Question

1. Suppose my utility function for asset position x is given by u(x) = In x.
a. Am I risk-averse, risk-neutral, or risk-seeking? (Hint: use derivatives to identify if the curve is concave, convex or linear)
b. I now have $ 20,000 and am considering the following two lotteries:
L_1: With probability 1, I lose $ 1,000.
L_2: With probability 0.1, I lose $10,000.
With probability 0.9, I lose nothing $0
Determine which lottery I prefer

Answer 1

Q1.

Here the utility function is Ln(x) whose second diffrential wrt x is -1/x^2 which is always negative so the curve is a concave one. and is RISK_AVERSE.

b)Here for Lottery L_1 we win 1000 with probability 1 that makes the Expected payoff as 1*(-1000) = -1000

and variation is Zero.

But for L_2 I lose 10000 with probabilty 0.1 and lose nothing with probabilty 0.9 so expected payyoff is 0.1(-10000) = -1000 the same as the earlier one, but its variation or the variance is

E(X^2) - [E(X)]^2 = 0.1(10^8) - 10^6 = 9*10^6 which is very high.

So out of the available two lotteries L_1 should be preffered as it has low variation in comparision to L_2 keepinfg the expected payoff same.

answered by: anonymous