Diamond Trading Company (DTC), a subsidiary of De Beers, is the dominant supplier of high-quality diamonds for the wholesale market. Assume they are a monopoly on the wholesale diamonds. The quantity that DTC chooses to sell thus has a direct impact on the wholesale price of diamonds. Let the wholesale price of diamonds (in hundreds of dollars) be given by the following inverse demand function: P = 120 - Qdtc. Assume that DTC has a cost of 12 (hundred dollars) per high-quality diamond.
a. Write DTC's profit function in terms of Qdtc, and solve for DTC's profit-maximizing quantity. What will be the wholesale price of diamonds at that quantity? What will DTC's profit be?