Exercise 1:

Diamond trading company (DTC) 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. Assume that DTC has a cost of 12 per high-quality diamond. Let the wholesale price of diamonds be given by the following (inverse) demand function: P = 120 - Q_DTC.

(a)Write DTC's profit function in terms of Q_DTC, 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. Assume that Adamantia has a cost of 12 per high-quality diamond. The wholesale price is now given by: P = 120 - Q_DTC - Q_ADA.

(b)Write the best-response function 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 between the market for wholesale diamonds and under the duopoly of DTC and Adamantia and under 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?