ECON 2009A – Managerial Economics

QUESTION

Department of EconomicsCarleton UniversityECON 2009A – Managerial EconomicsASSIGNMENT 3 – Due Nov 18 at the beginning of the class1. (25 points) A weapons producer sells guns to two countries that are at war with each other. Theguns can be produced at a constant marginal cost of $5. The demand for guns from the twocountries can be represented as:QA = 100QB = 802p4p(a) (6 points) Why is the weapons producer able to price discriminate in this context?(b) (10 points) What price will it charge to each country? What will the monopolist’s profit be intotal and in each country?(c) (4 points) If the weapons producer were not able to price discriminate and wants to sell inboth countries, what price would it charge? What would be its profit? (Hint: draw the demandcurves for each country and the total demand curve. Is the total demand curve a straightline?)(d) (3 points) Compare your answers in the two questions above. Will the producer sell in bothcountries?(e) (2 points) Which country will benefit from price discrimination? Which country will be worseoff from price discrimination? Explain briefly2. (25 points) Each identical consumer has the following demand for golf, q = 100p, where q isthe number of rounds of golf played per year and p is the price per round. The only golf course inan isolated town incurs a marginal cost of $10 per round of golf, which is equal to its average cost.It wishes to charge a membership fee and a fee per round of golf.(a) (10 points) What price will it set for the membership fee and for each round of golf? Howmany rounds of golf will each golfer play?(b) (5 points) What is the golf course’s profit if there are 100 golfers?(c) (10 points) How does the golf course’s profit per golfer in the above situation compare to thecase in which the golf course is banned from charging a membership fee and can only chargea price per round of golf? Explain.3. (25 points) A monopolist serving two consumers groups with inverse demand curves PS = 12QS and PW = 10QW faces a constant marginal and average variable cost of $2 and considers1a variety of two-part tariffs. The monopolist faces no fixed costs. For your calculation, call thefirst consumer group the “strong-demand” and refer to the second consumer group as the “weakdemand”. Furthermore, assume that each group consists of one consumer only.(a) (7 points) Derive the monopolist’s profit with a two-part tariff that sets the per-unit price equalto marginal cost and the fixed fee equal to the implied consumer surplus for the strongdemand group.(b) (7 points) Derive the monopolist’s profit with a two-part tariff that sets the per-unit price equalto marginal cost and the fixed fee equal to the consumer surplus for the weak-demand group.(c) (4 points) Derive the profit-maximizing two-part tariff that sets the per-unit price PA abovethe marginal and variable cost and the fixed fee equal to the implied consumer surplus forthe weak-demand group. Calculate the implied monopoly profit. Hint: write each of thecomponents of the monopolist’s profit as a function of PA and solve for the value of PA thatmaximizes profit, i.e. where@⇡@PA= 0.(d) (7 points) Derive the monopolist’s profit with a group-specific two-part tariff that sets the perunit price equal to the marginal cost and the fixed fees equal to the implied consumer surplusfor each consumer group. Note that this pricing scheme allows the monopolist to perfectlyprice discriminate using the fixed fees.4. (25 points) A computer hardware firm sells both laptop computers and printers. Through the magicof focus groups, their pricing team determines that they have an equal number of three types ofcustomers, and that these customers’ reservation prices are:LaptopPrinterBundleCustomer A$800$100$900Customer B$1,000$50$1,050Customer C$600$150$750(a) (15 points) If the firm were to charge only individual prices (and not sell bundles), what pricesshould it set for its laptops and printers to maximize profit? Assuming for simplicity that thefirm has only one customer of each type, how much does it earn in total?(b) (10 points) After conducting a costly study, an outside consultant claims that the companycould make more money from its customers if it sold laptops and printers together as abundle instead of separately. Is the consultant right? Assume again that the firm has onecustomer of each type, how much does the firm earn in total from pure bundling?2

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