Product Price Model Based on Random Exponential Pattern of Consumer Population Behaviour

Elzbieta Kopciuszewska, Pawel Kopciuszewski, Mateusz Mokrogulski and Krzysztof Kompa

European Research Studies Journal, 2025, vol. XXVIII, issue 4, 171-190

Abstract: Purpose: The main purpose of the article is to find the dynamic stability of the market equilibrium point under the specific assumptions of the consumer’s surplus. The provided analysis takes advantage of the supply and demand for a hypothetical good using statistical methods. Design/Methodology/Approach: The research is based on the mathematical model with statistical distributions of selected microeconomic random variables. The equations refer to the consumer’s willingness to buy a good (a deterministic equation), the purchase probability (a stochastic equation) and the price of the good as a function of the marginal cost and the fraction of consumers who buy the good (a deterministic equation). The three above equations are interdependent. The price equilibrium point is found using numerical approximations of the final equation. Findings: The model estimates the equilibrium price for a hypothetical good. In this paper it is assumed that the consumer may buy a product even if his or her surplus is negative. Moreover, a dynamic component, i.e. the derivative of the price over time has been added. Practical implications: The dynamic stability of the equilibrium point has been mathematically proven. The paper also contains the application of the model and the equilibrium price to the case of the Polish mortgage market in the fourth quarter of 2022. Originality value: The proposed rule is general and can be applied to other goods and markets.

Keywords: Demand and supply curves; willingness to pay; consumer surplus; exponential distribution; dynamic stability. (search for similar items in EconPapers)
JEL-codes: B13 C62 D11 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:ers:journl:v:xxviii:y:2025:i:4:p:171-190

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