Dr. Miles is a monopolist who sells a type of patent medicine through competitive retailers. The demand curve for this patent medicine is given by Q = 100 − 2P, where P is the price and Q is the number of bottles sold.
a. If Dr. Miles has zero marginal cost, how many bottles of medicine will she sell and at what price? Calculate the consumers' surplus. Calculate Dr. Miles's producer's surplus.
b. Now suppose that retailers are able to provide their customers with valuable services by explaining how the medicine is to be used, what ailments it is effective against, and so on. By incurring a cost of C in time and effort per bottle sold, the retailer can provide services that consumers value at V per bottle sold, where V is given by V = 5C − C2. What is the socially optimal amount of service per bottle for retailers to offer? What is the cost of this service?
c. Now suppose that retailers who offer services do not sell any additional medicine, because customers accept the services and then shop elsewhere, buying from a cut-rate supplier who offers no services. To combat this, Dr. Miles institutes a fair trade agreement under which she will sell at a wholesale price of P0 but retailers must charge a retail price of P1. Retailers have no other costs. Explain why retailers will incur costs of service equal to C = P1 − P0. What is the socially optimal value for C?
d. Taking C as given, write the equation of the new demand curve that retailers face after Dr. Miles institutes fair trade. Write the equation of the new demand curve Dr. Miles faces. In view of her wanting to face the highest possible demand curve, what value will Dr. Miles choose for C?
e. Using your answers to part (d), calculate the new price P0 that Dr. Miles will charge, the new quantity sold, the new consumers' surplus, and the new producer's surplus.