1. Solve this problem using a diagrammatic approach. Consider a variant of the static GE model in which the representative household has preferences given by U(C,l), where U() is a standard quasi-concave utility function. The representative firm's production function, F(K,Nd), is a standard concave production function. Suppose that the capital input is fixed at R. The government subsidizes labour supply. It does this by paying households 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) sat isfies your definition in part (i). [3 points] (vi) Show whether the equilibrium in part (iv) is or is not Pareto efficient. Explain. [3 points].

1. 1. Solve this problem using a diagrammatic approach. Consider a variant of the static GE model in
which the representative household has preferences given by U(C,l), where U() is a standard
quasi-concave utility function. The representative firm's production function, F(K,Nd), is a standard
concave production function. Suppose that the capital input is fixed at R. The government
subsidizes labour supply. It does this by paying households 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) sat isfies your definition in part (i). [3 points] (vi) Show whether the equilibrium in part (iv)
is or is not Pareto efficient. Explain. [3 points]