Question

You are thinking of buying a piece of art by a famous painter at an auction. If it’s a genuine piece, it’s worth $1,000,000. If it’s fake, which you think therI s a 10% chance of, it’s worth $0.

The expected value of the art work is $900,000

Imagine that you are the kind of person that doesn’t like uncertainty: you are risk averse. Specifically, your utility function over money is u(x) = x^0.5. What is your expected utility of the art purchase?

A.) 900 utils

B.) $900

C.) 500,000^0.5 utils

Referring to the previous question, now imagine that you already own the piece (but that you are still uncertain of its true value). How much would you sell it for?

A.) $500,000

B.) $810,000

C.) $1,000,000

Imagine that you sold the piece to a firm that buys and sells art, for a price equal to the correct answer from the previous question. That firm is risk neutral. How much expected profit will they have made on their acquisition of the painting from you?

A.) $190,000

B.) $90,000

C.) -$90,000

Answer 1

1. Risk aversion: E(u)=u(0)+u(1000000)/2)

= u(0.5)+u(1000000)/2)

thus the answer comes out to be option C (500000^.5utils)

2.I would have sold it for 1000000 as i am uncertain about its actual price therefore i would sell it fro the actual price

3. option C is the correct answer

As risk neutral party's decisions are not affected by the degree of uncertainty in a set of outcomes. so a risk neutral party is indifferent between choices with equal expected payoffs even if one choice is riskier. Eg: if offered either $50 or a 50% chance each of $100 and $0, a risk neutral person would have no preference, In contrasr , a risk averse person would prefer the first offer, while a risk seeking person would prefer the second