Price Discrimination RESERVATION PRICE: A customer's reservation price is the most he is willing to pay for a unit of purchase. If I will pay up to 12 dollars for a movie ticket, 12 dollars is my reservation price. PERFECT PRICE DISCRIMINATION (1st degree price discrimination). This occurs when the seller can charge a different price for each unit of purchase for each customer that is just equal to the customer's reservation price. Thus, if Smith would buy 1 unit for 10 dollars and a second unit for 8 dollars, and Jones would buy 1 unit for 5 dollars and never buy a second unit, those are the prices the seller would charge under perfect price discrimination. SIGNALLING/SCREENING. There are two types of sellers, good and bad. The buyer would like to tell the type of a given seller, so he can pay a lower price if the quality is worse. PRICE DISCRIMINATION. There are two types of buyers, ones with a high reservation price and ones with a low reservation price. The seller wants to tell the type of the buyers, so he can charge a higher price to the buyer with the higher reservation price. In 3rd degree (interbuyer) price discrimination, the seller can observe the buyer's type directly. In 2nd degree (incentive compatible) price discrimination, the seller must charge different prices for different qualities or quantities to separate buyer types. PARETO IMPROVEMENT. When some players are made better off by a change, while nobody is made worse off.

Crimping the Product Suppose 10 ``eager'' customers have a reservation price of 50 for high quality and 15 for low, while 10 ``slow'' customers have a reservation price of 20 for high quality and 10 for low. We cannot tell which customers are eager and which are slow. Product cost is 1 regardless of quality. (a) If quality is low, what price should be charged? (b) If quality is high, what price should be charged? (c) If we offer two products, with low and high quality, how much should be charged? Why wont a price of 10 for Low and 50 for High work? The prices of 10 and 50 wont work because they are not incentive compatible for the Eager customers, even though they are incentive compatible for the Slow customers: U(slow, Low) = >= U(slow, High) = U(slow, Low) = >= 0 U(eager, Low) = >= U(eager, High) = NOT I.C.! U(eager, High) = >= 0

Optimal Prices Suppose 10 ``eager'' customers have a reservation price of 50 for high quality and 15 for low, while 10 ``slow'' customers have a reservation price of 20 for high quality and 10 for low. We cannot tell which customers are eager and which are slow. Product cost is 1 regardless of quality. So we have to make the High quality product more attractive for the Eager customers to ensure incentive compatibility. Let the High price be X. We need U(eager, High) = 50-X >= U(eager, Low) = U(eager, High) = 50-X >= 0 Thus, X=45. At a High price of 45 and a Low price of 10, profits are (10)(10-1) + 10(45-1) = 530. This is a Pareto improvement compared to just selling high quality. The seller and the Eager buyers are better off, and the Slow buyers are no worse off. CRIMPING: Even if it cost 2 per unit to crimp the product, it would be a Pareto improvement, because the sellers profit would be (10)(10-3) + 10(45-1) = 500, compared to 490 from just selling High quality at a price of 50. Low-ability workers choose not to get diplomas. High-ability workers choose to get diplomas. Employers offer N = 100 and D=200. Payoff(High, Diploma) = = 140. Payoff(High, No Diploma) = = 100. Payoff(Low, Diploma) = = 80. Payoff(Low, No Diploma) = = 100. Employers all earn zero profits. (If one employer could get more productivity from workers, then that firm would hire all the workers at the equilibrium wages and make positive profits.) This is an example from John Macmillan's book, Games, Strategies, and Managers. Not being able to distinguish different types of workers results in adverse selection. Signalling can result in a separating equilibrium in which high ability workers are paid more, but must pay for a costly signal. It is essential that the signal be costlier for the low- ability worker than for the high-ability worker. Otherwise, signalling will fail. If nobody expects signalling to work, it won't. No worker will acquire education, and that will be self-confirming, because no employer will want to pay workers with diplomas a higher wage. All workers will be ``pooled'' with the same low wage. If an employer can move first, before workers make their education decisions, then he may be able to break out of pooling by offering higher wages for educated workers. This is called ``screening''. Suppose all unions like money and job security, and hate strikes, but some hate strikes more than others, because there are two types of unions: Type 1: Likes Money Best. Risk Loving. High wages are most important, strikes are not so bad. Type 2: Likes Security Best. Risk -Averse. High wages are not so important, but strikes are very bad.