Optimal pricing and inelasticity

The concept of demand price elasticity is fundamental in economics but the rare case of price inelasticity is mostly glossed over in the literature. Here the paper discusses some of the issues raised by price inelasticity. The paper makes an explicit distinction between price inelasticity of demand for the individual firm as opposed to price inelasticity for the aggregate market demand. It argues that in the special case of product differentiation, there may actually not exist a one-to-one price/quantity relationship that realistically describes the aggregate market demand. The paper studies the implications for an individual firm of facing a price inelastic demand. Standard marginal analysis breaks down in the face of this market failure. The firm has no incentive of charging the socially optimum price, but it can realize a large profit by exercizing market power to sell a small quantity at as high a price as consumers can bear. In such cases, government regulation is generally advisable. The paper suggests avenues for further inquiry.