Consider a variant of the static GE model in which the representative household has preferences given by U(C, (), where U(.) is a standard quasi-concave utility func- tion. The representative firm's production function, F(K, N*), is a standard concave production function. Suppose that the capital input is fixed at K. The government subsidizes employment. It does this by paying firms a subsidy s for each unit of labour employed. The government finances this subsidy by taxing households using a lump sum tax. The government balances its budget. The subsidy rate is s > 0, and the lump sum tax is given by T. Treat the subsidy rate as an exogenous variable and the tax as endogenous. (i) Formally define a competitive equilibrium in this economy. [3 points] (ii) Write down the household's optimization problem. Depict the solution to the household's problem in a diagram. [3 points] (iii) Write down the firm's profit maximization problem. Depict the solution to the firm's problem in a diagram. [3 points] (iv) Depict the competitive equilibrium in a diagram. [3 points] (v) Show that your diagram in part (iv) satisfies your definition in part (i). [3 points] (vi) Show whether the equilibrium in part (iv) is or is not Pareto efficient. Explain. [3 points]