Price Discrimination - Explanation

Explanation

The purpose of price discrimination is generally to capture the market's consumer surplus. This surplus arises because, in a market with a single clearing price, some customers (the very low price elasticity segment) would have been prepared to pay more than the single market price. Price discrimination transfers some of this surplus from the consumer to the producer/marketer. Strictly, a consumer surplus need not exist, for example where some below-cost selling is beneficial due to fixed costs or economies of scale. An example is a high-speed internet connection shared by two consumers in a single building; if one is willing to pay less than half the cost, and the other willing to make up the rest but not to pay the entire cost, then price discrimination is necessary for the purchase to take place.

It can be proved mathematically that a firm facing a downward sloping demand curve that is convex to the origin will always obtain higher revenues under price discrimination than under a single price strategy. This can also be shown diagrammatically.

In the top diagram, a single price (P) is available to all customers. The amount of revenue is represented by area P, A, Q, O. The consumer surplus is the area above line segment P, A but below the demand curve (D).

With price discrimination, (the bottom diagram), the demand curve is divided into two segments (D1 and D2). A higher price (P1) is charged to the low elasticity segment, and a lower price (P2) is charged to the high elasticity segment. The total revenue from the first segment is equal to the area P1,B, Q1,O. The total revenue from the second segment is equal to the area E, C,Q2,Q1. The sum of these areas will always be greater than the area without discrimination assuming the demand curve resembles a rectangular hyperbola with unitary elasticity. The more prices that are introduced, the greater the sum of the revenue areas, and the more of the consumer surplus is captured by the producer.

Note that the above requires both first and second degree price discrimination: the right segment corresponds partly to different people than the left segment, partly to the same people, willing to buy more if the product is cheaper.

It is very useful for the price discriminator to determine the optimum prices in each market segment. This is done in the next diagram where each segment is considered as a separate market with its own demand curve. As usual, the profit maximizing output (Qt) is determined by the intersection of the marginal cost curve (MC) with the marginal revenue curve for the total market (MRt).

The firm decides what amount of the total output to sell in each market by looking at the intersection of marginal cost with marginal revenue (profit maximization). This output is then divided between the two markets, at the equilibrium marginal revenue level. Therefore, the optimum outputs are Qa and Qb. From the demand curve in each market we can determine the profit maximizing prices of Pa and Pb.

It is also important to note that the marginal revenue in both markets at the optimal output levels must be equal, otherwise the firm could profit from transferring output over to whichever market is offering higher marginal revenue.

Given that Market 1 has a price elasticity of demand of E1 and Market of E2, the optimal pricing ration in Market 1 versus Market 2 is .