Foreign Trade

Abstract

The pure theory of trade constitutes, in principle, no more than an application of the general theory of value, distribution and resource allocation. It follows at once, of course, both that each possible approach to general economic theory has its corresponding theory of trade and that any changes or developments in general theory must have implications for the theory of international trade. In particular, this is true of certain debates over value, distribution and capital goods which flourished in the 1960s, following the publication of Piero Sraffa’s Production of Commodities by Means of Commodities (1960).

The pure theory of trade constitutes, in principle, no more than an application of the general theory of value, distribution and resource allocation. It follows at once, of course, both that each possible approach to general economic theory has its corresponding theory of trade and that any changes or developments in general theory must have implications for the theory of international trade. In particular, this is true of certain debates over value, distribution and capital goods which flourished in the 1960s, following the publication of Piero Sraffa’s Production of Commodities by Means of Commodities (1960).

It need hardly be said that capital goods – that is, produced inputs, whether they be long-lived or short-lived – are of the very greatest importance in all modern economies. And it is no less true that international trade flows, far from consisting solely of consumption commodities, contain a large and growing volume of producer goods. International trade statistics are not conveniently classified into ‘finished consumer goods’ and ‘other goods’ but it appears from the classifications that are available that finished consumer goods probably account for less than some 30 per cent of the value of world trade. Any adequate theory of trade and resource allocation must, then, be able to deal, in a clear and coherent manner, with the important role of produced inputs and it is therefore to be expected that produced inputs would feature prominently in trade theory and that ‘capital theory’, broadly interpreted, should have significant implications for trade theory. But in fact, when we turn to basic trade theory, we find that capital goods are noticeable only by their absence, all the attention being centred on final consumption commodities.

With respect to capital theory, it is now well known that, in a competitive, constant-\returns-to-scale economy using produced inputs (a) relative prices depend on the rate of interest, even for a given technique; (b) capital-intensity depends on the rate of interest, even for a given technique; (c) the choice of technique need not be monotonically related to the rate of interest; and (d) capital-intensity, in a multi-technique economy, need not be inversely related to the rate of interest. (See, for example, the QJE Symposium 1966; Pasinetti 1977.) Also well-known are the results that, in an economy experiencing steady growth, there is a ‘consumption-growth rate’ trade-off which is identical to the ‘wage-profit rate’ frontier and that only if the growth rate equals the profit rate – the so-called Golden Rule case – is it ensured that the competitive choice of technique will be optimal with respect to the consumption/growth trade-off.

Suppose now that production is carried out using inputs of homogeneous land, as well as homogeneous labour, and produced inputs. Let there be a given, positive rate of interest on the value of capital (the produced inputs); it is then no longer the case that a rising rent/wage ratio must necessarily be associated with a falling land/labour ratio; quite the opposite relationship may hold (Metcalfe and Steedman 1972; Montet 1979). It follows that, in the presence of a positive rate of interest, an increase in the relative price of the more land-intensive commodity may be associated with a decrease in the output of that commodity (and an increase in the output of the labour-intensive commodity). In other words, there may be a ‘perverse’ supply response.

In brief, then, capital theory discussions have alerted us (or realerted us, for Wicksell (1901) was well aware of some of these complications) to the distribution-relative nature of relative commodity prices, to the fact that capital-intensity depends on distribution as well as on technical conditions, to the possibility that both capital-intensities and land-labour ratios may respond in ‘unexpected’ ways to changes in interest, wage and rent rates, to the fact that supply responses can differ from those traditionally supposed and to the possibility that competitive technique choice need not be optimal with respect to the consumption-growth rate trade-off. We now turn to the implications of these findings for the pure theory of trade.

