Answer this question using calculus

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 services, but differ in their preferences over consumption and leisure. Denote the utility of household one by u(C1, 1) and the utility of house- hold two by v(C2, 12), where Ci and l; are the consumption and leisure choices of a household of type i. Suppose fraction o of households are of type 1. Be careful that you have the correct number of prices and the correct market clearing conditions. (a) Formally define a competitive equilibrium in this economy. [3 points] (b) Write down the household's problems, and generate first order conditions. [3 points] (c) Write down the representative firm's problem, and generate first order conditions. [3 points] (d) Generate equations that characterize the equilibrium allocation and prices. [3 points] (e) Explain why we cannot use a simple social planner's problem to evaluate efficiency in this model. [3 points]