An index of Inequality is constructed which decomposes into two components, corresponding to vertical and "horizontal" equity respectively.Horizontal equity Is defined in terms of changes in the ordering of a distribution.The proposed index is a function to two inequality aversion parameters.One empirical application is for comparison of a pre-tax distribution with a post-tax distribution, and an example of this is given for the distribution of incomes in the UK in 1977.There is a trade-off between "horizontal" and vertical equity, and for particular combinations of the inequality aversion parameters the original distribution.willbe preferred to the final distribution.The paper concludes with an application of the proposed index to a model of optimal taxation.

This paper explores the portfolio behavior of investors differing with respect to both tax rates and risk aversion, emphasizing the role of constraints on individual and firm behavior in ensuring the existence of and characterizing portfolio equilibrium. Under certain conditions on the securities available in the market, which also are necessary for shareholders to be unanimous in supporting firm value maximization, investors will be segmented by tax rate into two groups, one specialized in equity and the other in debt. Though the relative wealths of the two groups determine the aggregate debt-equity ratio, each firm will be indifferent to its financial policy.