‘Textbook’ Ricardian Theory

The reader will be thoroughly familiar with the textbook version of Ricardian trade theory, in which wages are the only kind of income, labour is homogeneous and – as a result of these two assumptions – the autarky price ratios in an economy are exactly proportional to the quantities of labour required to produce the various commodities. Yet when we turn to Ricardo’s famous Chapter VII, ‘On Foreign Trade’ (1817), we see at once that Ricardo supposes there to be a positive rate of profit and, indeed, shows how the opening of trade can increase that rate. To this extent, then, ‘textbook’ Ricardian trade theory is a travesty of Ricardo’s theory. Any attempt to excuse this vulgarization of Ricardo would probably appeal to the fact – and it is a fact – that in his Chapter VII Ricardo, whilst acknowledging the presence of both wages and profits, took no account of the influence of distribution on autarky relative prices; he simply identified these latter with relative labour quantities. Yet a large part of Ricardo’s Chapter I, ‘On Value’, is concerned precisely with the fact that, as was noted above, relative commodity prices depend on distribution and not on technical conditions of production alone. The apparent inconsistency is explained by Ricardo’s readiness to assume that relative labour costs provide a ‘good enough approximation’ to relative prices, even though he fully acknowledged that prices really depend on distribution. This explanation, though, is not a justification of Ricardo’s procedure in Chapter VII, for he gave quite inadequate grounds for his claim about the ‘good enough approximation’. It follows that we should examine carefully what happens to Ricardo’s propositions concerning foreign trade when full recognition is given to the distribution-relative nature of autarky prices.

Consider then a two-country, two-consumption commodity model in which, in each country, the autarky price ratio of the two consumption commodities depends on the ruling (r, w) under autarky. Such a dependence could arise from the use of (nontradeable) machines in making the consumption commodities; or from the fact that the consumption commodities are also capital goods, being used in the production of one another; or from the fact that wages are paid in advance and that the production period over which they have to be advanced differs as between the two consumption commodities. There are many different models which capture the dependence of relative prices on (r, w), all of them providing examples of what Samuelson (1975) has called ‘time-phased Ricardian systems’. Now if, in either economy, the autarky rate of interest should happen to be zero, the autarky price ratio of the two consumption commodities will indeed equal the ratio of their total (direct and indirect) labour costs. This must be true when the only form of income payment is that of wages paid to homogeneous labour. But if, as will generally be the case, the autarky interest rate is not zero and fluke technical conditions do not obtain, that autarky price ratio will not equal the corresponding labour cost ratio.

Let free trade be opened between our two economies. Will the direction of trade be determined by a comparison of the two countries’ autarky price ratios or by a comparison of their labour cost ratios? By the former, of course, since competition works via wages, interest rates and prices. Each country will export that commodity for which it has the lower relative autarky price. It may or may not export that commodity for which it has the lower relative labour cost and certainly the pattern of trade is not determined by technical conditions alone but depends also on the autarky (r, w) in each country, simply because autarky relative prices so depend. Notice the corollary that two economies with the same technical conditions, for producing commodities by means of homogeneous labour and produced commodities, could enter into free trade if their autarky (r, w) would be different. It is not the case that ‘Ricardian’ trade models must necessarily suppose different technical conditions in each country – even if it is the case both that Ricardo did make such an assumption and that it is eminently sensible to do so.

Consider now a single, small economy of the kind considered above, which faces given terms of trade for trade in the two consumption commodities. Its pattern of trade will depend on how the given terms of trade compare with its autarky price ratio. But whether its fully-specialized, free trade consumption bundle lies outside its autarky consumption-possibility-frontier will depend on that pattern of trade and on how the terms of trade compare with the economy’s labour cost ratio. Since this latter ratio is not equal, in general, to the autarky price ratio, it is not ensured that the with-trade bundle will lie outside the autarky frontier. Consider Fig. 1, in which c₁ and c₂ are quantities of the first and second consumption commodities per unit of employment. C₂C₁ is the autarky consumption-possibility-frontier, whose absolute slope is of course equal to the labour cost ratio for the two consumption commodities. P₂P₁ is a line whose absolute slope is equal to the economy’s autarky price ratio and T₂T₁ a line with slope equal to the given terms of trade. Since T₂T₁ is less steep than P₂P₁ the economy will be driven to specialize in commodity 2 – but, since T₂T₁ is steeper than C₂C₁, the economy’s free trade consumption bundle, T, which must of course lie on T₂T₁, will be below the autarky frontier C₂C₁ (unless at C₂ itself). It will be clear that this result would not obtain if T₂T₁ were either steeper than P₂P₁ (with specialization at C₁) or less steep than C₂C₁ (with specialization at C₂). But the fact remains that Ricardo was able to be ‘sure’ about the gain from trade only because he illegitimately supposed C₂C₁ and P₂P₁ to have the same slope. This argument can be extended to a steadily growing economy, to show that in the ‘Golden Rule’ case the with-trade bundle must lie outside the achievable autarky frontier but that if the growth-rate is less than the profit-rate then it may or may not do so (as in Fig. 1, which provides simply a special case of this result, with a growth-rate of zero). Since the adoption of a particular specialization can, from a formal point of view, be thought of as a particular choice of technique, the present argument is just an application, to the trade context, of the capital theory result concerning competitive choice of technique and its possible non-optimality in terms of consumption and growth. It is important to notice that this result, concerning the possible (not certain) ‘loss from trade’, belongs to the class of ‘comparative dynamics’ results; it is best thought of as providing a comparison between a small closed economy and an (otherwise identical) small open economy. It is not a result about the effects on a given economy of the process of opening up to trade, full account being taken of what happens during the transition from the autarky state to the free trading state. But the same is true, it must be noted, of the textbook demonstrations of the gain from trade, in a ‘Ricardian’ framework, with which the reader is familiar.

