Question

Risk Aversion

Suppose an individual has utility of wealth given by ?(?) = √?.

a. Does this utility function exhibit positive marginal utility of wealth, i.e. is ? ′ (?) > 0? What does this mean?

b. Does this utility function exhibit increasing or decreasing marginal utility of wealth, i.e. is ? ′′(?) > 0, or ? ′′(?) < 0? What does this mean?

c. Is this utility function consistent with risk aversion? Explain.

d. Define what a risk premium is and why it is important.

Answer 1

A) MU = dU/dw

= .5/√w

U'(w) > 0, so MU is positive

As Wealth rises, Utility rises

.

B) U"(w) = dMU/dw

= -.25*w^(-3/2) < 0

So Decreasing MU

so utility rises at Decreasing rate .

.

C) as U is Concave, U"(w) < 0,

so individual is Risk Averse.

.

d) risk premium is difference between Expected value & certainty equivalent CE.

it is important bcoz market risk premium is the additional return an investor should get from holding a risky market portfolio instead of risk-free assets.