Price discrimination or price differentiation exists when sales of identical goods or services are transacted at different prices from the same provider. In a theoretical market with perfect information, perfect substitutes, and no transaction costs or prohibition on secondary exchange (or re-selling) to prevent arbitrage, price discrimination can only be a feature of monopolistic and oligopolistic markets, where market power can be exercised. However, product heterogeneity, market frictions or high fixed costs (which make marginal-cost pricing unsustainable in the long run) can allow for some degree of differential pricing to different consumers, even in fully competitive retail or industrial markets. Price discrimination also occurs when the same price is charged to customers who have different supply costs. Price discrimination can exist when three conditions are met: consumers differ in their demands for a given good or service, a firm has market power, and the firm can prevent or limit arbitrage.
Consider a firm that can sell q(p) units when it charges price p. The firm’s profits are π(p) = pq(p) - c(q( p))
Where c is the cost function, function q is the demand facing the firm, that is, it gives the quantity the firm can sell. In the case of monopoly, the demand facing the firm and the market demand are the same. Assume that q is a downward-sloping demand curve. This means that the firm has some pricing power. This pricing power is known as monopoly power or market power. The assumption rules out perfect competition, for under perfect competition, a price increase would send the quantity demanded from any particular firm to zero.
The first-order conditions for profit maximization entail
0 = π’( p) = q( p) + ( p – c’(q( p)))q’( p)
The elasticity of demand, which measures the responsiveness of demand to price, is given by
The elasticity is not necessarily constant, but depends on p. However, this dependence is suppressed for