Question

2) Describe Larry, Judy and Carol's risk preferences. Their utility as a function of income is given as follows Larry: UL(I) = 101 Judy: UJ(I) = 312 Carol: UC (1)=201.

Answer 1

2)

The risk preference of a consumer is divided into three categories and determined through the change in marginal utility with the income I. The consumer is risk-averse if they have the diminishing marginal utility of income or $\frac{\partial MU}{\partial I}<0$ . The consumer is risk-neutral if they have the constant marginal utility of income or
MU ar
. The consumer is risk-lover if they have the increasing marginal utility of income or $\frac{\partial MU}{\partial I}>0$ .

• Larry: $U_L(I)=10\sqrt{I}$ .
  $\therefore MU_L=\frac{\partial U_L(I)}{\partial I}=\frac{10}{2\sqrt{I}}=\frac{5}{\sqrt{I}}$
  $\therefore \frac{\partial MU_L}{\partial I}=-\frac{5}{2I^{3/2}}<0$
  Therefore, Larry is risk-averse.
• Judy: $U_J(I)=3I^2$ .
  $\therefore MU_J=\frac{\partial U_J(I)}{\partial I}=6I$
  $\therefore \frac{\partial MU_J}{\partial I}=6>0$
  Therefore, Judy is risk-lover.
• Carol: $U_C(I)=20I$ .
  $\therefore MU_C=\frac{\partial U_C(I)}{\partial I}=20$
  $\therefore \frac{\partial MU_L}{\partial I}=0$
  Therefore, Carol is risk-neutral.