Consider Chad, who expects to live for two periods: “now” (period 0) and the “future” (period 1). He earns an income of Io= $20,000, dollars now, and I1= $5,000 in the future when he will be retired from his full-time job. His problem is to decide how much to consume in period 0 and how much in period 1. The market interest rate is r = 10%. Use a consumer’s choice diagram with future consumption on the vertical axis and present consumption on the horizontal axis to address the following points.
a. Sketch Chad’s inter-temporal budget constraint and indicate the numerical values of the intercepts and the slope.
b. Suppose that in the absence of a public pension, Chad chooses to save money in period 0. Illustrate this situation on your diagram with indifference curves. Show how much he saves on your diagram.
c. Suppose now that there is a pay-as-you-go public pension system in place which charges Chad a premium of T = $4,000 in period 0 and pays him benefits of B = (1+r)T in period 1. Show how will this affect his savings decision?
d. Now suppose the pension benefits are given by B = (1+ ρ)T, where ρ < r. Draw a modified version of your diagram in part c to represent this situation. What do you expect to happen to the amount Chad saves?