Oligopoly
1. ClipIt is a paper clip manufacturer. The company enjoys a patented technology that allows it to produce paper clips faster and at a lower cost than its only rival, FastenIt. ClipIt uses this advantage to be the first to choose its profit-maximizing output level in the market. The inverse demand function for paper clips is P = 500 - 2Q, where Q = Qc + Q f . ClipIt’s costs are Cc(Qc )= 2Qc , and FastenIt’s costs are C f (Q f )= 4Q f .
(a) What is ClipIt’s profit-maximizing output level? FastenIt’s? (Hint: What oligopoly model is most appropriate for this scenario?)
(b) What is the market’s equilibrium price? (c) How much profit does each firm earn?
(d) Would it be profitable for your firm to merge with FastenIt? (Hint: If they merged, the resulting monopoly would have access to ClipIt’s technology and use it to produce paper clips).
2. The Winston Tobacco Company feels that it is faced with the following segmented demand function for its cigarettes:
!10 - 0.1Q when 0 = Q = 20
P =
12 - 0.2Q when Q > 20
where Q is the number of cartons sold and P is the price per carton.
(a) Why is such a segmented demand function likely to exist? What type of industry structure and firm behavior is indicated by this relationship?
(b) Determine Winston’s marginal revenue function. (c) Given that Winston’s total cost function is
TC1 = XXXXXXXXXX6Q + 0.05Q2
determine Winston’s profit maximizing price and output level. (Use MC1 = XXXXXXXXXX1Q.) (d) Given that Winston’s total cost function increases to
TC2 = XXXXXXXXXX4Q + 0.05Q2
what is their profit maximizing price and output level? (Use MC2 = XXXXXXXXXX1Q.)
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Game Theory
3. You, a real-estate developer, own a piece of land in Nassau, Bahamas, next to an equal size piece of land owned by a competitor. Both of you have the choice of building a casino or a hotel. Your payoffs are as follows (competitor’s payoff is listed first, yours second):
You
Casino Hotel
Competitor
Casino $3 million, $3 million $20 million, $5 million
Hotel $5 million, $20 million $2 million, $2 million
(a) What is(are) the solution(s) to this game?
(b) How much is it worth to you to get your casino building permit first?
Pricing Strategies
4. An amusement park is considering changing its pricing approach from a pay-per-ride system to a single entrance ticket entitling the ticket holder to unlimited rides. Assume that the park is not close to approaching the attendance capacity. The marginal value for rides for the typical entrant is listed below:
Quantity Marginal value
1 $2.50
2 2.00
3 1.50
4 1.00
5 0.50
6 0.10
7 0.00
(a) Assuming that the marginal cost is zero to provide the rides to those in attendance, what is the best pay-per-ride price (consider only 50 cent increments)?
(b) If instead, the park wanted to charge a fixed entrance fee, what is the profit maximizing entrance fee?
(c) Under which system are profits higher? (d) Under which system is ride usage higher?
(e) If, instead, the marginal cost of providing a ride were $0.30, what revision in the pricing scheme, if any, would you suggest?
5. You are a manager of a new health spa in downtown New York. A market study estimated the average customer’s monthly demand curve for visits to spa to be Qd = XXXXXXXXXX25P. The cost of operating is C(Q) = 40Q, where Q is the number of visits (and visitors; assume everyone visits exactly once per month). The owner has been charging a $70 per-month membership fee and a $60 per-visit fee. Part of your salary is 10 percent of the monthly profits. Suggest a pricing strategy that will increase your salary.
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