Problem 3. Suppose my utility function for asset position x is given by U(x) = x

Question

Problem 3. Suppose my utility function for asset position x is given by U(x) = x2 Am I risk averse, risk-neutral or risk seeking I know have $20,000 and am considering the following two lotteries: a) b) a. L: with probability 1, I lose $1000 b. La: with probability 9, I gain $0, with probability 0.1, I lose $10,000. Detemine which lottery I prefer. Now assume the utility function for asset position x is given by (x) = 2x + 1 c). Am I risk averse, risk seeking, or risk neutral. d) Given the 2 lotteries in part(b), which would I prefer.

Explanation / Answer

a) Utility is related to x^2 . So i am risk seeking

b) U(1) = 19000^2= 361000000

U(L2) = 0.9* 20000^2 +0.1*10000^2= 370000000

I will prefer lottery 2

c) utility function is linear, so I am risk neural

d) I will prefer anyone of these lotteries as expected loss is same

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