In our 2 period consumption savings model (with no leisure, u(c1, c2), suppose interest income in period 2 is taxed at the rates, where 0 < t2 < 1. The individual has zero initial wealth A0 = 0. Exogenous real income in period 1 and 2 are y1 = 1 and y2 = 0.
a) Write down period 1 and period 2 budget constraints for the consumer.
b) Using each period budget constraint, derive the consumer's Lifetime Budget Constraint (LBC).
c) Graphically show the optimality condition for the consumer's decision. This is, in the c2 vs c1 space plot the budget constraint line, the indifference curve and the optimal consumption choice.
d) What is the effect on savings if the interest income tax is increased? Show graphically.
e) Let u(c1, c2) = lnc1 + lnc2. Solve explicitly for the optimal consumption in both periods. Discuss briefly the effect of the interest income tax on each period consumption.