Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zN D where Y is the output of the consumption good, z is the exogenous total factor productivity, N D is the labour hours. Government has to finance its expenditures, G, using a lump-sum tax, T, on the representative consumer. There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are:

U(c, l) = ln c + (1 ) ln l (1) where 0 < < 1 is a parameter.

(a) Write down the definition of a competitive equilibrium for the above economy 1

(b) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, lump-sum tax, T, and output, Y in equilibrium.

(c) Solve for the optimal allocation of leisure, l, the consumption, c, employment, N, output, Y . Contrast these quantities with those in competitive equilibrium from (1b). Explain.

(d) Suppose that the government spending, G, increases. Using your answers in (1b), determine and explain how endogenous quantities and prices behave in this economy. Can changes in G be responsible for business cycles we observe? Explain. (Note that consumption, employment, and wages are all pro-cyclical in data.)

(e) Suppose that the total factor productivity, z, increases. Using your answers in (1b), determine and explain how endogenous quantities and prices behave in this economy. Can changes in z be responsible for business cycles we observe? Explain. (Note that consumption, employment, and wages are all pro-cyclical in data.)

f) Is there a Laffer Curve for this economy? Explain