Question

In: Economics

Iron Man, Captain America and Thor have the following utilities for wealth: Iron Man : U(W)...

Iron Man, Captain America and Thor have the following utilities for wealth:

Iron Man : U(W) = W

Captain America : U(W) = 10√ W

Thor : U(W) = W2/100

Suppose all are faced with the following gamble: with probability 50/50 their wealth is either $100 or $0.

1. Calculate the expected utility of the gamble for each individual.

2. What can you say about the risk associated with these preferences? Are these individuals risk averse, risk neutral or risk lovers?

3. If each individual could choose either to participate or not in the gamble, what would each person choose to do?

Expert Solution

1.

The expected utility formula can be given as. -

Where, U(x) is the utility from the gamble, x being the sum of money won or lost, and pi being the probability of winning (so 1 - pi is the probability of losing).

We get -

Iron Man -

Captain America -

Thor -

2.

Looking at the shape of the utility curves when plotted, we can classify their risk behaviour -

Iron Man -

He is risk neutral

Captain America -

He is risk averse

Thor -

He is risk seeking

3.

Based on their risk behaviour -

Iron man is indifferent to taking the gamble

Captain America will not take the gamble

Thor will take the gamble

Rahul Sunny answered 2 years ago

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