1. True or False: Price discrimination always increases economic efficiency relative to what would be achieved by a single, uniform monopoly price. Explain

2. A monopolist has two sets of customers. The inverse demand for Group 1 is described by P=200-2X. The monopolist faces constant marginal cost of 40.

                a. Show that the monopolist’s total demand, if the two markets are treated as one is:
                                X=0;                       P>/200

                                X=200-P;              100<P</100

                                X=300-(3/2)P;    0<P</100

b. Show that the monopolist’s profit maximizing price is P=120 if both groups are to be charged the same price. At this price, how much is sold to members of Group 1 and how much to members of Group 2? What is the consumer surplus of each group? What are total profits?

3. Now suppose that the monopolist in #3 can separate the two groups and charge separate, profit-maximizing prices to each group.

                a. What will these prices be? What is consumer surplus? What are total profits?

  b. If total surplus is consumer surplus plus profit, how has price discrimination affected total  surplus?

4. The Mount Sunburn Athletic club has two kinds of tennis players, Acers and Netters, in its membership.  A typical Ace has a weekly demand for hours of Q_A = 6 – P. A typical Netter has a weekly demand of Q_N = 3 – P/2.  The marginal cost of a court is zero and there are a thousand players of each type.  If the MSAB charges the same price per hour regardless of who plays, what price should it charge if it wishes to maximize club revenue?

5. A food co-op sells a homogenous good called groceries, denoted g. The co-op’s cost function is described by: C(g) = F + cg; where F denotes fixed cost and c is the constant per unit variable cost.  At a meeting of the co-op board, a young economist proposes the following marketing strategy: Set a fixed membership fee M and a price per unit of groceries p_M that members pay. In addition, set a price per unit of groceries P_N higher than p_M at which the co-op will sell groceries to non-members.

a. What must be true about the demand of different customers for this strategy to work?

b. What kinds of price discrimination does this strategy employ?

6. A night-club owner has both student and adult customers. The demand for drinks by a typical student is Q_s = 18 – 3P. The demand for drinks by a typical adult is Q_A = 10 – 2P. There are equal numbers of students and adults. The marginal cost of each drink is $2.

a. What price will be club owner set if it is not possible to discriminate between the two groups? What will the total profit be at this price?

b. If the club owner could separate the groups and practice third-degree price discrimination, what price per drink would be charged to members of each group? What would be the club owner’s profits in this case?

7. A local phone company has three family plans for its wireless service.  Under each of these plans, the family gets two lines (phones) and can make local and long distance (within the US and Canada) calls for free so long as the total number of minutes used per month does not exceed the plan maximum.  The price and maximum minutes per month for each plan are: Plan 1: 500 minutes for $50; Plan 2: 750 minutes for $62.50; and Plan 3: 1000 minutes for $75. Assuming that there are equal numbers of consumers in each group and that the value of a marginal minute for each group declines at a rate of $0.0004 per minute used, work out the demand curves consistent with this pricing. What surplus will each consumer group enjoy?

8. A monopolist faces the following inverse demand curve: P= (36 – 2Q) z; where P is price; Q is her total output; and z is the quality of product sold. Z can take on only one of two values. The monopolist can choose to market a low-quality product for which z=1. Alternatively, the monopolist can choose to market a high-quality product for which z=2. Marginal cost is independent of quality and is constant at zero. Fixed cost, however, depends on the product design and increases with the quality chosen. Specifically, fixed cost is equal to 65z².

9. Imagine that Dell is considering two versions of a new laptop. One version will meet high performance standards. The other will only meet medium performance standards. To make the second, Dell uses cheaper materials and then crimps the keyboard of the high-performance machine with the result that the marginal cost of the each product is an identical $500. There are two types of consumers for the new laptop. “Techies” have the (indirect) utility function V_t = 2000(z-1). “Norms” have the (indirect) utility function V_n = 1000z, where z is a measure of product quality. Dell can choose the quality level for each machine from the interval (1,3), subject only to the restriction that the medium- performance machine have a lower z quality then the high-performance machine. If Dell knows that there are N_t Techies and N_nNorms, and if Dell also can identify which type any consumer is, what is its optimum price and product quality strategy?

10.  Return to Problem 9, above. Suppose Dell cannot identify each customer but only knows the numbers of each type. Show that Dell’s profit-maximizing strategy is determined by the relative numbers of each type.

Attachments:

• 1504163452-Econ Practice Problems.docx