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Suppose a monopolist manufacturer sells his products

24 / 10 / 2019 Assignments

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Suppose a monopolist manufacturer sells his products

1. Suppose a monopolist manufacturer sells his products through a monopolist retailer. Themarginal cost of production is c = 5. Assume that retail demand is Q(p,s) = s(10-p)100,where s is retailer’s level of effort to sell the product. The cost of effort is ?(s) = s2 and itdoes not depend on the quantity sold.a. If manufacturer sets the wholesale price w= 6, what will be the retail effort leveland the retail price? How much output will be sold? What will be the profits ofeach firm?b. Would the profits of the manufacturer rise or fall if the wholesale price is w = 7?c. What is the optimal effort level, price and output if the manufacturer and theretailer are fully integrated?2. Two major music companies-Sony and Warner Music-have been subject to an antitrustinquiry by the FTC over allegations that they illegally discouraged retail discounting ofcompact disks. The investigation is centered on the practice of announcing suggestedprices. Suggested prices are not illegal, only agreements among firms on such prices areillegal. But in practice, retailers that advertise or promote CDs at a price below thesuggested price are denied cash payments by the manufacturers, in effect "forcing" suchsuggested prices. How would you decide on this case?3. You have been hired to market a new music recording that is expected to have targetsales of $20 million for this coming year. The marketing department has estimated that a1 percent increase in advertising the recording would increase the recordings sold byamount of 0.5 percent, and 1 percent increase in the price of the recording would reducethe number sold by about 2 percent. How much money should you commit to advertisingthe recording the coming year?4. A firm has developed a new product for which it has a registered trademark. The firm’smarket research department has estimated that the inverse demand function for thisproduct is P(Q, A) = 160 – Q + A1/2 where P is the price, Q is the annual output, and A isthe annual expenditure for advertising. The total cost of producing the new good is C(Q)= Q2 + 20Q. The unit cost of advertising is constant at T = 1.a. Calculate the optimal output level Q*, price P*, and advertising level A* for thefirm.b. What is the consumer surplus and the firm’s profit if it follows this optimalstrategy?c. Find the firm’s profit-maximizing output, price, and profit if the firm did notadvertise.d. By how much does the use of advertising in this market change the firm’s profitand the consumers surplus for the customers of the firm?

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