Tutorial 7

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The University of Sydney *

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2001

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Economics

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Apr 30, 2024

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1 ECOS2001 Intermediate Microeconomics Tutorial 7 Chapter 10 Question 1 Suppose the inverse demand for a product produced by a single firm is given by P = 200 5 Q and that for this firm MC = 20 + 2 Q . 1. If the firm cannot price-discriminate, what are the profit-maximizing price and level of output? 2. If the firm cannot price-discriminate, what are the levels of producer and consumer surplus in the market? What is the deadweight loss? 3. If the firm has the ability to practice perfect price discrimination, what output level will it choose? What are the levels of producer and consumer surplus and deadweight loss under perfect price discrimination? Question 2 Suppose you own two hair salons, one in Washington, D.C., with lots of competition, and one in Charlottesville, Virginia, with little competition. In Washington, the price elasticity of demand is 2, while in Charlottesville, it is 1.5. Assume the marginal cost of providing a haircut is $20. What are the optimal prices and markups in each location? Question 3 Suppose you are a pricing analyst for MegaDat Corporation. You have two types of clients who use your software product. Type A’s inverse demand for your software is P = 100 6 Q , where Q represents users, and P is in dollars per user. Type B’s inverse demand is P = 60 3.5 Q . Assume the marginal cost of supplying software is MC = 13Q. Answer the following questions: 1. If you can determine which buyer is which before a purchase is made, what price will you charge each type? 2. Suppose you cannot tell which type of buyer each client is. Suggest a possible way to use quantity discounts to have buyers self-select into the pricing scheme set up for them. Question 4 Country Club Inc. is a health club that offers two types of equipment: weight machines and a pool. It has three customers, Alex, Bobbi, and Chris. The following table shows their willingness to pay for the different products. Willingness to Pay ( $ /month) Weight Machine Pool Alex $70 $30 Bobbi 80 40 Chris 30 80
2 Each product has a constant marginal cost of $25 per month per user. Each customer is considering monthly access to each type of equipment. Answer the following questions: 1. What price will Country Club charge for each product if it wants each customer to purchase a membership to each product? Calculate producer surplus. 2. What price will Country Club charge if it decides to bundle the two products together? Calculate producer surplus. Question 5 Assume you have been hired as an intern at the Ravenwood Golf Club, and you are assigned the task of setting a pricing scheme for the course. The typical structure is to charge an annual membership fee and a per round fee. Each customer is estimated to have the following demand curve for rounds of golf per year: Q = 400 8 P If Ravenwood can provide rounds of golf at a constant marginal cost of $40 and charges that amount per round to its customers, what is the most customers would be willing to pay for an annual membership? Question 6 Promoters of a major college basketball tournament estimate that the demand for tickets on the part of adults is given by = 5,000 10 , Ad Q P and that the demand for tickets on the part of students is given by = 10,000 100 St Q P . The promoters wish to segment the market and charge adults and students different prices. They estimate that the marginal and average total cost of seating an additional spectator is constant at $10. 1. For each segment (adults and students), find the inverse demand and marginal revenue functions. 2. Equate marginal revenue and marginal cost. Determine the profit-maximizing quantity for each segment. 3. Plug the quantities you found in (2) into the respective inverse demand curves to find the profit-maximizing price for each segment. Who pays more, adults or students? 4. Determine the profit generated by each segment, and add them together to find the promoter’s total profit. 5. How would your answers change if the arena where the event was to take place had only 5,000 seats? Question 7 Carolina Atlantic sells specialty paper to commercial clients. The paper can be produced at zero marginal cost. Some clients are intensive users who are price-sensitive; their demands are given by P = 8 0.1Q where Q is the number of reams of paper desired per week. Other clients are less-intensive users of paper and have inverse demands given by P = 10 - 0.2Q. 1. Carolina Atlantic attempts to separate more-intensive and less-intensive buyers by implementing a quantity discount plan. What price should Carolina Atlantic set for each group? How should the quantity discount plan be structured? 2. Show that the quantity discount plan you outlined in (1) is not incentive-compatible.
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