumption points is shown in Figure IV as M'QRN'. It is clear that this consumption set strictly contains the consumption set of MO'N, for from the argument of the last paragraph M' is larger than M, N' is larger than N, and the slopes of M'Q and MO' are equal as are the slopes of RN' and O'N. Thus for any price ratio, world consumption can be greater in the intermediate-good case than in the case where there is no trade in intermediate goods. This result, that the world consumption (or production) set is larger when trade in intermediate goods is allowed, is not new but has been noted by Reiter 2 and McKenzie 3 and more recently has been discussed by Chipman 4 and McKinnon.' What we want to establish now is that even though the world consumption set is larger in the intermediate-good case, we cannot be sure that both countries will gain. In Figure V we have changed the production function for the first commodity in country 1, but have left all other production functions the same as in Figure III. We have altered fi in country 1 in a special way so that the closed-economy production possibility sets for both countries are the same as they are in Figures II and III (with a change of scale). We can now construct the world consumption set in the same way as we did previously by sliding the production set for the second country along the production set of the first, making sure that the consumption box, the box with corners 0 and 0', always has a nonempty interior. In Figure V consumption of commodity 1 disappears when G coincides with G", and consumption of commodity 2 disappears when G coincides 2. Stanley Reiter, "Trade Barriers in Activity Analysis," Review of Economic Studies, XX (June 1953). 3. McKenzie, op. cit., pp Chipman, op. cit., pp McKinnon, op. cit., pp

8 148 QUARTERLY JOURNAL OF ECONOMICS FIGURE V with G'. Then since G' and G" both lie on the straight line segment BE, it is clear that the only price ratio consistent with efficient world production is the price ratio equal to the slope of BE. The world price ratio is therefore unique and is independent of demand conditions. It is also clear that since consumption for both countries must take place at some point on the world price ratio, country 1 cannot possibly gain from trade. The world consumption possibility curve corresponding to Figure V is shown in Figure IV as the straight line M'QN" and clearly for some demand assumptions more of both commodities can be consumed than is possible for the consumption set corresponding to Figure III, and for all demand conditions at least as much of both goods can be consumed. Thus while in Figures II and III gains from trade are possible for both countries, this is not true in Figure V even though for Figure V the world consumption set is larger than in either of the other two cases. It is clear from Figure V that there does not exist a possible production point in which both countries specialize. Several interesting observations can be made about the case depicted in Figure V. First, if a country were to find itself in the 6. Chipman, op. cit., pp has considered a situation similar to that of Figure V. He does not consider the case where substitution in production is possible, but he does construct an example where the equilibrium world price ratio is unique regardless of demand conditions.

9 THE PRODUCTION POSSIBILITY CURVE 149 situation of country 1 (the country whose production possibility curve is ABEF), it should, from a selfish point of view, attempt to restrict trade in the amount of commodity 2 which is used as an input, for by so doing it may receive some of the benefits from trade. In any case restricted trade can be no worse than free trade, and even if country 2 follows suit and similarly restricts trade in intermediate goods so that the situation becomes the one shown in Figure II, there are many sets of demand conditions for which country 1 will gain relative to the situation of Figure V.7 Thus a prohibitive tariff on commodity 2 for use as an input will be a perfectly rational policy for country 1, and it may thus appear that we have discovered another valid tariff argument. However, careful scrutiny of this case reveals that it is just a variant of the optimum tariff argument, or in more general terms, a variant of the argument that tariffs can be used to improve the terms of trade. Nevertheless it does seem important to recognize the very strong influence that trade in intermediate goods may have on the equilibrium terms of trade. It is clear, for example, that the optimum tariff may be quite different depending on whether or not trade in intermediate goods is allowed. The situation of Figure V also relates to the question of the relation between gains from trade and the size of the two economies. This question was first treated by Mill, extensively discussed by Graham, and has recently been treated by Chipman.8 The main argument of the analysis can be summarized as follows. If the two countries possess production sets of the kind shown in Figure II, and if both countries have utility functions of the form U X1X21 then both countries will gain from trade if and only if each has an absolute advantage in the production of one of the goods, in the sense that each country can produce absolutely more of one of the commodities than can the other. In Figure II, for example, this condition is satisfied since OD > O'D' and O'C' > OC, and thus both countries will gain from trade. Figure V, however, indicates that this result requires substantial modification when trade in intermediate goods is taken into account. In Figure V, in autarky country 1 can produce more of commodity 1 than can country 2, and country 2 can produce more of commodity 2 than country 1 and 7. We are ignoring the possibility of bribes in our discussion. We should also observe that the fact that country 1 has restricted imports of the intermediate good does not necessarily imply that country 2 should do likewise, although there is a large class of cases in which it should. 8. See Chipman, op. cit., pp for a discussion of this question and for references.

