A firm that accounts for consumer behavior sets the selling price of a product considering the reference price of consumers. In the literature, a reference price is usually modeled as depending on past selling prices. That is, past selling prices implicitly constrain the current selling price of a product. In this article, the author explicitly measures this constraint with an optimal control framework. He works on the structural properties of a general demand function, which depends on both selling and reference prices. Analytical results prove the following claims. Adjusting reference prices effects increase the price elasticity of demand, the demand function becoming flatter. Thus, the reference price effect weakens the market power of the firm. Also, the reference price effect constitutes a main driver of the dynamics of the selling price. But contrary to intuition, selling price dynamics does not systematically imitate reference price dynamics.
dynamic pricing behavioral pricing reference price dependence optimal control