Abstract
In his 1939 article, Samuelson initiated the modern discussion of the gains from trade. Concerning himself with a small price-taking country and basing his cases on the compensation principle and the axiom of revealed preference, he established that the introduction of external trade could make all citizens better off. His approach received a considerable amount of notice, but no further result came of it for some time. It was not until two decades later that Kemp (1962), along with Samuelson (1962), revived the subject by showing, under a more general condition, that the consumption possibility frontier of the post-trade situation lies uniformly outside that of the pre-trade situation. Their findings, however, seem to call for further generalization.
This chapter is adapted from “Trade and Welfare in General Equilibrium,” Keio Economic Studies, Vol. 9, No.2, 37–73, 1972
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- 1.
Kemp is concerned with the welfare properties of tariff-restricted trade equilibria (including as a limiting case free trade equilibria), providing a proof of the proposition for a general n-commodity case. In a separate companion paper, Samuelson illustrates the same point by the help of the famous “Baldwin” envelope (see Baldwin 1952) for a special two-commodity case.
- 2.
We refer here to the crude usage of this measure disregarding the problem of income distribution. We shall have occasion to discuss it again in Footnote 14.
- 3.
Most of the existing literature in this field still remains within the confines of the views of “trade-as-exchange-of consumer goods.” In a famous survey of trade literature Bhagwati (1964, p. 42) warns that a vast range of interesting problems applicable to economies using intermediate and produced goods cannot get within the range of analysis until the theorists get away from the traditional picture of primary factors and integrated process of production. As he carefully notes, however, it does not follow that the present stock of knowledge will not survive the required change in the formulation of the models. On the contrary, we should make it clear in advance that our investigation will confirm all the traditional welfare propositions in the presence of trade in non-consumer commodities.
- 4.
The government’s lump-sum taxes and subsidies are exempt from the distortion of price system because they effectuate nothing but the direct redistribution of income sources such as commodity endowment, profits, and transfer receipt among individual consumers.
- 5.
- 6.
We will consider x, y, a, and e as column vectors, and p and q as row vectors in what follows.
- 7.
Thus, this model includes as a special case the classical setup in which primary factors, especially labor, are not tradeable.
- 8.
We assume that the unit of domestic currency is adjusted such that the exchange rate is always unity.
- 9.
Thus, if prices are given, a distribution V is a specification of the percentage share of individual consumers in the aggregate expenditure, and it can be represented by an interior point of the standard simplex.
- 10.
In particular, we have in mind an economy similar to the Arrow–Debreu model for the existence of competitive equilibria. See Debreu (1959) and Nikaido (1968, Chapter 5). McKenzie (1959) allows for negative equilibrium prices, the possibility of which we exclude by assumption in this chapter. The demonstration of an existence theorem is, however, outside the scope of the present analysis. The reader interested in this line of inquiry in the context of the present model is referred to Sontheimer (1971).
- 11.
It should be understood that some trade in labor is in no way at variance with the given set of consumers. At the present level of abstraction, we should be ready to account for the possibility that some kind of labor is traded internationally without affecting the set of consumers and the country’s endowment of leisure . For example, some laborers are able to offer their services for a foreign firm located inside the country.
- 12.
- 13.
See Samuelson (1956) and Negishi (1963). Chipman (1965) gives an extensive survey of the related literature. Consider a limiting case where there is an additive social utility function with every consumer possessing an identical, linear homogeneous utility function. Write the social utility as
$$ F\left({p}_c\right)={\displaystyle \sum_{k\in K}}u\left({x}^k\left({p}_c\right)\right) $$where u denotes the utility function common to all consumers and x k(p c ) the consumption vector chosen by the kth consumer at price p c . Because u is linear homogeneous, we obtain
$$ F\left({p}_c\right)=u\left(x\left({p}_c\right)\right)\ \mathrm{where}\ x\left({p}_c\right)={\displaystyle \sum_{k\in K}}{x}^k\left({p}_c\right). $$At each price, p c , u(p c ) is maximized over the set of the aggregate consumption vectors x such that \( {p}_cx\le {p}_cx\left({p}_c\right) \). In this case, we have a social indifference map regardless of the state of distribution. In fact, all distributions are deemed equally good. Thus, our welfare criterion degenerates to the crude convention of measuring social welfare in terms of per capita real income with no reference to distribution.
- 14.
For a discussion of the convex preference relationship, see, for example, Debreu (1959, pp. 59–61).
- 15.
Again, this should not be regarded as inconsistent with trade in primary factors.
- 16.
Note that if the price of an export (respectively import) commodity increases (respectively decreases) from situation S″ to situation S′, the term \( \left({q}^{\prime }-{q}^{{\prime\prime}}\right){e}^{\prime } \) will have to be, ceteris paribus, positive.
- 17.
By the same token, trade restricted by quotas is preferable to no trade . See Kemp (1964), p. 166.
- 18.
Both Kemp and Samuelson avoid the discussion of trade with subsidies.
- 19.
These two propositions correspond to the result of Kemp and Negishi (1970, theorems 3 and 4), which came to our notice after the completion of this study. They interpret conditions (4.19) and (4.20) rather narrowly assuming that the same tax subsidy scheme exists before and after trade. As is clear from the derivation of these conditions, this assumption is not necessary. We can freely identify situation S′ with any autarkic situation in regard to the domestic taxes and subsidies.
- 20.
- 21.
The price normalization is permissible when we assume away all taxes and subsidies.
- 22.
These assumptions are not at all novel in the literature on the pattern of trade . They reflect the doctrine of comparative advantage that a country’s pattern of trade is determined by its autarkic cost structure vis-a-vis the external cost structure. As Inada (1967) demonstrates , however, the possibility of locally unique multiple equilibria undermines their intuitive plausibility.
