Yoshihiko Otani

Equilibrium allocations of Walrasian preference games

Following Hurwicz (1972) we think of an allocation mechanism as a set of rules governing the behavior of economic agents. Given the economic environment (initial allocations, consumer preferences and the technology), the behavior prescribed by the allocation mechanism determines future allocations. Thus we may think of an allocation mechanism as a mapping from a set of economic environments to a set of allocations. A question which often comes up in discussions of allocation mechanisms is whether or not there are incentives for the economic agents to follow the prescribed rules. Is the mechanism “incentive compatible”? This question has received considerable attention in the public finance literature where the concern has been primarily with whether or not consumers will reveal their true prefrences as prescribed by mechanisms designed for the allocation of public goods. (See, for example, Samuelson (1969).) Hurwicz (1972) presented a game theoretic structure for the analysis of incentive compatibility. The economic agents are the players and their reported characteristics (preferences, endowments or technologies) are the strategy variables. When the strategies are “played” a reported environment is characterized and the allocation mechanism under consideration determines the resulting allocation. This allocation, as evaluated by the true consumer preferences, is the “payoff” to the strategies played. Hurwicz calls the mechanism “individually incentive compatible” if the vector of true characteristics is a Nash equilibrium strategy vector for this game. Hurwicz (1972) first used this structure to investigate the incentive compatibility of the Walrasian mechanism. He considered pure exchange economies with finitely many consumers in which initial endowments were taken to be known by all and thus not subject to misreporting. Thus preferences were the only characteristics reported strategically. He found that

Price Taking Firms

In this chapter we study the behavior of a price taking profit maximizing firm. Section 1 will be devoted to investigating the consequences of the short run profit maximization. We will obtain the basic properties of the short run profit functions, short run output supply functions and short run derived demand functions for variable inputs. Finally we ill note the duality between production functions and profit functions.

A simple proof of the LeChatelier-Samuelson principle and the theory of cost and production

Abstract We provide a simple proof of a version of the so-called strong LeChatelier-Samuelson principle particularly suitable for the application to the theory of cost and production. We will illustrate its usefulness and fundamental nature in the case of the classical theory of cost and production.

Rising marginal cost and concavity of the production function

Abstract Suppose a production function, f , is continuous, quasi-concave and weakly monotone on the non-negative orthant of Euclidean n -space. Let c (·, ·) be the associated cost function. Then it is shown that f is concave if and only if for each w , c ( w , ·) is convex.

Duopoly and Oligopoly

In this chapter, we will study simple interactions of firms that are few in number and that recognize the influence of each other’s actions on the outcome of their own actions.

Industry Supply and Industry Equilibrium in a Competitive Market

In this chapter, we will show how short-run and long-run supply maps for an industry can be derived in a more rigorous fashion than a standard approach in intermediate level textbooks so that short-run and long-run supply maps can be used in analyzing various cases of market equilibrium.

Topics in the Theory of the Firm

In this chapter we present two types of extensions of the traditional model of the firm. The first type explores different modes of management and the second type looks at the dynamics of the firm’s behavior.

Topics in Demand Analysis

In this chapter we present two additional topics in demand theory. The first topic deals with aggregate demand derived from individual demand. It introduces the reader to one of the topics on the current frontiers of economic research even though the problem itself is old. The idea is to explore the possibility of getting better behavior on the part of aggregate demand functions by exploiting the fact that if the number of consumers is very large, then exceptional behavior can be “insignificant” in some well defined sense.

Introduction to Welfare Economics and General Equilibrium Analysis

In the earlier chapters we dealt with the behavior of individual agents be they consumers or producers. We also dealt with markets for individual goods. In this chapter we discuss the simultaneous behavior of all agents. The discussion attempts to clarify the relationship between what is “good” for the group and what is “good” for its individual constituents. When we speak of this relationship we are in the realm of welfare economics. This will be done in Section 2. In our discussion we will assume that “good for the society” means Pareto efficient. What is “good for individuals” will mean a general competitive equilibrium. In the absence of externalities, in addition to some other less striking assumptions, it is shown that the two “good” coincide. We call attention to the shallowness of the philosophic import of this result which may be stated as follows: If every member of society is an island into themselves, then what is best for society coincides with what is best for the individual. (How else can it be?)

Production Possibility Set, Activity Analysis and Equilibria of Production Sectors

A production possibility set and the surface of a production possibility set called a product transformation curve (or surface) is a very popular concept employed often in undergraduate textbooks and in applied economics. It provides us with a summary of production sectors incorporating the initial endowment of resources and technological constraints. The usefulness of the concept of a production possibility set originates in two basic assumptions or restrictions on an economy: (a) that commodities can be classified into producible commodities and nonproducible commodities called primary factors of production, and (b) that the supply of primary factors are inelastic or fixed. Thus given the supply of primary factors of production and given technology sets of production sectors, the set of feasible production can be projected onto the space of producible goods and this generates a production possibility set summarizing the endowment of primary factors and technological restrictions in the space of producible goods. This reduction of the endowment of primary factors and production sectors into a production possibility set enables us to lower the dimension of commodities to consider and also it enables us to link prices of producible goods to prices of primary factors or factor prices. The surface of a production possibility set is sometimes called either a production possibility frontier or a product transformation curve (or surface).