Answer this question with diagrams.

Consider a variant of the static G.E. model in which the representa-tive consumer has preferences given by U(C,l), where U() is a standard, quasi-concave utility function. The representative firm's production function, F(K,N^d) is a standard, concave production function. Suppose that the capital input is fixed.

The government subsidizes employment. It does this by paying firms a subsidy of 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 rate as endogenous

(a) Formally define a competitive equilibrium in this economy. [3 points]

(b) Write down the household's problem. Depict the solution to the house-

hold's problem in a diagram. [3 points]

(c) Depict the competitive equilibrium in a diagram. [3 points]

Note: Make sure that the key part of your diagram is large enough that I can evaluate whether you have or have not depicted an equilibrium correctly.

(d) Show that your diagram in part (c) satisfies your definition in part (a).

[3 points]

(e) Show whether the equilibrium in part (c) is or is not efficient. Explain.

[3 points]

(f) Evaluate the following claim: "An increase in the subsidy rate increases the well-being of consumers because it increases the demand for labour, and therefore causes the wage paid to workers to rise." [3 points]