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2. Answer this question using calculus. Consider a version of the two household, static general equilibrium model with production, as seen in the notes. For this question, suppose that both households supply the same kind of labour scr'm'ccs, but differ in the that the rst type of household owns shares in the rms but the second does not. That is, prots are distributed evenly across the type 1 households, but the type 2 households get no prots. Suppose fraction cf) of households are of type 1. Be careful that you have the correct nimiber of prices and the correct market clearing conditions. (a) Formally dene a mmpetitive equilibriimr in this economy. (b) Write down the household's problems, and generate rst order conditions. (c) Write down the representative rm's problem, and generate rst order conditions. Generate equations that characterize the equilibrium alloca tion and prices. (d) Explain why we cannot use a simple social planner's problem to evaluate efciency in this model