Unformatted text preview: University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain HW 10 Please help improve the course by sending me an email about typos or suggestions for improvements For 3rd degree price discrimination problems, it may be useful to refer to this summary: Question 1 About this question: in the lectures, we solved a two part tariff problem when the demand curves were parallel. In such cases, it is easy to say which consumer "type" is the "low" type from which we know to set the access fee A equal to the CS of the low type: 1 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain In this question you will solve for the optimal two part tariff (access fee and usage price) when the demand curves, instead of being parallel, cross. This makes the problem more difficult because it's not clear at the outset which type is "low". For example, consider the following two figures: Type 2 is "Low" Type 2 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Type 1 is "Low" Type The access fee is always equal to the CS of the low type, but that depends on the usage price P. When P is "high" it may be that type 2 is the "low" type so that A = CS of type 2 or when P is "low" it may be that type 1 is the "low" type so that A = CS of type 1. Thus, when asked to solve for a two part tariff with crossing demand curves, you need to solve the problem is three steps: Step 1: Assume type 1 is "low", set A = CS of type 1 and solve for optimal P and A. Calculate Step 2: Assume type 2 is "low", set A = CS of type 2 and solve for optimal P and A. Calculate Step 3: Compare the profits of step 1 and 2: choose the two part tariff corresponding to the higher profits. That said, here's the question: Ajax Tennis Club identifies two groups of tennis players: Type 1: "Serious players" with individual demand for rounds of tennis: Q1 = 10 P Type 2: "Casual players" with individual demand for rounds of tennis: Q2 = 4 (1/4)P Where Q = Rounds of tennis per week, P = Hourly usage fee. Suppose Ajax's TFC is $10,000 per week and MC = 0. Assume there are 1,000 players of each type. Assume for now that under two part tariff pricing, the club wants to attract both types of consumers. You can use this Two Part Tariff Excel Model to check your answers. 3 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (a) When is type 1 the "low" type and type 2 the "high" type? And vice versa? (b) Solve for the optimal access fee A and usage price P by assuming that type 2 is the low type. (c) Now assume that type 1 is low. Solve for the optimal weekly access fee and the optimal hourly usage fee. Hint: your answer will be strange. Then you will have to think about why it's strange. (d) Now suppose there are 1,000 low type players and NHigh high type players. How many high type players must there be for Ajax to exclude low type players? Assume P = MC. Question 2 In this question, you will practice 3rd degree price discrimination. Suppose you are pricing manager of parking Toronto's Pearson airport. You've identified two market segments: "short" and "long" term parkers. The demands for each segment are: Short term: Ps = 3 Qs/200 Long term: PL = 2 QL/200 P is hourly rate and Q is number of cars. There is a single garage with 600 spaces and you have to allocate spaces between the two segments. Let the MC of parking be negligible. (a) What is the garage's objective? (b) Suppose the garage charges a single price for both segments. What is the optimal price? Hint: the short and long term parkers are being "aggregated". (c) Suppose the garage charges each segment a different price what are each segment's optimal prices? Hint: first try the problem as if there is no constraint (not the Lagrangian) and then if necessary as if there is a constraint (the Lagrangian). What is the price elasticity in each segment? (d) Repeat question (c) with a capacity of 400 instead of 600. (e) If the parking garage had a capacity of 400, what is the value of adding another short term parking spot? What about long term parking spot? Question 3 (2007 2008 Final Exam Question) PooJoe is a French car maker. It manufactures cars in France at MC = $100. Demand for cars in France is given by the equation PF = 3,000 5QF. PooJoe also exports cars to Japan where demand is given by the equation PJ = 1,500 6QJ. Suppose transportation cost between countries is $200 per car. 4 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (a) How many cars should be manufactured for the French and Japanese markets? Assume that French Customs doesn't allow cars bound for Japan to be "reimported" back into France. Calculate the French and Japanese prices. Show all calculations clearly. Hint: That cars cannot be reimported means there can be on no arbitrage between France and Japan. Moreover, think carefully about the French and Japanese MC. (b) Now suppose French Customs allows cars exported to Japan to be reimported back to Japan. What should be the French and Japanese prices and number of cars? Show all calculations clearly. Hint: express profits only in terms of the French and Japanese prices and use the no arbitrage condition to solve for either the Japanese or the French price. (c) (Optional) Solve part (b) using the equations price gap = cost of arbitrage and M1 + M2 = 0 technique (recall that you should express everything in prices). Question 4 (Summer 2008 Final Exam Question) The Toronto Classical Music Society is holding two concert series in Fall 2008. The first series presents the works of Berlioz/Tchaikovsky and the second series presents the works of Bartok/Stravinsky. Market research indicates there are four segments of classical music patrons: Romantics, Neoclassical, Tchaikovsky lovers, and Sophisticates. The following table gives the willingnesstopay for a ticket to each series: Patron Segment Romantic Neoclassical Tchaikovsky lover Sophisticate Berlioz/Tchaikovsky Series $40 $20 $45 $5 Bartok/Stravinsky Series $20 $40 $5 $45 The MC for serving each patron is $5. Assume there are 100 patrons in each segment. (a) Are the patron's preferences suited for superior profits through pure bundling? (b) Describe the economic approach for identifying segments and explain how it differs from the marketing approach. (c) Suppose the Society sells tickets for each series individually. What are the optimal prices for the two series? Show all steps and calculations clearly. 5 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (d) Suppose the Society sells tickets to both series as a bundle. What is the optimal price for the bundle of Berlioz/Tchaikovsky and Bartok/Stravinsky series? Show all steps and calculations clearly. (e) Suppose the Society can sell tickets individually and as a bundle. What are the optimal mixed bundle prices? Show all steps and calculations clearly. 6 ...
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 Fall '08
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 Economics, Microeconomics, Pricing, Supply And Demand, Arbitrage, S. Ajaz Hussain

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