There is a representative consumer with preferences u(c, l, g) = ln(c)+ ln(l)+ ln(g), where c 0 is private consumption, 0 l 1 is leisure, and g is the consumption of the public good. The parameters and are both strictly positive. The consumer is endowed with one unit of discretionary time. There is also a representative firm producing according to y = zn. There is no capital. The government is unsure about the best way to finance the exogenous level of public spending 0 < g < z. One of two instruments may be used, either a proportional tax 0 < t < 1 or a lump-sum tax T on household income. The entire tax revenue is used to fund public spending.

(a) Write down the budget constraints of the consumer and the government for each alternative tax instrument.

(b) Write down and solve the firm's problem.

(c) Write down the social planning problem.

(d) Formally define a competitive equilibrium under proportional taxation.

(e) Compute the equilibrium level of employment under each taxation plan. Compare them, and explain.

(f) Suppose an increase in g. Compute how equilibrium employment changes when the household is subject to proportional taxation. Is taxation distortionary in this case? Explain.

(g) Compute now the response of equilibrium employment to an increase in g when the household faces the lump-sum taxation. Compare with your answer to the previous question, and explain.

(h) What is the best tax instrument to fund public spending? Explain