(2) What’s the effect on the steady state of an increase in h ? Please draw a
diagram to facilitate your explanation. (4%)
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.(10%)
(1) 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? (4%)
(2) 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 (1) how much
will you save and how much will you consume each period? (4%)
(3) Suppose the interest rate rises (starting from the situation in part (1)). Will
you save more or less? Please explain your answer with an equation. (2%)
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