On the Equivalence of Input and Output Market Marshallian Surplus Measures.

This article investigates the changes in Marshallian surplus under monopolistic and competitive output production conditions. An equation states that the negative of the factor derived demand vector, is the vector of partial derivatives of the profit function when output is monopolistically produced. By the basic line integral theorem, another can be written, which states that the change in Marshallian surplus in the factor markets is precisely equal to the change in monopoly profits that occurs because of the factor-price vector change. This result holds regardless of the number of changed factor prices and regardless of the number of final outputs. By use of the basic line integral theorem the equation, which states that under competitive output conditions the change in Marshallian surplus in the factor markets is precisely equal to the change in total surplus that occurs fie to the factor-price vector change, can be written. An interesting by-product is that the joint derived factor-demand functions, usually satisfy the integrability conditions, a result which generally does not hold for a consumer's demand functions derived from utility maximization. The derived factor-demand functions are integrable under monopolistic output production when there is path independence in the output markets.