Suppose that a consumer has income y in the current period and income y' in the future period, and faces proportional taxes on income in both periods. That is, the consumer pays a tax ty in the current period and t'y' in the future period. The government wishes to collect tax revenue to finance its spending g in the current period and g' in the future period. The real interest rate is r.
a. Derive the consumer's inter-temporal budget constraint.
b. Derive the government's inter-temporal budget constraint.
c. Suppose that the government's total spending does not change, but the government changes the way it finances this spending, by increasing t and reducing t'. What effect, if any, does the change in the tax rates have on the consumer's choice of current and future consumption, and on savings? Does Ricardian equivalence hold? Explain why or why not.