Suppose that there are three firms, firm 1, firm 2 and firm 3, producing differentiated widgets. The demand curves facing each firm are symmetric and are given by the following equation: Qi = 250 -20Pi +5Pj + 5Pk.Each firm has a marginal cost equal to 25. The profit function of firm i is given by: ?i = (Pi – 25)(250 – 20Pi +5Pi + 5Pk), (i, j,k)=(1,2,3)Solve for the Nash equilibrium prices.Suppose that firms 1 and 2 decide to merge.If there are no cognizable efficiencies, calculate the UPPI for an increase in P1.Suppose that the merger makes possible a reduction in marginal cost of 10 percent with products 1 and 2 post merger. Calculate the UPPI for an increase in P1.Calculate the equilibrium prices after the merger, assuming 10 percent cognizable efficiencies for products 1 and 2.
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