Two duopolists face an inverse demand curve

p = 14Q for a commodity, where Q is the combined output of the two rms. Both rms have

constant marginal cost of c = 2. Let q1 = BR1(q2) and q2 = BR2(q1) denote the best response

functions of rm 1 and rm 2 respectively, in the simultaneous move game.

(i) Derive expressions for BR1(q2) and BR2(q1).

(ii) Find the Cournot equilibrium, by using iterated elimination of strictly dominated strategies.

(iii) Suppose that this game is repeated in continuous time and the two rms adjust their

outputs as follows:

dq1

dt

= 2 (BR1(q2) q1) + 4 (q2 BR2(q1))

dq2

dt

= BR2(q1) q2

where BR1 and BR2 are the functions found in (i).

(a) By studying the above dynamic system, identify the long run prevailing price.

(b) Compute the time path of the equilibrium price.

(c) Assume that the initial conditions are such that all constants in the solution in (b) are pos-

itive. Explain whether or not you could recommend buying this commodity at t = 2

p

5.