- A Golden Jubilee Note on Graaff's Optimum Tariff Structures
The year 1999 marked the golden jubilee of the publication of Jan de V. Graaff’s (1949) influential analysis of the optimum tariff, so it seems reasonable to appropriate part of our title from Alan Deardorff and Robert Stern (1994). In their contribution to this issue of HOPE, Murray Kemp and Koji Shimomura explore the conditions that invalidate Graaff’s assertion that the optimum tariff vector may be null. Their paper and Kemp’s 1967 piece, which clarifies other issues in Graaff’s analysis, stimulated us to see whether there are any unrecognized gems in Graaff’s analysis that merit exploration.
In discussing C. F. Bickerdike’s analysis of the optimum tariff, F. Y. Edgeworth (1908, 394) recommends illustrating principles by examples: “A mathematician’s appeal to common sense and ordinary probabilities is not inadmissible when he deals with applied mathematics and the application is to human affairs.” To illustrate Bickerdike’s principle he then constructs an example in which Guernsey exports early vegetables to England in exchange for hardware. We try presumptuously to do for Graaff what Edgeworth did for Bickerdike.
Graaff’s analysis is important because of his approach to the problem of the optimum tariff and because of his results. The structure of his article is crisp and provides a general frameworkfor others to [End Page 421] follow. He seemed content to carefully lay out the structure and sketch his results, leaving the details for others to fill in, as he did to some degree in his subsequent (1957) book. His article introduces to analysis of the optimum tariff Paul Samuelson’s (utility) possibility locus for the home country (Samuelson 1947, chap. 8). “Movements towards the locus are secured by establishing the conditions necessary for the Paretean General Optimum; movements along the locus by lump-sum taxes and bounties—assumed to cost nothing to collect and distribute” (Graaff 1949, 49). Then Graaff notes that “attainment of the possibility locus requires that the marginal rates of transformation through foreign trade should equal the marginal social rates of transformation at home” (55). This leads him to the expression for the structure of optimum tariffs in a multicommodity world, without any restrictions on cross-price elasticities. This approach and this formula are his major contributions.
Also important is that Graaff accepts Abba Lerner’s (1936) symmetry theorem, noting that when only two commodities are traded, “we have here but one international price ratio. To adjust the domestic import-export price ratio to it we need not tax both imports and exports: a single tax will do the trick” (53). 1 He also notes, “Thus we have an infinity of optimum tariff structures, each corresponding to a different initial distribution of wealth [i.e., to where we end up on the utility possibility locus], but all determined by the same rule” (56; emphasis in original). Since his frameworkis new, so is this conclusion.
We wish to focus on two additional issues. Graaff in both his article and his booksuggested that the optimum tariff vector might be null. 2 [End Page 422] He also suggested it might have some negative elements, and he loosely sketched out some arguments why he believed this to be the case. But his logic remains murky. Had he used the results provided a few years earlier by W. F. Stolper and Paul Samuelson (1941) in the same journal, he could have made his arguments more convincing. That is what this note attempts to do.
Specifically, we demonstrate that when there are international transfers denominated in a nontradable, even when only two goods are traded, the optimum tariff may be positive, zero, or negative. The logic is that a tariff alters foreign prices, and if it has the correct sign it may raise the real value of the transfer to the tariff-imposing country. For this case, we derive the optimum import tariff. Second, we explore two other cases where the optimum tariff structure may be free trade, using the Stolper-Samuelson model with incomplete specialization. These cases are drawn from remarks of Graaff’s. Third, we explore Graaff’s suggestion that export...