engleski

Solving profit maximization problems by using geometric programming

Profit maximization is one of the most important (micro)economic problems and therefore it is of great importance to understand the problem itself, the solution procedure as well as the solution itself. In the relevant literature there are several solution procedures for the problem in question. The basic solution procedure is based on differential calculus used to solve optimization problems with or without constraints. Hereby for optimization problems with constraints we have substitution method and Lagrange multiplier method. However, there is also a more elegant way to solve the profit maximization problem, which does not involve differential calculus whose application is nontrivial. It involves the use of geometric programming. There are many papers which emphasize the strength of techniques of geometric programming in solving the problem in question, as well as in solving the wider class of problems. However, one should be careful when applying geometric programming, especially on of its parts called signomial programming. In the existing literature there are some explanations on how to solve certain profit maximization problems by using signomial programming. Nevertheless, it has not been proved that solutions obtained in this way are indeed (global) optimum. Therefore, the aim of this paper is to pinpoint the shortcomings of signomial programming approach and its application, as well as to highlight the advantages of geometric programming approach on selected examples of profit maximization. We transform the chosen profit maximization problems into equivalent problems that can be solved directly by applying geometric programming. In this way, we derive the solutions for which we know for sure that they are (global) optima, which is not the case with the application of signomial programming. To the best of our knowledge, this is the first time that the problem of profit maximization has been solved by transforming it into equivalent problem suitable for application of geometric programming.

long-run and short-run profit maximization, Cobb-Douglas production function, signomial geometric programming, geometric programming

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