2. Suppose you are in a two-period world where there is only the present and the future.
You are currently an economics major in college. According to a recent study, you
will earn about $98,000 in the future. But as a college student working part time
at McDonald's, you are only pulling in $15,000 today. You also have bequests from
your parents, which are assets worth $10,000. Suppose that the real interest rate is 5
percent, $\beta$ = 1, and utility is logarithmic.
(a) What is the net present value of your human and total wealth (that is, $\tilde{X}$)?
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(b) What is your consumption today? In the future?
(c) What happens to your consumption if, rather than making $98,000, you make
$102,000 in the future?
(d) Suppose the discount factor is less than one, $\beta$ < 1, and the interest rate is zero,
$R$ = 0. How would this change your answer?