Mathematical modeling of economic processes

Abstract

We study the optimization of production output as a process of finding the conditional maximum of the Cobb-Douglas production function in the presence of the budget constraint. This function is often used in the analysis of economic development. The use of the Lagrange method allows obtaining a stationary point of the Lagrange function. The examination of this point reveals the presence of a conditional maximum at it. The obtained coordinates of the point of conditional maximum of the output volume mean that, under the optimal functioning of the firm, i.e., such functioning, for which the greatest production output is achieved with a fixed budget, the budget should be distributed between fixed assets and labor resources in proportion to the corresponding elasticities of the production output. These coordinates allow finding the values of the largest production output and the marginal maximum output with respect to the budget.