The Effects of Price Elasticity Dynamics on a Firm’s Profit

Abstract

This paper studies the dynamic behavior of price elasticity and its effects on the overall profit.Although price elasticity has a significant effect on sales, its dynamics have not been examined sofar in pricing models. In this paper, a simple pricing model is suggested in which, price elasticity isconsidered dynamic. The suggested pricing model is concerned with a monopolist that its objectiveis to maximize profit by determining the optimal price. Dynamics of price elasticity is described bya quadratic model, with product lifetime as the single dependent variable. By solving the modelusing the theory of optimal control, a system of differential equations is obtained which can be usedto find the optimal price trajectory. Finally, an example is provided to show how the dynamicbehavior of price elasticity can influence the firm's overall profit.

Keywords

• Dynamic Behavior of Price Elasticity
• Dynamic Pricing
• Learning Effects
• Optimal Control.