Practice Session 3 Price Discrimination

Transcription

1 Practice Session 3 Price Discrimination INDUSTRIAL ORGANIZATION Economics department, Universidad Carlos III de Madrid 1. Key Questions 1. What is price discrimination? 2. What is the purpose of price discrimination? 3. What types of price discrimination exist? 4. What kind of information is necessary in order to perform each type of price discrimination? 5. What can make price discrimination di cult to implement? 6. Which mechanisms can we employ in order to implement each type of price discrimination? 7. Who are the winners and losers in each type of discrimination, with respect to a perfectly competitive outcome? 8. How is total surplus distributed under rst degree discrimination? 9. What is a two part tari? In what type of discrimination is it used? 10. Under which type of price discrimination the rm uses two di erent prices, each in a market with di erent demand, and there is no possibility of arbitrage between the two markets? 1

2 Industrial Organization UC3M 2 2. Problems 1. A monopolist faces a single consumer whose demand function is q = 74 p. Marginal costs equal zero. a) What is the optimal price strategy in case of a linear tari (that is, when a single price is chosen)? What about the case of a two-part tari? Compare both previous cases in terms of social welfare and comment on them. b) Now suppose there are two types of consumers, whose aggregate demands have equal shares. These are given by q 1 = 66 p 1 y q 2 = 82 p 2. Suppose that there is perfect arbitrage between consumers of the same type, but there is no arbitrage between consumers of di erent types. Moreover, the monopolist can recognize the type of consumer that enters his shop. What type of price discrimination can the monopolist use? Calculate his surplus, explaining all the steps that are necessary to obtain the result. Answer the following question, without making any calculation: Does welfare increase if the government forbids all types of price discrimination? c) Now suppose the monopolist is incapable of recognizing the type of consumer that enters his shop. Moreover, there is no arbitrage between consumers of the same type, neither between consumers of di erent types. What type of price discrimination can the monopolist use now? Calculate the optimal two-part tari and the monopolist s surplus. 2. Consider a monopolist who faces a linear demand p = a bx, and whose production costs are C(x) = cx. a) Show that the elasticity of demand is an increasing function of x. b) Compute the welfare loss due to monopoly (compare total surplus in the case of pure monopoly with the perfect competition case). How does this loss change when b changes? (Use a graph in order to represent changes in surplus). c) Suppose the monopolist performs rst degree price discrimination; compute consumer surplus and producer s surplus and compare them to the perfect competition case. Are there welfare losses?

3 Industrial Organization UC3M 3 d) Suppose now that the monopolist faces a linear demand p = 90 x, and has total production costs C(x) = 2x + F, where F = 90 is the xed cost that he must pay in order to produce a positive amount of the good. The Regulation Authority wants to reach the rst-best. The Authority suggests the monopolist to follow the rule price equal to marginal cost. Compute the monopolist s surplus and total surplus. e) Suppose there is no regulation; what be the monopoly equilibrium? Is it possible to reach the rst-best? Compute the di erence in welfare terms between the initial allocation (with regulation) and the alternative allocation. 3. GUINDOSA is a rm which has obtained a patent over a new material, used to produce surgery tools. The marginal cost of each tool is 50 euros, and the demand for such tools in Madrid (M) and Barcelona (B) are the following: P M = 300 0;2q M P B = 250 0;1q B a) Compute equilibrium prices, quantities, pro ts, consumer s surplus and welfare loss, if any, in each market. b) List the types of price discrimination and explain each of them. c) If GUINDOSA performs price discrimination, what type of discrimination would it choose? d) Suppose that in Madrid the demand is segmented in two parts, and that arbitrage is impossible: the demand for those rms who rent materials in public hospitals P and the demand for hospitals who do not want to rent R. Such demands are the following: P P = 250 0;125q P P R = 350 0;05q R e) As a consequence of the new regulation, selling equipment between rms who rent and those who do not rent is no longer forbidden. How do the pro ts of GUINDOSA change?

4 Industrial Organization UC3M 4 4. Suppose that SUIZA HISPANIA (from now on SH) is a rm that produces and sells sport cars. Using information obtained from a market study, the rm must decide how many models of cars to produce and sell. The market study concluded that there are 2 types of buyers who are interested in the rm s prototypes: those who, in relative terms, are willing to pay more for the AVENTADOR prototype (consumers of type GILITO) and those who are willing to pay less (consumers of type RATA). The following table summarizes the willingness to pay and the number of consumers of each type: N. of Individuals Aventador Lanza Consumers type GILITO e e Consumers type RATA e e SH s marginal production costs depend on the quality of the product. The marginal cost of the Lanza model equal , while the marginal cost of the Aventador model equal a) Suppose that SH only has the possibility of selling a single model, that is, the high quality model or the low quality model. Derive the optimal quality, the optimal price and the rm s pro ts. Justify your answer. b) Suppose that SH can o er 2 di erent models. Derive the optimal prices and compute the rm s pro ts. Justify your answer. c) How many models of vehicles would SH sell if it could decide between selling one or two models? Suppose that consumers of type RATA become of type GILITO: how many models of vehicles would SH sell if it could decide between selling one or two models? Justify your answer. 5. * The owner of a club knows that the demand for drinks is more elastic among young consumers than among older consumers, and is trying to determine which is the price scheme that would maximize his pro ts. In particular, the owner estimated that the individual demand functions of each group are the following:

5 Industrial Organization UC3M 5 People younger than 25 years ( young ): q Y = 18 5p Y People older than 25 years ( old ): q O = 20 4p O Every night, 100 people of each age group visit the club. The owner has a cost of 2 euros for each drink. a) Suppose that the owner can charge an entry fee to the club, A i, and a price for every drink, p i, for each age group, where i = Y; O. Compute the entry fee A i and the price of drinks p i, for each age group, that maximize the owner s pro ts. b) Suppose now that, in order to charge for entry to the club (A i ), the owner has to hire private guards, who cost 2000 euro per night. If there are no guards, the owner cannot charge for entry and can only put a price p i on drinks (but can still charge a di erent price for each age group). Would you suggest to hire private guards or not? Why? c) Now suppose that, by a municipal ruling, the owner of the club cannot charge di erent entry fees, nor di erent prices, by age group. Of course, he can still charge entry fees A and a price p for each drink. As before, in order to charge for entry, he still has to pay the cost of 2000 euros for the guards (and if he does not pay the guards, he can only put a price p on each drink). Would you suggest that he hires guards in this case? Why? [Hint: There are two ways to solve this problem: 1) obtain the owner s pro ts for each case and compare them; or 2) obtain the owner s pro ts in the case of no entry fee, compare it to the pro ts of not having guards of case b), and comment on your answer starting from this point].