Foreign Trade, Fig. 1

While ‘factor price equalization’ is most often discussed within the Heckscher–Ohlin–Samuelson (HOS) framework, it is of interest to consider whether free trade in all commodities will bring about real wage rate and interest rate equalization in the type of model considered here. If all the freely trading economies have the same available choice of techniques, in a constant-returns-to-scale and homogeneous labour world, then it is certainly true that, if they all have the same rate of interest, they will all have the same set of relative prices. But the converse does not hold, when there is a choice of techniques; all the economies could face the same set of relative commodity prices and yet have different interest rates and real wage rates. Hence free trade in all commodities does not entail wage and interest equalization, even when all the economies have the same technical possibilities and are incompletely specialized. (The same negative conclusion holds, even when there is no choice of technique, if there are non-traded commodities.)

(On the pattern of trade and the gain from trade see Mainwaring 1974; Samuelson 1975; Steedman and Metcalfe 1973a, 1979; Steedman 1979a. On interest rate (non-) equalization see Mainwaring 1976, 1978; Samuelson 1975; Steedman and Metcalfe 1973b.)

Land, Labour and a Positive Interest Rate

We now turn to the much-loved HOS model of international trade, in which two countries produce the same two commodities, using the same two primary inputs (which are in fixed supply) and having the same, constant-returns-to-scale technology. The primary inputs are qualitatively the same in both countries, fully mobile within each economy but completely immobile between them. There are no factor-intensity reversals, there is completely free trade and all consumers, in both countries, share a common homothetic preference map (so that consumption proportions depend only on the commodity price ratio, being quite independent of income distribution). If the two primary inputs are homogeneous land and homogeneous labour, and if there are no produced inputs (capital goods) of any kind, then the HOS theorem on the pattern of trade (in both its price and quantity forms), the factor price equalization theorem, the Stolper-Samuelson theorem and the Rybczynski theorem are all logically valid theorems.

Suppose now that, retaining all the other assumptions, we allow the two consumption commodities also to be capital goods, being necessary inputs to the various productive processes. What difference does this introduction of produced inputs make to the standard theorems? None whatever! It is now more appropriate to think of land/labour intensities in production in terms of total (direct and indirect) uses of land and labour but, since the intensity ranking of commodities in these total terms is necessarily the same as that in direct terms, this introduces no really significant difference from the model without produced inputs. Thus far then, produced inputs make no difference. But the position changes as soon as we allow not only for the presence of such produced inputs but also for a given, positive rate of interest on the value of those inputs (circulating capital goods). The presence of a positive interest rate does not alter the fact that the relative price of the land-intensive commodity will be a monotonically increasing function of the rent/wage ratio. But, as was pointed out above, it does mean that an increase in the rent/wage ratio is not necessarily associated with a fall in the land/labour ratio; it then follows that, if land and labour are always fully employed, an increase in the relative price of the land-intensive commodity may be associated with a fall in its net output. In Fig. 2, which relates to a single economy, y_i is the net product of i,p_i is the price of i, SS is the full employment ‘relative supply curve’ and DD is the ‘relative demand curve’ derived from the common homothetic preference map; the figure illustrates the case of a ‘perverse’ supply response. It will be seen at once that such a supply response immediately gives rise to the possibility of multiple equilibria, the ‘first’ and ‘third’ equilibria both being stable.

