Consider a differentiated duopoly market in which firms compete by simultaneously setting prices. Suppose market demand for the firms is given by: y1 = 22 - 2p1 + P2 y2 = 22 - 2p2 + P1 Firm one produces at constant marginal cost c1 = 10 and no fixed cost. Firm two produces at marginal cost c2 and no fixed costs. Assume that the firms maximize profits. (a) Find the best-reply functions and draw them in a graph. (b) Suppose that C2 = 10 so the firms are identical. Find the pure-strategy Nash equilibrium. (c) Suppose finally that firm one does not know firm two's marginal cost c2, but believes that it is c2 6 {4, 16} with equal probability. Firm two knows its marginal cost. Find the best-reply functions and the pure-strategy Nash equilibrium in this case