Consider the following Bertrand duopoly, where the market demand is given by the inverse demand function = 280 2. Firm 1 and Firm 2 have identical cost structure, where the only cost is the marginal cost of 40.

a) Suppose that the firms can charge any positive prices (even in fractions of dollars). Prove that the only nash equilibrium is the case where both firms charge 40.

b) Suppose that they can charge prices in whole dollars (no cents). Prove that both firms charging 40 is a nash equilibrium

c) Suppose that they can charge prices in whole dollars (no cents). Prove that both firms charging 41 is a nash equilibrium.

d) Suppose that they can charge prices in whole dollars (no cents). Prove that there is no other equilibrium other than the ones mentioned in part b) and c).