Individual rationality and mechanism in the history of microeconomic theory

Introduction The subjective theory of value characterizes the values of commodities based on the utilities of individual economic agents, and individual values are equalized to market prices through a market trade. We suppose that a certain stream of subjective theories of value consisted of the theory of UTILITY and scarcity before the marginal revolution, 1 the general equilibrium theory founded in the marginal revolution, and the theory of mechanism design described in terms of game theory. However, we prefer to group them together under the heading ‘microeconomic theories’ because all the fundamental topics they cover, to which we refer in this chapter, are included in Microeconomic Theory by Mas-Colell et al. (1995). Even though the theory of UTILITY and scarcity, the general equilibrium theory, and the theory of mechanism design are called by different names, they have distinct characteristics; however, they share the idea about value called utilitarianism in a wide sense of welfarism. During the history of microeconomic theory, the marginal revolution has been considered one of the most historic events, but the structure of the theory of UTILITY and scarcity is very close to that of the general equilibrium theory, as Kawamata (2009) suggests. Microeconomic Theory (Mas-Colell et al. 1995) covers the general equilibrium theory by using new welfare economics and game theoretical topics. In the general equilibrium theory, a competitive equilibrium (a resource allocation and a price system) is determined at the general equilibrium of a market economy. In a classical economic environment without factors of market failure, a competitive equilibrium is Pareto efficient, and any Pareto-efficient allocation is attainable as a competitive equilibrium through a certain reallocation of resources. This property of market mechanism is called the fundamental theorems of welfare economics, which is not held if the factors of market failure such as non-convexity, externalities, and public goods prevail in an economic environment. Regarding the problems of non-convexity, externalities are solvable within the framework of the general equilibrium theory by formulating public policy with recourse to the taxation system. However, the problem of public goods accompanies that of incentive compatibility, which needs the game theoretic framework of the theory of mechanism design. Game theory can overcome the difficulties suffered by the general equilibrium theory. Although the development of the theory of mechanism design is a more important historical event than was the marginal revolution, it has been rarely debated throughout the history of microeconomic theory. Thus, the purpose of this chapter is to characterize the properties of the theory of UTILITY and scarcity, the general equilibrium theory with new welfare economics, and the theory of mechanism design from the viewpoint of mechanism theory and to review the history of microeconomic theory. As Carr (1961/64) points out, a history is a dialogue between the past and the present. A past theory may implicitly assume certain factors that are explicitly assumed in the present theory. It follows that we can better understand past theories by interpreting them in the present theory which has developed from past theories and vice versa. In order to logically understand a theory, it must be formulated as a consistent axiom system (Shoenfield 1967). According to an axiomatic approach, any theory can be characterized by a language and an axiom system described in terms of that language. In particular, microeconomic theory is described by an economy or a non-cooperative game and the equilibrium of the economy or of the game. By characterizing economic theories as axiom systems and comparing them with each other, we can more clearly see the characteristics of economic theories. For example, the economic theories used before and after a scientific revolution in economics such as the marginal revolution or Keynesian revolution, when characterized by their respective axiom systems, are distinct from one another. Since most original texts are incomplete as an axiom system, we cannot help interpreting the original theory based on a complete axiom system relative to a certain set of theorems, which is an extension of the original theory and thus is not equivalent to it. This chapter is organized as follows. In the next section, we examine the theory of UTILITY and scarcity before the marginal revolution, finding that it had the same structure as has the marginal utility theory, while the subsequent section covers the general equilibrium theory after the marginal revolution, which is systematized on the basis of the rational behavior of economic agents and the market mechanism. The microeconomic theories in these periods can be characterized by the fundamental theorems of welfare economics. The chapter goes on to refer to the original development of the theory of mechanism design, which follows the general equilibrium theory to resolve market failures. In the last section, I summarize the results.