Optimization of an economic entity’s income under resource constraints : one variant of the analytical solution

Abstract

PURPOSE: The main objective of the research was to develop a mathematical model for the optimal distribution of resources between two production processes to maximize the total economic entity’s income.

DESIGN/METHODOLOGY/APPROACH: The study constructs a mathematical model assuming that production processes are described by arbitrary Cobb-Douglas production functions. An analytical expression for the general form of the contract curve is derived for the model with two production functions and two factor inputs. Additionally, the production possibility frontier (PPF) function is defined analytically, and the parameters for which the PPF curve takes different shapes are examined. The research employs an analytical approach to address the resource allocation problem. The model provides a framework for determining the optimal resource distribution between two production processes to maximize firms' total income.

FINDINGS: The study defines the contract curve and production possibility frontier functions for the two-product model analytically. It identifies the parameters influencing the shape of the PPF curve. The research demonstrates that the proposed model allows for an analytical solution to the resource distribution problem, which is crucial for maximizing firms' income.

PRACTICAL IMPLICATIONS: The proposed solution enables firms with production processes described by the Cobb-Douglas production function to find optimal resource allocation options, thereby increasing their total income and market share.

ORIGINALITY/VALUE: This study fills a gap by providing an analytical solution to the problem of optimal resource distribution between two production processes, which has been insufficiently addressed in existing literature.