Wages and Utilities in a Closed Economy

The broad objective of this paper is to propose a mathematical model for the study of causes of wage inequality and relate it to choices of consumption, the technologies of production, and the composition of labor in an economy. The paper constructs a Simple Closed Model, or an SCM, for short, for closed economies, in which the consumption and the production parts are clearly separated and yet coupled. The model is established as a specialization of the Arrow-Debreu model and its equilibria correspond directly with those of the general Arrow-Debreu model. The formulation allows us to identify the combinatorial data which link parameters of the economic system with its equilibria, in particular, the impact of consumer preferences on wages. The SCM model also allows the formulation and explicit construction of the consumer choice game, where expressed utilities of various labor classes serve as strategies with total or relative wages as the pay-offs. We illustrate, through examples, the mathematical details of the consumer choice game. We show that consumer preferences, expressed through modified utility functions, do indeed percolate through the economy, and influence not only prices but also production and wages. Thus, consumer choice may serve as an effective tool for wage redistribution.