Consider Blanche, who expects to live for two periods: “now” (period 0) and the “future” (period 1). She earns an income of $40,000 dollars now, but zero in the future since she will be retired. Her problem is to decide how much to consume in period 0 and how much to save for period 1. The market interest rate is 6%. Her utility function is U=(Co)^(3/4) (C1)^(1/4). and hence her marginal rate of substitution between present and future consumption is dC1/dC0 = 3C1/C0. 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. In the absence of a public pension, show how much she will save?
b. Suppose that there is a pay-as-you-go public pension system in place which charges Blanche a premium of $6,000 in period 0 and pays her benefits of $6,360 in period 1. How much will Blanche save now?
c. How will the pay-as-you-go public pension affect total saving in society? (Explain your answer.)
d. What is meant by the “wealth substitution effect” of a public pension?