Two firms serve a market in which demand is described by P 40-5(Q+Q). Each firm's marginal cost is 20.

a. Suppose each firm maximizes its own profit, treating the other's quantity as constant. Find an expression for firm 1's optimal output as it depends on firm 2's. In equilibrium, what common level of output will each firm supply?

b. Suppose, instead, that the firms collude in setting their outputs. What outputs should they set and why?