Knowledge that Transforms

The purpose of this study is to introduce the element of time into the analysis of optinial taxation of international capital movements. As with Irving Fisher, in his Theory of Interest, the . . supply and demand we have to deal with are . .. the supply and demand of future income, and we shall interpret a rate of interest as . . that sort of price which links one point of time with another point of time in the markets of the world (pp. 32-33). The analysis stresses the formal identity between capital theory, involving exchange over time, and trade theory, involving exchange at the same point of time and argues that, as a consequence, the theory of the optimum tax on capital movements may be regarded as a branch of optimal tariff theory. The correspondence between trade theory and capital theory has appeared in many guises throughout the past century, and was recognized at least as early as 1907 by Fisher. His classic graphical apparatus anticipates much of the later opportunity cost approach to international trade, as well as the more recent work in general equilibrium encompassing both theories.1 In this latter work, time is broken up into a (finite) number of successive time periods, and the same physical item available at different time periods and locations is treated as a different commodity. Future production and consumption possibilities are assumed to be perfectly known today and economic agents acting as price takers engage in markets in which prices for delivery in future periods are quoted, and, under certainty, will correctly reflect future scarcity values. As an immediate consequence of this approach, optimum tariff theory is no less applicable when trade over time is included with trade at a given point in time. Prices quoted in the present reflect marginal rates of substitution not only between present commodities, but also between future commodities, and between present and future commodities. A country then stands to gain by taxing exchange over time in the same manner as it may in taxing exchange at the same point in time. Indeed, it has the same purpose-to influence the terms of trade. That the terms of trade over time are called interest rates, or that a lender is treated as an exporter and a borrower as an importer of present income makes little difference. The resulting optimum taxes on trade are simply those taxes which equate the marginal rates of transformation through trade at the same point in time, and over time, with the marginal rates of transformation in domestic production and consumption. This is a somewhat different approach to the problem of optimal taxation of capital movements than that recently pursued by Murray Kemp and Ronald Jones. The major difference is the explicit role played in our analysis by the element of time-of waiting -which allows for pure borrowing or lending, in addition to the financing of imported capital goods by current exports. In a later section we will relate the two approaches.

The formulation of the argument for distributional equality by William Breit and William Culbertson is an improvement on that of The Economics of Control and is more effective in class. Their generalization of the to the case of increasing marginal utility (of income) offset by a greater degree of diminishing marginal utility elsewhere, is also an improvement. Their point that Paul Samuelson did not escape the ''equal ignorance assumption is well taken. Ambiguity, being a case of lack of clarity is a charge that can never successfully be refuted. However, I would like to deny a switching of conclusions. Perhaps the ambiguity would have been avoided if I had added the following words in Roman type to the italicized sentence quoted: . . if it is desired to maximize the total satisfaction in a society, the rational procedure, in the absence of the knowledge that would enable us to equalize the marginal utilities, is to maximize the probable total satisfaction-i.e., to divide income on an equlitarian basis. The theorem on page 32 is not than the and mild one of page 29. It is the same proposition. The ingenous device of the 100 million coconut islands in one way does more than is claimed for it and in another way, does less. If it were possible to divide the total population into pairs which had the same utility functions, the equalization of income within each pair would never involve a wrong movement to be offset by a right oine. That is why there is certainty of improvement from equalization on every island. Furthermore, there would be an absolute maximization, with certainty, of the total satisfaction of the pair on each island from their joint income. On the other hand, the parable assumes that the combined incomes of the pairs have somehow already been equalized; that for every individual in the half of the total population with incomes less than the mean, his partner in the other half of the population (with an identical utility function) has an income greater than the mean by the exact amount that his is less than the mean. (This implies incidentally that no individual has an income as as twice the mean unless his partner has a zero income.) If this is not the case, some islands will be richer than others. We will then have to equalize the incomes of the islands before we could conduct Breit and Culbertson's experiment. The parable, therefore, while not necessary for the meek that income equalization maximizes the probable total satisfaction, is not sufficient for the bold proposition (to which I have never subscribed) that income equalization increases total satisfaction with absolute certainty. Breit and Culbertson's development of their parable reflects the same discomfort they have seen in others. The pair on the island are not satisfied with the proof that the equalization of the incomes has maximized their probable satisfaction. Sharing a widespread human craving for certainty, they want to be quite sure that they have at least increased their actual total satisfactions. This assurance is unfortunately not available as long as the utility functions are unknown. Breit and Culbertson also are seeking for a certainty of gain in a much bolder and more interesting regarding realized satisfactions instead of the maximization of a mere probability, and are accurately represented by the island pair they have invented. They have imagined a certainty of gain only by imagining the discovery of identicalutility twins. But the whole point of the * University of California, Berkeley.

In his article on technical progress in this Review, Winston Chang presents . . . the asymmetrical results out of Harrod's and Solow's classifications [of bias] in relation to that of Hicks (p. 913) for a two-sector model. He also shows . .. that the usual symmetrical results obtained for aggregate neutrality between the Hicksian and Harrodian schema, ... in general, do not apply to Solow-neutrality (p. 913). This note demonstrates that the asymmetries to which Chang refers result from the manner in which he defines the Solow measure of bias in the capital-goods sector. If this measure is redefined, the asymmetries vanish. Chang defines the Solow parameter, UL], (j= 1, 2), as the proportional rate of reduction in the labor-output ratio in sector j at a constant wage rate (pp. 913, 918): UL] -eLj| =O, where eLj-(Yj-Lj); Yj is the output of sector j, Lj is labor employed in sector j, (^) over a variable represents the relative change in that variable, and w is the wage rate measured in terms of the consumption good.' It follows that the laboroutput ratio under consideration in sector 1 is labor per unit of capital good (L,/Y1) whereas the corresponding ratio in sector 2 is labor per unit of consumption good (L2/Y2). Chang defines the Solow measure of bias in sector j as yj=(i/OKj)ULj, where OKj (O< OK< 1) is the share of capital in sector j.