Suppose Frank will earn $1 M during his working life and must decide how to spread that between consumption during his working life (Cp) and consumption during retirement (Cf). Assume that the real interest rate between the two periods is 100% and that both Cp and Cf are normal goods.
(a) prepare out the equation for Frank's budget line and illustrate it in a diagram with Cp on the horizontal axis and Cf on the vertical axis. What is the relative price of Cp? Identify it on your diagram.
(b) Suppose Frank chooses to consume $0.5 M during his working life. How much does he save? What is Cf? Illustrate this choice with an indifference curve and identify the level of saving.
(c) Suppose that the government decides to tax away all interest income, so that the real after-tax rate of interest between the two periods falls to 0%. Illustrate the new budget line in your diagram. Suppose Frank still chooses to consume $0.5 M during his working life. Illustrate this choice with an indifference curve. What does this choice tell you about the income and substitution effects of the change in the interest rate with respect to Cp?
(d) Show that Frank would prefer that the government not tax interest income but rather tax his current earnings by $0.25 M.
(e) Go back to the original situation of parts (a) and (b). Now suppose the government institutes a mandatory public pension plan that has Frank paying $0.25 M today, but with a promise of receiving $0.5 M in the future. Is he made better off? What happens to his amount of private saving?