Fundamental Properties of a Surplus Function

Abstract

The surplus function as defined in the present paper describes the maximum surplus which can be achieved at a given composition of households and firms and at a given distribution of utility. It is shown that the partial derivative of the surplus function with respect to the number of firms is the profit level of such a firm whereas that with respect to the number of households is the difference in value between endowments and private consumption of such a household. These properties of the partial derivatives are called fundamental because they imply the limit theorem on the core of an economy, the rule of financing club goods efficiently, the Henry George Theorem well-known from urban economic theory, as well as a normative justification of why profits are required to vanish.