Consider the following duopoly model. Let a > 0. If qi0 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 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(p;) 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 qi units is Ci(qi) q, hence it is quadratic in the produced quantity. = Compute all Bertrand equilibria. Is it possible to find a Bertrand equilibrium with the payoffs of the Cournot equilibrium?