Generalization of the Firm’s Profit Maximization Problem: An Algorithm for the Analytical and Nonsmooth Solution

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 non constant price and maximum constraints for the inputs. We formulate the problem by previously calculating the analytical minimum cost function. This minimum cost function will be calculated for each production level via the infimal convolution of quadratic functions and the result will be a piecewise quadratic function. To solve this family of optimization problems, we present an algorithm of quasi-linear complexity. Moreover, the resulting cost function in certain cases is not $$C^{1}$$ and the profit maximization problem will be solved within the framework of nonsmooth analysis. Finally, we present a numerical example.