Foreign Trade, Fig. 2

Let two economies, A and B, have the same positive rate of interest; let A be relatively better endowed with land and let commodity 1 be the land-intensive commodity. Figure 3 extends Fig. 2 to this case, SⁱSⁱ being the full employment relative supply curve for economy i. Suppose that point A represents A’s autarky equilibrium, while point B represents B’s. At every (p₁/p₂) lying between the autarky price ratios, S^AS^A and S^BS^B both lie on the same side of DD; hence no such price ratio can be an equilibrium terms of trade. The terms of trade lie outside the autarky price range. Whether the international equilibrium is found to the left of B or to the right of A, economy A (which is well endowed with land) will be exporting commodity 1 (which is the land-intensive commodity). Thus the HOS quantity theorem holds good. Yet the HOS price theorem, which is sometimes thought rather trivial, as actually false here. Since A has the higher autarky (p₁pp₂), it has the higher autarky rent/wage ratio, so that A is exporting the commodity which uses intensively A’s relatively expensive factor under autarky. Notice also that if international equilibrium is found to the left of B, (p₁/p₂) will have fallen, with trade, in economy A and thus the wage/rent ratio will have risen; in fact trade will have benefited A’s relatively scarce factor (labour), contrary to the usual HOS prediction.

Foreign Trade, Fig. 3

If A and B have the same positive interest rate, as above, they have the same relationship between (p₁/p₂) and the rent/wage ratio; it is thus not surprising that free trade will equalize rents and wages (with incomplete specialization) and that the Stolper–Samuelson theorem also holds good. If A and B have different positive interest rates, however, almost everything collapses. The exception is the Rybczynski theorem and it is important to understand why. All ‘capital theoretic’ problems for HOS theory reduce in the end to the fact that relative commodity prices vary with the rate of interest – but relative prices are fixed by assumption in the Rybczynski theorem, so that that theorem must be immune to such problems.

Consider now a single, small economy of the kind discussed immediately above. In the presence of a positive interest rate, the price ratio at which a switch of techniques takes place will not be equal, in general, to the physical rate of transformation between the two net outputs. It follows that, when we compare the small open economy with an otherwise identical autarkic economy, we find that the value of consumption in the small open economy, at the given international prices, may be either greater than or less than the corresponding value in the autarkic economy. The ‘comparative static’ gain from trade may be either positive or negative.

In the land and labour model, then, the presence of produced inputs makes no difference per se. But a positive rate of interest on their value does make a difference to some (but not all) HOS theorems, if it is the same in both countries, while a difference in interest rates undermines all the standard HOS results, other than the Rybczynski theorem. For the single, small, open economy the presence of a positive interest rate means that the ‘comparative’ gain from trade can be positive or negative.

(For the closed economy background see Metcalfe and Steedman 1972; Montet 1979; for the trade theory applications Samuelson 1975; Steedman and Metcalfe 1977; for the gain from trade Metcalfe and Steedman 1974; Samuelson 1975.)

Labour and Capital

In the typical textbook presentation of HOS theory the two ‘factors’ in given supply are not labour and land, as above, but labour and ‘capital’. (Although Samuelson (1948, 1949) was careful to stipulate labour and land.) Yet that typical presentation suggests no immediate connection between the two produced commodities and the physical composition of the capital stock, despite the fact that ‘capital goods’ are, by definition, produced means of production! Indeed, one interpretation of most textbook theory is that ‘capital’ is simply a misnomer for land, the problems of capital theory being evaded by a simple misuse of terms. Alternatively (and more favourably), the ‘given capital supply’ can be interpreted to mean that the total value of capital goods must always be equal to – or, at least, not greater than – an exogenously given value. An immediate difficulty with this interpretation is that, since relative autarky prices differ between the two economies, the very ranking of the two countries’ capital/labour endowments ratios may depend on which standard of value is used to measure capital. And what does it mean economically to suppose that total capital value is given in terms of one standard and yet, necessarily, is not given in terms of all other possible standards (since relative commodity prices are to be determined endogenously)? Even if we ignore these questions – which there is no justification for doing – we know from capital theory that value capital/labour ratios need not be related inversely or, indeed, even monotonically to the rate of interest. This, of course, immediately suggests that some of the HOS theorems may be at risk. Moreover, it can be shown that in a model with many produced inputs, the price ratio between any two particular commodities need not be monotonically related to the rate of interest, even when one of the two commodities is always more value capital-intensive than the other. But if neither the capital/labour ratios nor the relative commodity prices need be monotonically related to the rate of interest – even in the absence of factor-intensity reversals – then it will at once be clear that HOS theorems (other than the Rybczynski theorem) cannot be logically valid when one of the two factors is a ‘given value of capital’. This stems fundamentally from the simple fact that Wicksell clearly stated many years ago:

