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).