Question

# (B) This question has to do with uncertainty regarding the rate of return to investment.

The representative individual maximizes:

EU =

chy

1-y

+BEL- -], y<1

where y> 0 is the coefficient of relative risk aversion. There is only one physical asset

in the economy, namely capital. The individual has an initial wealth, W, consumes

W-K in period 1, and saves (invest) the rest. The return from the investment is

consumed in the second period. Thus

C₂ = KZ,

where Z is the stochastic return on capital. The log of Z is assumed to be normally

distributed with mean and variance o² (obviously and o² refer to a different

random variable here as compared to Question A(b)(ii) above). Thus the expectation of Z

is e(+¹/2) (you are not required to know how to derive this). Note that if Z is lognormal,

so are powers of Z. Hence the expectation of Z" is e(+¹²/2)

(a) Calculate the optimal savings decision. (Note that Hall's Euler equation does not

apply here. Why not?) How does an increase in ² affect saving?

uncertainty on savings? (See also question (c) below - in fact, you may wish to

attempt (c) first.)

(c) Holding constant the expectation of Z, how does saving respond to a change

in o²?

(d) How is your answer to (c) affected if y>1, and what is the economic rationale

for this?

Fig: 1