Kiyoshi Kuga

Inequality measurement: An axiomatic approach

The theory of inequality measurement is examined using some basic axioms which extend the Pigou/Dalton principle of transfers. From these basic axioms various inequality indices may be derived as an alternative to ad hoc methods, or to methods involving prior specification of a social welfare function. The key idea is the concept of ‘distance’ between two income shares. Conventional inequality indices are analysed in terms of their implied distance functions.

Tariff retaliation and policy equilibrium

This paper deals with an equilibrium of tariff policies among countries when retaliation does take place. A country may improve its position as compared with the free trade by imposing a tariff on imports. This should be at the expense of some other countries, and those that are left worseoff will retaliate by countervailing tariffs. The warfare will continue until no country finds it advantageous to alter its own tariff policy. The problem of tariff warfare and policy equilibrium has so far been analyzed by Scitovsky (194 l-2), Johnson (1953-4), Gorman (1958), and Honvell (1966) in simple settings of two-country, two-commodity models. The present work is an extension along their line to a manycountry, many-commodity case. The brief outline of our argument may be described as follows. We are concerned with a model of world economy in which different commodity-prices prevail among different countries and each country executes import tariff policies that are country-wise and commodity-wise discriminative. Each country is supposed to have a set of alternative tariff po. licies and a social choice function according to which its economic position is evaluated. In each country, the tariff revenue is assumed to be refunded to the private sector in a lump-sum fashion. For a fixed world tariff structure in which each pursues accrtain policy, a world equilibrium is established in the sense that the demand fo,: and supply of each commodity is balanced in the world market. Each country then enjoys a welfare level prescribed by the social choice function. For different ta.riff structures, we obtain different world equilibria, and different welfare levels for each country.

THE FACTOR-PRICE FRONTIER IN A NEOCLASSICAL MULTI-SECTOR MODEL*

production functions. However, this proposition can be established rigorously only after it has been proved that unique equilibrium prices exist for all given admissible values of the own-rates of return. We prove the latter theorem in Section 3. The existence of a generalized factor-price frontier for our model follows immediately. Moreover, as a by-product we obtain a nonsubstitution theorem which states that for given (admissible) own-rates of return, the equilibrium real wage in terms of any numeraire is determined independently of the composition of output.3 Our nonsubstitution theorem is analogous to those proved by Samuelson [6, 7] and Bruno [2] for Leontief models, and by Morishima [4] for a steady-state neoclassical model with equal own-rates of return. These topics are discussed in Section 4. Section 5 is concerned with the properties of the set of admissible ownrates of return. It is shown that our restrictions are a natural generalization of a two-sector model with a single capital good. Furthermore, we obtain our results, including the validity of our main theorem, under the assumption that labor is required, either directly or indirectly, in the production of every commodity; this condition is much weaker than the alternative assumptions that either labor is required to produce every good or that the technology is indecomposable. In Section 6 we prove that another of Brunos [2] results for the linear

General Saddlepoint Property of the Steady State of a Growth Model with Heterogeneous Capital Goods

Using examples Hahn [9] clarified that the asymptotic stability of the steady state in the macro growth models does not extend to a world with many heterogeneous capital goods. Despite his contribution and those that followed, important questions remain as to whether the presented model has the dynamic causality and whether the alleged instability is of a more general nature. To date no definite conclusion is yet available. The purpose in this paper is to present a clear-cut view of the problem, and to provide a conclusive evidence that in general the steady state of the Hahn-type growth model has the saddlepoint property.

On the Symmetry of Robinson Elasticities of Substitution: The General Case

1. The elasticity of substitution (ES) is used for indicating substitutability among production factors. Various definitions have been suggested in the literature. Commonly to them is observed a striking property (symmetry) that ES of factor j for factor i is identical with that of factor i for factor j (Allen partial ES (Allen (1934)), Direct partial ES (McFadden (1963)), Shadow partial ES (McFadden (1963))). The property is not met, however, with Robinson-Morishima ES (Robinson (1933), Morishima (1967), Kuga and Murota (1969)) when more than two factors of production are involved. The Robinson-Morishima ES (<f) of factor j for factor i is defined as the proportionate change in the ratio of amounts of factors divided by a proportionate change in the marginal rate of substitution of xj for xi when all the input factors vary so as to leave all other marginal rates of substitution unchanged along a given output level. More formally, we have