Suppose the inverse demand for a good can be represented by the function P(q) = a - bq. Given the prices of the factors of production and the technology of production, the cost function to produce this good is c(q) = 0.5q²

a) Suppose that production is carried out by two identical firms that produce this good. What will be the quantity produced by each firm at equilibrium if these two firms choose their quantities simultaneously?

b) Suppose now that these two firms form a cartel. How much will each firm produce?

c) Show that in the solution to (b) each of the firms has an incentive to cheat.