Knowledge that Transforms

In a widely cited note in this Review (1975), Giora Hanoch drew attention to the distinction between two different concepts of returns to scale, one concerning the relative change in output for equiproportionate changes in all inputs along a ray from the origin, and the other concerning the change in output relative to costs along the expansion path. Hanoch demonstrated that the two concepts give equal measures for the point-elasticity of scale, ?, at any point on the expansion path for any production function. However, if the production function is nonhomothetic, the rate of change in with output along a ray is generally not equal to its rate of change along the expansion path. Hanoch also demonstrated that the shape of the average cost curve depends upon the change in along the expansion path, not along a ray, and that the assumption of a downward-sloping technically optimal surface (where -=1), with - I below it, is neither necessary nor sufficient for classical U-shaped average cost curves. This note utilizes the envelope theorem to provide an alternative derivation of Hanoch's results concerning the relationship between changes in along a ray and changes in along the expansion path. This approach gives greater intuitive insight into Hanoch's conclusions. It allows graphical illustration of the results, with obvious pedagogical rewards. In addition, the derivation provides one significant new result, namely, a general proposition that the rate of change in ? along a ray must be algebraically less than its rate of change along the expansion path at a point where the ray and the expansion path intersect.

This paper summarizes certain aspects of my research into the trade and employment effects in the United States of a significant multilateral reduction in tradedistorting measures by the world's major trading nations. The study differs from earlier investigations into this question such as those by Giorgio Basevi (1968), Stephen Magee (1973), Robert Stern (1964), and Beatrice Vaccara and Walter Salant (1960) in that the industry breakdown is much more detailed and the consequences of a multilateral tariff reduction on both U.S. export and import-competing industries is taken into account. By estimating not only the net trade and employment effects of a significant tariff reduction in over 350 industries but also in the 50 states and on some 14 occupational groups, it is hoped that the results will be useful for those who are now embarked on the so-called Tokyo round of trade negotiations within the framework of the General Agreement of Tariffs and Trade (GATT). Another novel feature of the study is the estimation of the net employment effects of multilateral tariff cuts under the assumption of flexible exchange rates.