Suppose a household can expect to earn $2 M during its working life. Its problem is to allocate this income between present (working life) consumption (Cp) and saving for future consumption during retirement (Cf). Assume that the real after-tax interest rate between the two periods is 50%. and that both Cp and Cf are normal goods.
- What is equation of the household's budget line? Illustrate in a diagram being sure to identify the horizontal (Cp) and vertical (Cf) intercepts. What is the relative price (opportunity cost) of Cp?
- Suppose(whenfacedwiththisbudgetline)thatthehouseholdwouldprefertohaveequal consumption in both periods. How much does it consume in the present? How much does it save? How much does it consume in the future? Illustrate this choice with an indifference curve and identify the level of saving in your diagram.
- Suppose that the real after-tax interest rate between the two periods falls to 0%. Illustrate the new budget line in your diagram. Suppose the household still chooses to consume the same amount during its working life. How much does it save? How much does it consume in the future? 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?
- Supposethat,giventhelowinterestrate,thegovernmentbecomesconcernedthathouseholdsarenot saving enough for retirement and institutes a mandatory public pension plan that has the household paying a "contribution" of $0.4 M today, but with a promise of receiving a "benefit" of $0.4 M in the future. Is the household made better off? What happens to the amount of private saving?