Again, consider the special case solved in the text where β = 1 and utility takes the log form. Suppose the real interest rates is 5 percent. Now, we give the consumer a ﬁnancial proﬁle that might look like that of a middle-aged college professor contemplating retirement: initial assets are f0 = $50,000, and the path for labor income is y0 = $100,000 and y1 = $10,000. a) What is the individuals human wealth?
b) According to the neoclassical model, how much does the college professor consume today and in the future? How much does the college professor save today?
c) If current labor income rises by $20,000, by how much will savings change?
d) By how much does consumption today rise if future labor income rises by $10,000?
e) If the interest rate rises to 10 percent, by how much do total wealth and today’s consumption change? By how much does savings change? Why are these eﬀects so much smaller than for the student?
f) Would it matter if the professor could not borrow