1. (8 points) Consider a Bertrand duopoly. Both firms produce an identical good at the same constant marginal cost of $0.80. Demand is given by Q = 100 P. If the two firms charge the same price, they share market demand equally. The firms are located in Singapore, where the smallest currency denomination is $0.05. The firms thus can only choose prices in increments of $0.05. a) (1 point) Suppose that both rms choose the same price, p. What is the profit of a rm as a function of p? b) (2 points) Now suppose that one firm unilaterally deviates from the arrangement in (a) by charging a price $0.05 lower than p. What is that firm's profit as a function of p? c) (5 points) A Nash equilibrium occurs when no firm has an incentive to deviate by lowering its price. Using your answers in (a) and (b), set up an inequality that characterizes the Nash equilibrium. Then solve for the Nash equilibria in this game. (Hint: What we are doing with this inequality is we are considering symmetric Nash equilibria, that is, equilibria where both players play the same strategy. There are two symmetric Nash equilibria to this game)