MATHEMATICAL MODELING OF OPTIMAL PRODUCT PRICING BASED ON DEMAND ELASTICITY

The presented paper examines the use of the mathematical apparatus of demand elasticity to optimize pricing policy and determine the price at which a company’s revenue reaches its maximum. The main objective of the study is to construct a theoretical and applied model that quantitatively describes consumer reactions to price changes and identifies the point at which further increases or decreases in price cease to be economically beneficial. In the theoretical section, the concept of elasticity is analyzed as the ratio of relative changes in a function and its argument. It is shown that this indicator reflects the degree of demand sensitivity to price and can be expressed as a universal coefficient linking sales dynamics with price levels. Based on this, a relationship between the demand function and the revenue function is developed, allowing for an analytical determination of the domain in which a company’s income increases and the domain in which it decreases. It is mathematically proven that the point of maximum revenue coincides with the state of unitary elasticity, where the relative change in price is exactly offset by the corresponding change in sales volume. The practical part of the research focuses on constructing a demand model using empirical data and subsequent analysis through the method of least squares. The resulting regression relationship made it possible to quantitatively determine the intervals of elastic and inelastic demand, as well as to identify the specific price range that maximizes revenue. The conducted study demonstrates that methods of mathematical analysis can be successfully applied in the field of pricing and profit management. The use of the concept of demand elasticity provides a formalized and objective approach to determining the optimal price of goods or services, enabling well-grounded managerial decisions, consideration of consumer behavior, and forecasting of the company’s economic performance.