Draw a budget constraint and an indifference curve for an individual who works in period one and is retired (earns no income) in period two. He consumes some of his income in period 1 and saves the rest of his income for period 2. Place consumption in period 1 on the horizontal axis, and consumption in period 2 on the vertical axis. He has to choose how much to consume now and how much to save for the future. Suppose he earns $1,000,000 in period 1 and receives 10% interest on any income saved for period 2. The interest is taxed at 30%. Draw his budget constraint, labeling the axes, and draw an indifference curve that maximizes his utility. Label consumption in each period, C1 and C2. Label savings in period 1. (Remember that any income that is not consumed is saved for period 2).
Now consider a change in tax law that is designed to encourage savings. The tax rate on interest income is reduced to 10%. Illustrate the shift in the budget constraint, and draw a new indifference curve that maximizes utility. How has consumption in each period changed? How has savings changed? Describe and illustrate the income and substitution effects. Will one effect necessarily dominate the other? Which effect dominates on your graph?