Suppose that we have an economy with many identical households. There is a government that exogenously consumes some output and pays for it with lump sum taxes. Lifetime utility for a household is: U = ln Ct + ln Ct+1 The household faces two within period budget constraints given by:

Ct + St = Yt Tt Ct+1 = Yt+1 Tt+1 + (1 + rt)St

(a) Combine the two budget constraints into one intertemporal budget constraint.

(b) Use this to find the Euler equation. Is the Euler equation at all affected by the presence of taxes, Tt and Tt+1? 308

(c) Use the Euler equation and intertemporal budget constraint to derive an expression for the consumption function.

The government faces two within period budget constraints:

Gt + S G t = Tt Gt+1 = Tt+1 + (1 + rt)S G t

(d) In equilibrium, what must be true about St and S G t ?

(e) Combine the two period budget constraints for the government into one intertemporal budget constraint.

(f) Suppose that the representative household knows that the government's intertemporal budget constraint must hold. Combine this information with the household's consumption function you derived above. What happens to Tt and Tt+1? What is your intuition for this?