Suppose a government lives for two periods. It makes an exogenous amount of government expenditures each period. These have nominal value P₁G₁ = 100 and P₂G₂ = 50. It also charges households a lump sum tax, Tt each period. This government does not have to raise sufficient taxes to cover expenditures each period. Instead it can issue bonds internationally which pay a nominal return R = 10%. These bonds have a maturity of one period. However, the government begins its life with no debt and must end its life with no debt. Assume that there is no money in this model and the government makes no transfer payments.

(a) Write down the government’s budget constraint in each of the two periods.

(b) Assume that initially the government had planned to balance its budget every period. That is, P_tG_t = T_t and B_t = 0 for all t. However, now the government decides to smooth households’ tax bills and set the same amount of taxes for each period. What are the values of T₁, B₁ and T₂?

(c) If household’s discount the future at a rate of 1/(1+R) what is the effect of this tax cut on households’ present value of lifetime resources? Carefully explain your answer.

(d) Now suppose that households discount the future at a rate of 1/(1+r) where r = 0.05. Does this change your answer to part (c)? If so how? If not, why not? In either case explain your answer.