and specified range. 3. BERTRAND COMPETITION AND PRODUCT DIFFERENTIATION Consider the following game of price competition between two firms with dif- ferentiated products. For each firm j E {1, 2}, demand for their product is given by ; (P1, P2) = 1 - p; + bp-j, for some b > 0. Both firms are profit maximizers. Both firms face the same constant marginal cost equal to c > 0. 2 (1) Solve for the symmetric Nash equilibrium of the simultaneous price-choice game. (2) Compute the firms' equilibrium output and profit. (3) Determine how an increase in the parameter b impacts the equilibrium out- come. (4) Suppose that the two firms merge into a single corporation, a monopoly. Determine the optimal monopoly profits. Does there exist a (finite) value of b > 0 such that these monopoly profits equal the sum of the duopolists' equilibrium profits from before the merge