Question: I think you set up a 2x2 difference equation but not sure Two duopolists face an inverse demand curve p = 14-Q for a commodity,

I think you set up a 2x2 difference equation but not

I think you set up a 2x2 difference equation but not sure

sure Two duopolists face an inverse demand curve p = 14-Q for

Two duopolists face an inverse demand curve p = 14-Q for a commodity, where Q is the combined output of the two firms. Both firms have constant marginal cost of c = 2. Let q1 = BRi(q2) and q2 = BR2(q1) denote the best response functions of firm 1 and firm 2 respectively, in the simultaneous move game. BR1(q2) = 6-0.5q2 BR2(q1) = 6-0.5q1 dq1 dt = 2(BR1(q2) - 91) + 4(q2 - BR2(q1)) dq2 dt = BR2(91) - 92 (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 = 27 V5

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