Consider the two-period consumption problem with exogenous income and a given interest rate r. Suppose that the government taxes interest income at the rate . The government's revenue will be zero in period 0 and r (y0 c0) in period 1.

1. Write out the individual's budget constraint.

2. Now suppose the government eliminates the taxation of interest income and instead institutes lump-sum taxes of amounts t0 and t1 in period 0 and period 1, respectively. Write out the individual's budget constraint under this alternative tax regime.

3. What condition must the new taxes satisfy so that the change does not affect the present value of government revenue?

4. If the lump-sum taxes satisfy the condition in part 3, is the old consumption bundle, not affordable, just affordable, or affordable with room for extra consumption?

5. If the new taxes satisfy the condition in part 3, does first-period consumption rise, fall, or stay the same?