10 150 QUARTERLY JOURNAL OF ECONOMICS yet we have just established that here only country 2 can gain from trade regardless of what demand conditions we assume. The Mill-Chipman result also establishes that if one country is absolutely larger than the other, in the sense that one country could produce more of either good than the other, 9 then with the same demand assumptions as above the larger country will not gain from trade. In Figure V by redrawing the diagram so the 0 is closer to G" (which does not change our former conclusions in any essential way) we can make country 1 smaller than country 2 in the autarkyproduction sense, and we have a case in which only the larger country gains from trade regardless of demand conditions. We should also note that although Figure V makes it appear that in the sense of potential output of commodity 1, country 1 is larger than country 2, this is a result of the particular diagram we have drawn and is not a general conclusion. For example the straight line portion of the production possibility curve for country 2 can be extended any amount in the direction of E' without changing the analysis, and by so doing we can make country 2 larger in the sense of potential output of both goods. Of course, we do not mean to imply that no general statement can be made about which country will gain from trade even when specific demand conditions are assumed; we are only suggesting that the introduction of intermediate goods substantially complicates the situation, and that conclusions derived in the no-intermediate-good case cannot be expected to apply without modification. The change we made in the assumptions about the production function 1 1 in country 1 which allowed us to derive Figure V resulted in some fundamental changes in our conclusions, and it is thus of some interest to see just what this change means from an economic point of view. First, the production point E of Figure V represents a technology which has a smaller value added per unit of output than that represented by E in Figure III, although the total return to labor is the same in the two diagrams.' Thus the 9. In other words, if both countries were drawn from the same origin, if the production possibility set of one lies strictly within the production possibility set of the other, then the second country is absolutely larger. 1. To establish this claim we recall that BE (which is the equilibrium price ratio) is tangent to 11 at E and the slope of BE is the marginal product of the intermediate input. This marginal product multiplied by the total quantity of the intermediate input gives us the share of output of the intermediate input, and this is just the distance from C to the Xi component of E. Thus labor's share is the remainder OD, and this is the same in Figures III and V which establishes that the return to labor is the same in the two diagrams. Since the total quantity of labor is the same in Figures III and V, and since total gross output is larger in V, then with constant returns to scale, value added per unit of output is smaller in Figure V.

11 THE PRODUCTION POSSIBILITY CURVE 151 technological change which takes place in moving from Figure III to Figure V can be said to be labor-saving but intermediate-goodusing. We should also observe that while at first sight the assumption made about 12 in country 1 in Figure V might appear to be extreme, even in this case value added (by labor) per unit of output is in excess of.3 in this industry, and this is certainly not an unreasonable number. We leave it to the reader to draw conclusions about which kinds of countries might be expected to be like country 1 and which like country 2. While our analysis has concentrated on showing that the introduction of trade in intermediate goods cannot be assumed to be beneficial to both countries even though it will increase the size of the world consumption set, it should be noted that the converse of this argument is also true. In other words, a situation which results in a gain for only one country when there is trade in consumption goods only, may very well result in gains for both countries when trade in intermediate goods is allowed. Finally, the introduction of intermediate goods in production requires a redefinition of what we mean by specialization. For example, if Figure II represents a situation in which intermediate goods are used in production, but where trade is allowed only in final consumer goods, then Figure II does not represent a case where both countries specialize and in fact in this situation both countries produce positive amounts of both goods. If we then allow trade in intermediate products, one or both countries will specialize, but, of course, without knowing the underlying technology there can be no presumption as to what the final pattern of specialization will be. This conclusion will be of importance if we are interested in inferring what the final world equilibrium position will be from observations of an autarky or tariff-ridden world. If trade in intermediate products exists, we will need considerably more information than we would if only consumer goods were traded. UNIVERSITY OF WESTERN ONTARIO