Whereas labour and land are measured each in terms of its own technical unit … capital … is reckoned, in common parlance, as a sum of exchange value – whether in money or as an average of products. In other words, each particular capital-good is measured by a unit extraneous to itself. [This] is a theoretical anomaly which disturbs the correspondence which would otherwise exist between all the factors of production. ([1901] 1967, p. 149)

To illustrate the above negative conclusions, we may use an example in which there are two consumption commodities (two kinds of ‘corn’), each producible by means of many alternative types of machine. The consumption commodities are tradeable but the machines are not. Full numerical details of this example can be found in Metcalfe and Steedman (1973); here we confine ourselves to the diagrammatic presentation of Fig. 4, in which k_i is the value capital/labour ratio involved, directly and indirectly, in the production of the ith consumption commodity, expressed in terms of the first consumption commodity. It will be seen on the right of Fig. 4 that neither k₁ nor k₂ is monotonically related to r but that k₁ > k₂ at all r; on the left we see that, the absence of factor-intensity reversal notwithstanding, the price ratio (p₁/p₂) is not monotonically related to r. It follows at once that the ‘factor price’ equalization theorem, the Stolper-Samuelson theorem and the price form of the HOS theorem on the pattern of trade are not of general logical validity. But if the pattern of trade theorem is not valid in its price form then it will not be valid in its quantity form either, even if it is the case (which it may not be) that the economy with the higher capital/labour endowment ratio has the lower autarky interest rate.

Foreign Trade, Fig. 4

When produced inputs are introduced into HOS theory in the form that one of the two ‘factors’ is taken to be a given total value of capital, that theory simply disintegrates. This is so notwithstanding the apparent denial of this negative conclusion by Ethier (1979), who states that ‘The central message … is simple. The four basic theorems of the modern theory of international trade … are insensitive to the nature of capital’ (p. 236). In fact Ethier’s paper constitutes a striking confirmation of our negative conclusion, because in order to maintain the appearance that capital has no influence on HOS trade theorems, Ethier finds himself compelled to replace the familiar theorems, which predict trade outcomes on the basis of exogenous data, by entirely different theorems, which merely describe trade outcomes in terms of trade equilibrium prices, etc.

(For the example used in this section, see Metcalfe and Steedman 1973; on Ethier’s conjuring with HOS theorems, see Metcalfe and Steedman 1981.)

Growth, International Investment and Transitions

To focus on the role of capital goods in trade and in trade theory is, implicitly, to direct attention also to such matters as growth (capital accumulation), international investment and transitions between steady growth paths. Since the typical trading economy uses many produced inputs – some traded and some not – accumulates capital goods and experiences (often embodied) technical change, along both quantitative and qualitative dimensions, the ideal theory of trade would be able to handle all these closely related issues, in a manner which was both informative and simple. Needless to say, such an ideal theory is not available; international trade theory in these respects can, in the long run, be no more advanced than the general theory of accumulation and technical progress. The preceding discussion can, however, serve to warn us that growth models in which there is a single, physical capital good can almost certainly not be readily generalized to the many capital good case and are thus of very limited interest. It is also useful to note, as a simple matter of fact, that while the number of countries in the world is of the order of 200, the number of distinct commodities – when defined at the level of detail relevant to careful value theory – runs into millions. This both tells us that incomplete specialization must be the rule and directs our attention to economic growth models in which the number of commodities can be arbitrarily large; the von Neumann model perhaps deserves to be used more extensively by trade theorists than it has been, its very abstract nature notwithstanding.

