Editing Price discrimination (section)

==Consumer surplus==
[[File:Pricediscrimination.small.png|right|thumb|Sales revenue without and with price discrimination]]
The purpose of price discrimination is to increase profits by capturing [[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 market price. Price discrimination transfers some of this surplus from the consumer to the seller.<ref name=":12" /> In a perfectly competitive market, price discrimination is not possible, because attempts to increase price for some buyers would be undercut by the competition.<ref name=":22" />

Consumer surplus need not exist, for example in monopolistic markets where the seller can price above the market clearing price. Alternatively, should fixed costs or [[economies of scale]] raise the [[marginal cost]] of adding more consumers higher than the [[marginal profit]] from selling more product, consumer surplus may be captured by the seller. This means that charging some consumers less than an even share of costs can be beneficial. 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 of connecting the building, and the other willing to make up the rest but not to pay the entire cost, then price discrimination can allow the purchase to take place. However, this will cost the consumers as much or more than if they pooled their money to pay a non-discriminating price. If the consumer is considered to be the building, then a consumer surplus goes to the inhabitants.

A seller facing a downward sloping demand curve that is convex to the origin always obtains higher revenues under price discrimination than under uniform pricing. In the top diagram, a single price <math>(P)</math> is available to all customers. The amount of revenue is represented by area <math>P,A,Q,O</math>. The consumer surplus is the area above line segment <math>P,A</math> but below the demand curve <math>(D)</math>.

With price discrimination, (the bottom diagram), the demand curve is divided into segments (<math>D1</math> and <math>D2</math>). A higher price <math>(P1)</math> is charged to the low elasticity segment, and a lower price <math>(P2)</math> is charged to the high elasticity segment. The total revenue from the first segment is equal to the area <math>P1,B,Q1,O</math>. The total revenue from the second segment is equal to the area <math>E,C,Q2,Q1</math>. The sum of these areas will always be greater than <math>P,A,Q,O</math>, 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 seller.

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 useful for the seller to determine the optimum prices in each market segment. This is shown in the next diagram where each segment is treated 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).
[[File:Price_discrimination_(third_degree).svg|center|thumb|700x700px|Multiple Market Price Determination; splitting the demand line where it bends (bend: right; split: left and center)]]
The seller 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 <math>Q_a</math> and <math>Q_b</math>. From the demand curve in each market the profit can be determined maximizing prices of <math>P_a</math> and <math>P_b</math>.

The marginal revenue in both markets at the optimal output levels must be equal, otherwise the seller could profit from transferring output to whichever market is offering higher marginal revenue.

Given that Market 1 has a [[price elasticity of demand]] of <math>E_1</math> and Market 2 of <math>E_2</math>, the optimal pricing ration in Market 1 versus Market 2 is <math>P_1/P_2 = [1+1/E_2]/[1+1/E_1]</math>.

The price in a [[Perfect competition|perfectly competitive]] market will always be lower than any price under price discrimination (including in special cases like the internet connection example above, assuming that the perfectly competitive market allows consumers to pool their resources). In a market with [[perfect competition]], no price discrimination is possible, and the average total cost (ATC) curve will be identical to the marginal cost curve (MC). The price will be the intersection of this ATC/MC curve and the demand line (Dt). The consumer thus buys the product at the cheapest price at which any manufacturer can produce any quantity.

Price discrimination is a sign that the market is imperfect, the seller has some monopoly power, and that prices and seller profits are higher than they would be in a perfectly competitive market.