Question: The neoclassical consumption model, a student's perspective: Consider the special case solved in the text where ß = 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 ftoday = $5,000, and the path for labor income is ytoday = $10,000 and yfuture = $100,000.
(a) What is the individual's human wealth? Total 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 rises 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?