When thinking of capital accumulation, the international economist will naturally pay considerable attention to the role of international investment. Here it is most important to recognize that, although they are often connected in practice, there is a perfectly clear – indeed a sharp – distinction between international investment as a flow of finance, on the one hand, and trade in physical capital goods, on the other. This is obvious enough perhaps when stated explicitly but it is to be noted that the idea of a ‘factor’ capital, conceived of as a sum of value, in fact makes it dangerously easy to confuse financial flows with capital goods flows. The trade theorist would do well to avoid the concept of a ‘quantity of capital’ altogether, referring only to stocks and flows of specified capital goods, on the one hand, and to international flows of finance, on the other. Such a practice would not only make it easier to avoid capital theory traps but would also facilitate thought about the badly needed integration of pure trade theory with international monetary economics.

We turn now to the question of ‘transitions’. Consider first a closed economy whose homogeneous land and homogeneous labour are allocated between strawberry production and raspberry production. No produced inputs are used – not even strawberry and raspberry plants! (Which reminds us, incidentally, of just how strained is any picture of direct production of consumption commodities by primary inputs.) If free trade should suddenly become possible, at terms of trade different from the autarky price ratio, there is no difficulty at all in reallocating the land and labour to the newly desired output pattern. The ‘transition’ from the autarky steady-state to the with-trade steady-state is problem free and can be achieved instantaneously. By contrast, consider now the analogous ‘transition’ for an economy which does use produced inputs. Except by a complete fluke, the economy’s industries will use the various produced inputs in different proportions from one another and it will now not be possible to change to the free trade pattern of output instantaneously. Since the production of the produced inputs takes time, there will have to be a ‘transitional’ period, during which the physical composition of the economy’s aggregate capital stock is adjusted to the new output pattern. Just how long this period will be depends, of course, on how different the input requirements are as between industries, on whether or not some previously used capital goods simply have to be scrapped, on how many of the capital goods are tradeable and how many non-tradeable, etc. Changing the pattern of net output is a far more complicated process in an economy using produced inputs. This issue is avoided in textbook discussions of the gain from trade and in the ‘comparative dynamics’ results given above. Yet it can hardly be denied that the issue is important in many trade policy applications and in many day-to-day debates about trade protection, industries which are under increased international competitive pressure, and so on. It is therefore important that trade theorists should develop explicit analyses of transitional processes in the presence of produced inputs. At the same time, however, it would be quite wrong simply to dismiss ‘comparative dynamic’ results showing that a ‘loss from trade’ is possible, merely on the grounds that (by definition) they do not take account of transitions. The traditional comparisons of a world of autarky economies with a world of trading economies are designed to show that the with-trade state of the world (which we observe) is preferable to the autarky state (which is purely hypothetical). For the purpose of such an abstract, hypothetical comparison, the analysis of transitions would have no significance and it is indeed the purely ‘comparative’ analysis which is relevant. (There is, of course, no inconsistency in saying also that a transitional analysis is relevant for the study of an actual economy considering the possibility of, say, changing its tariff structure.)

(A trade theory application of the von Neumann model is given in Steedman 1979c, for a single, small economy; growth in a two country world is discussed by Parrinello 1979. On transitions see Metcalfe and Steedman 1974; Smith 1979.)

Conclusion

Sufficient reason has perhaps been given above to justify the rather general conclusion that when one finds trade theorists referring to ‘capital’ one should immediately be ‘on guard’. The presence of produced inputs, with a positive rate of interest on their value, does make a considerable difference to the logical coherence of HOS theory, as has been seen in some detail above. Moreover, ‘textbook’ Ricardian trade theory, which appears to make no reference to ‘capital’ at all, ought to make such reference and, if it did, would discover that here again the presence of a positive interest rate makes it far harder to reach any clear cut, logically valid theorems. In seeking to develop a trade theory which does give central importance to capital goods and hence to profits, accumulation and technical progress (e.g. Steedman 1979a) one must expect that simple results may not be abundant. And one must recognize that the assumptions which make growth theory relatively easy, such as constant returns to scale and the absence of land, themselves do violence to the complex realities of international trade. (Its many shortcomings notwithstanding, HOS theory is right to stress the importance of land and labour endowments, even while it is wrong to take them to be qualitatively homogeneous and fully employed.) The role of capital goods is by no means the only important issue in trade theory and recognition of that role certainly makes trade theory more difficult. But can these be good reasons for ignoring capital goods, when that theory is intended to aid our understanding of a world in which produced inputs are, in fact, centrally important?

See Also

• Heckscher–Ohlin Trade Theory

• International Trade