= Exercise 1. Consider the following duopoly model. Let a > 0. If qi > 0 is produced by firm i € {1, 2}, then Q 91 +92 i

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Exercise 1 Consider The Following Duopoly Model Let A 0 If Qi 0 Is Produced By Firm I 1 2 Then Q 91 92 I 1 (207.47 KiB) Viewed 53 times

= Exercise 1. Consider the following duopoly model. Let a > 0. If qi > 0 is produced by firm i € {1, 2}, then Q 91 +92 is the aggregate quantity in the market and P = P(Q): = a - Q (assuming Q <a, else P = 0) is the per unit price. Hence, the total demand at price p > 0 is Q = D(p) =a − p (in case p > a, it is 0). If the firms announce prices p; > 0, then firm i sells D(pi) and the other firm has no demand if pi < P3-i. Moreover, both firms share D(p;) equally if p₁ = P2. Assume that the cost of firm i for producing q; units is C₁(qi) = q², hence it is quadratic in the produced quantity. 1. Compute the unique Cournot equilibrium.