28) Suppose you divide your life into two periods-working age and retirement age. When you
work, you earn labor income Y; when retired, you earn no labor income, but must live off your
savings and the interest it earns. You save the amount S while working, earning interest at rate r,
so you have (1 + r)S to live on when retired. Because you don’t need to consume as much when
retired, you want to set consumption when working twice as high as consumption when retired.
(a) Suppose you earn $1 million over your working life, and the real interest rate for retirement
saving is 50%. How much will you save and how much will you consume in each part of your
life?
(b) Suppose your current income went up to $2 million when working. Now what will you save
and how much will you consume each period?
(c) Suppose a social security system will pay you 25% of your working income when you are
retired. Now (with Y = $1 million, as in part (a) how much will you save and how much will you
consume each period?
(d) Suppose the interest rate rises (starting from the situation in part (a). Will you save more or
less?
29) In 1991 the federal government changed the withholding amounts for personal taxes. The
change meant that people wouldn’t have as much withheld from their paychecks. But there was
no change in the tax code itself, so the amount of tax due in April 1992 was not changed. How
would consumption and saving respond to this withholding change? (Note: you may assume a
real interest rate of 0%.)