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

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 so far in pricing models. In this paper, a simple pricing model is suggested in which, price elasticity is considered dynamic. The suggested pricing model is concerned with a monopolist that its objective is to maximize profit by determining the optimal price. Dynamics of price elasticity is described by a quadratic model, with product lifetime as the single dependent variable. By solving the model using the theory of optimal control, a system of differential equations is obtained which can be used to find the optimal price trajectory. Finally, an example is provided to show how the dynamic behavior of price elasticity can influence the firm's overall profit.