The profit maximization problem in economies of scale

Abstract

In this paper we present a generalization of the classic Firm’s Profit Maximization Problem, using the linear model for the production function, considering a decreasing price wi(xi)=bi−cixi and maximum constraints for the inputs or, equivalently, considering inputs that are in turn outputs in economies of scale with quadratic concave cost functions. We formulate the problem by previously calculating the analytical minimum cost function in the quadratic concave case. This minimum cost function will be calculated for each production level via the infimal convolution of quadratic concave functions whose result is a piecewise quadratic concave function.