5) Suppose a monopoly has demand given by p = a -b q (technically. this is an "inverse demand\" curve because price is on the le hand side). Derive the elasticity of demand as a function of Q or p. Use the elasticity to calculate marginal revenue. If marginal cost equals c, what is the profit-maximizing output and price? How do they vary with a. b, and c? Explain why that makes sense. 6) If the demand curve is Q{p) - p', what is the elasticity of demand? If the marginal cost is $1 and e - - 2, what is the profit-maximizing price? 7) Assume that title insurance is necessary to buy a house. {Title insurance compensates the buyer if it is later discovered that the seller did not actually have valid title to convey to the buyer]. Assume that McMansions (houses) are sold for a price of $1,000,000. Title insurance company's have a cost of providing insurance of $10,000 Economics 121 Page 3 per house. Whatever price title insurance companies sell their insurance for is in addition to the $1,000,000. a) If the title insurance market is perfectly competitive, at what price will title insurance sell? h} Derive the relationship between the elasticity of demand for title insurance and the elasticity of demand for McMansions (just the house). c) Assume that the elasticity of demand for housing (including title insurance} is e = -2 at all prices and that all title companies collude in determining their price and choose price as a monopoly would. What price would they charge? (1} Most states set a maximum price on title insurance. Do you think that is a good idea if title companies are not: in perfect competition