Reference no: EM132401420

Consider an economy in which the representative consumer has preferences given by U(c; l), where U() is a standard, quasi-concave utility function. The representative rm's production function, F(K;Nd) 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.

(b) Write down the firms' optimization problem. Depict the solution to the rm's problem in a diagram.

(c) Depict the competitive equilibrium in a diagram.

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

(e) Evaluate the following claim for this economy: An increase in the wage causes consumption to rise."

(f) Evaluate the following claim for this economy: An increase in the subsidy rate (say from zero to some positive number) increases the well-being of consumers because it increases the demand for labour, and therefore causes the wage paid to workers to rise."