Diamond Trading Company (DTC), a subsidiary of De Beers, is the dominant supplier of high-quality diamonds for the wholesale market. For simplicity, assume that DTC has a monopoly on wholesale...

Diamond Trading Company (DTC), a subsidiary of De Beers, is the dominant supplier of high-quality diamonds for the wholesale market. For simplicity, assume that DTC has a monopoly on 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 - Q_DTC. 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?

Frustrated with DTC’s monopoly, several diamond mining interests and large retailers collectively set up a joint venture called Adamantia to act as a competitor to DTC in the wholesale market for diamonds. The wholesale price is now given by P = 120 - Q_DTC
- Q_ADA. Assume that Adamantia has a cost of 12 (hundred dollars) per high-quality diamond.

(b) Write the best-response functions for both DTC and Adamantia. What quantity does each wholesaler supply to the market in equilibrium? What wholesale price do these quantities imply? What will the profit of each supplier be in this duopoly situation?

(c) Describe the differences in the market for wholesale diamonds under the duopoly of DTC and Adamantia relative to the monopoly of DTC. What happens to the quantity supplied in the market and the market price when Adamantia enters? What happens to the collective profit of DTC and Adamantia?