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History of Political Economy 32.3 (2000) 437-439

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Optimal Tariffs Revisited

Jan Graaff

This issue of HOPE contains two contributions commenting on a paper I wrote over fifty years ago. One is by Murray Kemp and Koji Shimomura; the other, by Ed Tower and John Gilbert. Both are incisive and sympathetic. I have been asked to respond.

My paper, “On Optimum Tariff Structures” (Graaff 1949), had two principal aims. The first was to show that the terms-of-trade case for tariffs could be argued without recourse to community indifference curves and without having to define the phrase itself. This was desirable because community indifference curves were, and are, fragile tools capable of intersecting at embarrassing moments and because defining terms of trade involves an intractable index number problem whenever more than two goods are traded.

The second aim of the paper was to warn against the fallacy that rough estimates of demand and supply elasticities could be inserted into the optimum tariff formula to determine the probable height of optimum tariffs in the real world. These attempts ignored the assumptions necessary to derive the formula. They also ignored the distinction between partial and general equilibrium elasticities and the fact that the formula itself was no more than one of a large set of first-order conditions whose simultaneous satisfaction was necessary (but not sufficient) for reaching [End Page 437] a welfare maximum in a country where lump-sum transfers were both possible and likely to be put into effect.

The paper may well have succeeded in achieving its main purpose, but in other respects it was less successful. An assertion that, under exceptional circumstances, free trade could itself be optimal—that is to say, that the optimal tariffs could all be zero—is the focus of both commentaries. Kemp and Shimomura prove that, on conventional assumptions, all the tariffs can be zero if, and only if, there is no trade in the free trade situation. This renders the assertion less than interesting. Tower and Gilbert search, with great skill, for alternative assumptions under which it might remain interesting. The crux of the matter is clearly the precise nature of the assumptions originally made, either explicitly or implicitly.

I do not propose to pursue this question in any detail. Kemp and Shimomura’s theorem is, as they themselves point out, sensitive to slight changes in the assumptions. My 1949 paper is clearly deficient in that the assumptions on which the optimal tariff formula was derived are not set out with sufficient clarity. For the benefit of future researchers—and in the spirit of John Chipman’s remark (cited by Tower and Gilbert) that “the study of past economic doctrines has much in common with archeology and paleontology”—I record the following fragment of evidence. The paper was written at much the same time as Theoretical Welfare Economics (Graaff 1957), although the latter was published a lot later. There the assumptions are set out more systematically. They permit certain external effects in both consumption and production and allow for the possibility of unbalanced commodity trade. Kemp and Shimomura adopt assumptions that are narrower than these. It is not surprising that they reach a different conclusion. Part of the value of their theorem is precisely that it indicates how restrictive assumptions have to be to eliminate the possibility of zero optimal tariffs with positive trade in the free trade situation.

In a telling aside Kemp and Shimomura remark that their theorem effectively restores the commonsense notion that “an optimizing country with market power will exercise that power.” This raises two interrelated questions. Under what constraints is the country assumed to be optimizing? To what end will the power be exercised? I take them in reverse order.

It cannot be taken for granted that market power will necessarily be used to institute a regime of optimal tariffs. It will, almost by definition, [End Page 438] turn the terms of trade in one’s favor, but that is not the full story. The domestic distribution of income may be tilted in a direction that is regarded...


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pp. 437-439
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Archived 2005
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