Question

Fred is thinking of starting a bowling alley near a college campus. Fred is an expected utility maximizer with utility function: U(W) = 1 – (3000/W), where W is his wealth. Fred’s total wealth is $12,000. With probability 0.2 the alley will be a failure and he’ll lose $9,000, so that his wealth will be just $3,000. With probability 0.8 it will succeed and his wealth will grow to $X. What is the smallest value of X that would be sufficient to make Fred want to invest in the bowling alley rather than have a wealth of $12,000 with certainty?

Answer 1

$14,250

Step-by-step explanation:

To determine what amount of money will make Fred take his chances and invest in this new business, we first have to solve this equation:

• current wealth - (% chance of losing money x wealth after losing money)

$12,000 - (20% x $3,000) = $12,000 - $600 = $11,400

Then:

$11,400 / 80% of getting wealthier = $14,250