Suppose an individual has preferences over consumption in period 1 and consumpti

Question

Suppose an individual has preferences over consumption in period 1 and consumption in period 2 (i.e., there is only one consumption good that can be consumed in each period and its price is unity). She has no exogenous wealth, receives an income y only in period 1 but can lend (save) at the interest rate r% per period.

a. Using a revealed preference argument, prove that a per-unit tax t on consumption in each period is weakly preferred to a comprehensive (percentage) income tax t (i.e., on both y and interest income) that raises the same present discounted value (PDV) of revenue.

b. Assuming strictly convex preferences and an interior optimum under both taxes, show that the consumption tax is strictly preferred.  

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