1. Suppose a monopolist manufacturer sells his products through a monopolist retailer. The marginal cost of production isc = 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 Φ(s) = s2 and it does not depend on the quantity sold.
a. If manufacturer sets the wholesale price w= 6, what will be the retail effort level and the retail price? How much output will be sold? What will be the profits of each 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 the retailer are fully integrated?
2. Two major music companies-Sony and Warner Music-have been subject to an antitrust inquiry by the FTC over allegations that they illegally discouraged retail discounting of compact disks. The investigation is centered on the practice of announcing suggested prices. Suggested prices are not illegal, only agreements among firms on such prices are illegal. But in practice, retailers that advertise or promote CDs at a price below the suggested price are denied cash payments by the manufacturers, in effect "forcing" such suggested prices. How would you decide on this case?
3. You have been hired to market a new music recording that is expected to have target sales of $20 million for this coming year. The marketing department has estimated that a 1 percent increase in advertising the recording would increase the recordings sold by amount of 0.5 percent, and 1 percent increase in the price of the recording would reduce the number sold by about 2 percent. How much money should you commit to advertising the recording the coming year?
4. A firm has developed a new product for which it has a registered trademark. The firm's market research department has estimated that the inverse demand function for this product is P(Q, A) = 160 - Q + A1/2 where P is the price, Q is the annual output, and A is the 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 the firm.
b. What is the consumer surplus and the firm's profit if it follows this optimal strategy?
c. Find the firm's profit-maximizing output, price, and profit if the firm did not advertise.
d. By how much does the use of advertising in this market change the firm's profit and the consumers surplus for the customers of the firm?