Frustrated with DTCs monopoly, several diamond mining interests and large retailers collectively set up a joint venture called Adamantia to act as a com- petitor to DTC in the wholesale market for diamonds. The wholesale price is now given by P =120−QD −QA, where QA is the quantity that Adamantia chooses to sell. Assume that Adaman- tia also has a cost of 30 (hundred dollars) per high-quality diamond. Answer the following questions and show your work. (A) Write DTC’s profit, ΠD, in terms of QD and QA in this duopoly situation. Find the DTC’s best response function. (B) Write Adamantia’s profit, ΠA, in terms of QD and QA. Find the Adamantia’s best response function.
Sub : Economics
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Frustrated with DTCs monopoly, several diamond mining interests and large retailers collectively set up a joint venture called Adamantia to act as a com- petitor to DTC in the wholesale market for diamonds. The wholesale
P =120−QD −QA,
where QA is the quantity that Adamantia chooses to sell. Assume that Adaman- tia also has a cost of 30 (hundred dollars) per high-quality diamond. Answer the following questions and show your work.
(A) Write DTC’s profit, ΠD, in terms of QD and QA in this duopoly situation. Find the DTC’s best response function.
(B) Write Adamantia’s profit, ΠA, in terms of QD and QA. Find the Adamantia’s best response function.
(C) What quantity does each wholesaler supply to the market in Nash equilibrium?
(D) What wholesale price do these quantities imply? What will the Nash equilib- rium profit of each supplier be in this duopoly situation?
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