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.
Firm 1
Firm 2
Leasing Building Buying Building
Leasing Building F1=500
F2=500
F1=750
F2=400
Buying Building F1=300
F2=600
F1=600
F2=200
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,
Y
E =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).

Sample Solution