Answer Happy

2. Suppose two firms engage in simultaneous quantity competition. Both firms have 0 marginal cost. Answer each of the following for the following demands. • A: P(Q)=24-Q 2 • B: P(Q)=24-2Q (a) Find the Nash Equilibrium quantities qNE and profits. 10 points (b) Find the Monopoly Quantity QM and Profit. 5 points (c) Now suppose the game is repeated infinitely and each firm has a common discount factor 8. Find the required discount factor to sustain the following grim trigger strategy as a SPNE: Play QM/2 if this has been played in every previous period, otherwise play qNE. 15 points (d) Now suppose that the market can potentially change from demand A to demand B. Specifically the market starts out with demand A. If the market demand is A, then with probability 1/2 the demand remains at A in the next period. With complementary (1/2) probability, the market reverts to demand B. In this case the demand remains at B in every subsequent period. Each period the firms observe the current demand and choose quantity simultaneously. Firms maximize expected discounted profit. i. Extra Credit: Calculate the required discount factor to sustain cooperation. 10 points ii. How does the required discount factor compare to those from the previous question? Whether or not you can do the calculation, you should argue this conceptually. 10 points