1. The market demand curve for a pair of Cournot duopolists is given as P=36-3Q, where Q=Q1+Q2. For each duopolists, the constant per unit marginal cost is $18/unit and fixed costs are zero.
a. Find the Cournot equilibrium price, quantity and profits.
b. Solve the problem for Bertrand duopolists.
c. Find the equilibrium price, quantity and profit for each firm, assuming the firms act as a Stackelberg leader and follower, with Firm 1 as the leader.
2. The following payoff matrix represents the long-run payoffs for two duopolists faced with the option of buying or leasing buildings to use for production. Determine whether any dominant strategies exist and whether or not there is a Nash equilibrium.
3. Let there be two consumers A and B, and two goods X and Y. Assume UA (XA,YA) = X2 Y and UB (XB,YB) = XY, given the initial allocation (XE =7, YE =2) for consumer A and (XE =2, YE =4) for consumer B. Solve for the optimal allocation of resources given an exchange economy by two players (A, B) and two goods (X, Y).
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