Suppose a dealer has a local monopoly in selling good X. It pays w to the manufacturer for each unit of X that it sells, and charges each customer p. The demand curve that the dealer faces is best described by the linear function Q = 30 − p, where the price is in units of thousands of dollars.
a. What is the profit-maximizing price for the dealer to set? At this price, how many units of X will the dealer sell and what will the dealer’s profit be?
b. Now let us think about how the situation looks from the manufacturer’s point of view. If it charges w per unit of X to its dealer, calculate how many units of X the dealer will buy from the manufacturer. In other words, what is the demand curve facing the manufacturer? Suppose that it costs the manufacturer $5,000 to produce each unit. What is the profit-maximizing choice of w? What will the manufacturer’s profits be? What price p will the dealer set and what profit will the dealer earn at the manufacturer’s profit-maximizing choice of price w? Graph your answer.