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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?

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

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