Question 1 (Consumption 15+10)

a)  Using the permanent income hypothesis in a two-period setting, derive the permanent     income (fixed consumption) for a consumer that will receive a stimulus check in the first period. Which factors will determine when/how this check will be spent?

b)  What would happen to your response in a) if the interest rate is expected to increase in the future?

Question 2 (RBC 15+5+5)

Suppose an individual lives for two periods and has utility lnC1  + lnC2 .

a) Suppose the individual has labor income of Y1  in the first period of life and zero in the second period. Second-period consumption is thus (1 + r)(Y1  − C1); r, the rate of return, is potentially  random (For your convenience, you can let r=E[r]+e, where e is a mean-zero random error).

i) Find the first-order condition for the individual’s choice of C1 .

ii) Suppose r changes from being certain to being uncertain, without any change in E[r]. How, if at all, does C1 respond to this change?

b) Suppose the individual has labor income of zero in the first period and Y2  in the second. Second-period consumption is thus Y2  − (1 + r)C1 . Y2  is certain, again, r may be random.

i) Find the first-order condition for the individual’s choice of C1 .

ii) Suppose r changes from being certain to being uncertain, without any change in E[r]. How, if at all, does C1 respond to this change? (Optional)