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.

翻译：本文的总体目标是提出一个数学模型，用于研究工资不平等的原因，并将其与消费选择、生产技术以及经济中的劳动力构成联系起来。本文构建了一个简单封闭模型（简称SCM），在该模型中，消费部分与生产部分被明确区分但又相互耦合。该模型是阿罗-德布鲁模型的一个特例，其均衡直接对应于一般阿罗-德布鲁模型的均衡。该公式使我们能够识别将经济系统参数与其均衡联系起来的组合数据，特别是消费者偏好对工资的影响。SCM模型还允许构建并明确阐述消费者选择博弈，其中不同劳动力类别的表达效用作为策略，而总工资或相对工资作为收益。我们通过示例说明了消费者选择博弈的数学细节。我们证明，通过修正效用函数表达的消费者偏好确实会渗透到整个经济中，不仅影响价格，还影响生产和工资。因此，消费者选择可作为工资再分配的有效工具。