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2. In class we discussed the Stackelberg market competition model in the case where there were two firms sequentially announcing their production quantities qı and q2. Recal that we assumed the firms wish to maximize profit (which equals revenue minus cost) The cost to firm i to produce q, units is cq, and the per unit sales price when Q q2 units are produced in total is P(Q)-α-Q if Q-α and zero otherwise. We assume Suppose now there are three firms, with Firm i announcing before firm i + 1. (a) Since Firm 3 must take and q2 as fixed, what would Firm 3s optimal production quantity be? Call this value qs (91,92). (b) Substituting qg(1, 2), and taking qi as fixed, what would Firm 2s optimal pro- duction quantity be? Call this value q2 (qı) (c) Substituting qǎ(Y1), determine Firm is optimal production quantity (d) What are the optimal production quantities for Firms 2 and 3? How do these pro- duction quantities compare to the equilibrium quantities in the Cournot model? (e) How do the firms profits compare in the Stackelberg model? How do they compare the the firms profits in the Cournot model?

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