please answer at least up to (ii)

_ "Two duopolists face an inverse demand curve p = 14 Q for a commodity1 where Q is the combined output of the two rms. Both rms have constant marginal cost of c : 2. Let q] : BR1(q2) and {1'2 : BRq denote the best response functions of rm 1 and rm 2 respectively, in the simultaneous move game. (i) Derive expressions for BR1[92) 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: d1: 2(BRI(92l In) +4iq2 BR2(11}) dim = BRa(1)'2 where 3R1 and BBQ 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 (h) are pos- itive. Explain whether or not you could recommend buying this commodity at t = 2171/5. [20 marks]