7.5. Consider the two-period setup analyzed in Section 7.4. Suppose that the gov ernment initially raises revenue only by taxing interest income. Thus the indi- vidual's budget constraint is C+Cz/11+(1-7)r] +Y/1+(1-1)], where is the tax rate. The government's revenue is zero in period 1 and rr(Yi - C In period 2, where C is the individual's choice of C, given this tax rate. Now suppose the government eliminates the taxation of interest income and instead institutes lump-sum taxes of amounts T and T in the two periods; thus the individual's budget constraint is now C+C/(1+r) (Yi-T)+(Y2-T2)/(1+r). Assume that Y, Y, and r are exogenous.

(a) What condition must the new taxes satisfy so that the change does not affect the present value of government revenues?

(b) If the new taxes satisfy the condition in part (a), is the old consumption bundle, (C. C), not affordable, just affordable, or affordable with room to spare?

(c) If the new taxes satisfy the condition in part (a), does first-period consump- tion rise, fall, or stay the same?