- 23.
- 24.
Jones (1967) presents a synthesis of the two cases in a capital-mobile, Heckscher–Ohlin model.
- 25.
Provided, of course, that there is a non-empty set of domestic tax subsidy schemes preferable to free trade, not to mention the autarkic state.
- 26.
Bhagwati (1971) gives a detailed taxonomic account of some of such policies.
- 27.
Perhaps for the purpose of reparation payment or economic aid to the rest of the world.
- 28.
Dixit considers this problem in the context of a closed economy on the assumption that all supply prices are constant and that there is a positive net transfer of purchasing power to consumers from somewhere resembling manna from the heaven. For a closed economy in which we have no terms of trade effect to worry about, Dixit’s restrictive assumption is in fact unessential to the desired result.
- 29.
Note that these two propositions are concerned only with the case where the constrained variable is the value of consumption or production of tradeable commodities. The result does not extend to the case with restricted value of consumption or production of non-tradeable commodities.
- 30.
Tan (1971) also extends these results to three special models that allow for inter-industry linkages, the use of intermediate goods, and non-tradeable commodities. Our method provides an alternative and more general treatment of the problem.
- 31.
Similarly, Bhagwati and Ramaswami (1963) asserts that a tariff is not necessarily superior to free trade in the presence of domestic distortions . But this assertion is also misleading. Using the same model , Ohyama (1972), along with Kemp and Negishi (1969), demonstrates the existence of a tariff superior to free trade.
- 32.
In this statement, we consider endowment expansion as phenomena such as the natural growth of cattle and timber woods. Naturally, we must except population growth, which affects the set of consumers.
- 33.
Earlier economists were as well aware of this possibility. For instance, Edgeworth (1894, p. 40) discussed the possible adverse consequence of technological progress in the export industries, attributing the paradox to John S. Mill.
- 34.
Bhagwati (1968b) extends this possibility to the case of domestic distortions such as external economies and diseconomies and inter-industry factor reward differentials , which we assume to not be used in this chapter. The underlying logic is, however, the same as in the case of tariffs.
- 35.
One must distinguish the transfer of tradeable commodities from that of non-tradeable commodities.
- 36.
See, for example Mundell (1960), pp. 79–80.
- 37.
In this special case, the term\( {p}^{\prime}\left({y}^{\prime }-{y}^{{\prime\prime}}\right), \)as well as\( \left({q}^{{\prime\prime} }-{q}^{\prime}\right){e}^{{\prime\prime} } \), vanishes to zero. In fact, \( {p}^{\prime }{y}^{\prime}\ge {p}^{{\prime\prime} }y, \) but \( {p}^{\prime }{y}^{\prime }={p}^{{\prime\prime} }{y}^{\prime}\le {p}^{{\prime\prime} }{y}^{{\prime\prime} }={p}^{\prime }{y}^{{\prime\prime} }. \)
- 38.
- 39.
Negishi considers the infant industry argument from the point of view of the world. We shall return to this problem later in Sect. 4.11 to discuss the world gains from trade.
- 40.
At this point, it should be recalled that, under the convexity of social preference relationship, condition (4.26) is merely sufficient (and not necessary) for the justification of infant industry protection.
- 41.
Haberler (1950) provided a diagrammatic demonstration of the essential argument, which was somehow neglected in later controversies.
- 42.
If \( {w}^{\prime }=0 \), we have
$$ {p}^{{\prime\prime}}\left({x}^{\prime }-{x}^{{\prime\prime}}\right)={p}^{\prime}\left({y}^{\prime }-{y}^{{\prime\prime}}\right)+{p}^{\prime}\left({a}^{\prime }-{a}^{{\prime\prime}}\right)={p}^{\prime}\left({z}^{\prime }-{z}^{{\prime\prime} }-{w}^{{\prime\prime}}\right)+{p}^{\prime}\left({a}^{\prime }-{a}^{{\prime\prime}}\right). $$ - 43.
- 44.
Similarly, trade may not be conducive to the world real income if non-self-financing tariffs are prevalent. This point generalizes Jones’ observation (1961, pp. 173–174) about a Grahamesque, multi-country, multi-commodity model.
- 45.
Strictly speaking, this correspondence fails to apply to the propositions on a price-taking country that depend not only on the absence of the terms of trade effect but also on the constancy of the price of each tradeable commodity. Thus, Propositions 4.11 and 4.11 cannot be held valid for the world.
- 46.
An adept blueprint of such a world economy is found in Tinbergen (1962).
- 47.
As in the case of public goods that are not subject to the exclusion principle, the consumption or production of some commodities by an economic agent may affect a number of other economic agents at the same time. In such an event, it would be necessary to establish an agreement among those affected on the individual shares in the price of the externalities. For closely related concepts, see Musgrave (1959).
- 48.
But for the governmental intervention in the economy as a law-enforced broker between potential sellers and buyers, the scheme would be largely impractical because of the thinness of many markets for externalities. In fact, it would be economically equivalent to an alternative remedy by means of domestic taxes and subsidies if both are administered properly.
- 49.
For example, consider a fisherman who suffers from a water-polluting factory only in business aspects. He is not in the position to supply his diseconomies beyond the degree of water pollution at which he goes out of business. Otherwise, he would supply an infinite amount of diseconomies at any positive price.
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Ohyama, M. (2016). Trade and Welfare in General Equilibrium. In: Macroeconomics, Trade, and Social Welfare. Advances in Japanese Business and Economics, vol 14. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55807-1_4
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