Question: Consider the special case solved in the text where = 1 and utility takes the log form. Suppose the real interest rate is 5

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 middle-aged college professor contemplating retirement: initial assets are ftoday = $50,000, and the path for labor income is ytoday = $100,000 and yfuture = $10,000.
(a) What is the individual’s human wealth? Total 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 saving 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 saving change? Why are these effects so much smaller than in exercise 1?
(f) Would it matter if the professor could not borrow?

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