1. Consider a Cournot duopoly. Both firms have the same constant marginal cost (3 : 1. The inverse demand function of the market is given by P = 10 Q, where P is the market price, andQ is the aggregate output. (a) Solve for the Nash equilibrium of the game including rm out- puts, market price, aggregate output, and firm profits. [20] (b) Now suppose these two firms play a 2stage game. In stage 1, they produce capacities til and 62, which are equal to the Nash equilibrium quantities of the Cournot game characterised by part (a). In stage 2, they simultaneously decide on their pricespl and p2. The marginal cost for each rm to sell up to capacity is]. It is impossible to sell more than capacity. The residual demand 1011:; (1-; \"10%\"? pg for firm'i :j, is D, (phpj) = min illgag}; ifp,' 2 pi . 111111{1[) phat} if P4