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 clarity in exposition. Rearranging the equation slightly, the first-order condition for profit maximization can be expressed as
The left-hand side of this expression is the proportion of the price which is a markup over marginal cost. It is known as the “price-cost margin.” Historically, it is also known as the “Lerner Index.” The price-cost margin matters because, in the standard neoclassical model, a competitive industry prices at marginal cost. Thus, the price-cost margin can be viewed as a measure of the deviation from marginal cost. A price-cost margin of zero means that price equals marginal cost, which is the competitive solution. If costs are not negative, the left-hand side is not greater than one, and profit maximization entails elasticity at least as large as one. At any price where the elasticity is less than one, a price increase is profitable. If demand is everywhere inelastic, the firm always wants a higher price.
The formula for the monopoly price can be rewritten to show
This formula suggests that maximizing profits entails marking up marginal cost by a fixed percentage that depends on the elasticity of demand. Price discrimination can only exist in markets where consumers cannot engage in arbitrage. Under arbitrage, a consumer who is offered a lower price for a good by a firm purchases an excess quantity of the good and resells the good to consumers who are denied the lower price by the firm. Reasons why arbitrage may be difficult or impossible: • High transportation costs,
• Legal impediments to resale,
• Personalized products or services,
• Thin markets or matching problems,
• Informational problems, and
• Contracts and warranties
Types of price discrimination:
First degree price discrimination:
This type of price discrimination requires the monopoly seller of a good or service to know the absolute maximum price (or reservation price) that every consumer is willing to pay....