[A general definition of majority decision in terms of a hierarchy of voting councils has been given by Murakami [3, 4]. The present article establishes a set of necessary and sufficient conditions for Murakami's majority decision or representative system in terms of properties of a group decision function for two alternatives. One corollary of the general theorem is Murakami's conjecture, which says that if a group decision function is dual, strongly monotonic, and nondictatorial, then it is a representative system.]

A typical proof of the existence of a perfectly competitive market equilibrium employs an appropriately continuous price-to-price mapping that depends on excess demands. If trade tax-subsidy distortions are introduced into the model, the excess demand mappings may have disconnected image sets and destroy the continuity of the price-to-price mapping. This difficulty is overcome by developing a technique which explicitly takes account of the dependence of demand on both income and prices and simultaneously solves for equilibrium prices and income levels for all agents. This technique is then applied to establish two existence theorems for models of international trade with trade tax-subsidy distortions.

[This paper is designed to make revealed preference an operational tool of research on utility theory. The preference relations are shown in Boolean matrices and digraphs to facilitate the processing of a large quantity of empirical data and to classify different types and degrees of consumer rationality.]

[This paper determines the time series behavior of investment, output, and prices in a competitive industry with a stochastic demand. It is shown, first, that the equilibrium development for the industry solves a particular dynamic programming problem (maximization of "consumer surplus"). This problem is then studied to determine the characteristics of the equilibrium paths.]