Consider the special case solved in the text where β = 1 and utility takes the log form. Suppose the real interest rate is 5 percent. Let’s give this consumer a ﬁnancial proﬁle that might look like that of a typical economics student: initial assets are f0 = $5000 (sure…), and the path for labor income is y0 = $10,000 and y1 = $100,000.
a) What is the individuals human wealth?
b) How much does a neoclassical consumer consume today and in the future?
c) By how much does consumption today rise if current labor income increases by $10,000?
d) By how much does consumption today rise if future labor income increases by $10,000? Why does your answer here diﬀer from that in part (c)?
e) If the interest rate rises to 10 percent, what happens to total wealth and consumption today?
f) What happens to consumption if the student is constrained for some reason and cannot borrow today?