Question

A professional baseball player just signed a contract to pitch for the Houston Astros. The contract specified that the player would earn $1,000,000.if he were healthy and could pitch. The contract also specified that he would earn $0. if he became I injured and unable to putch. There is a 10% (.1 probability) chance that the pitcher would become injured.

1). What is the Expected Utility for the Beneficiary( Baseball Pitcher) with insurance?
2). What is the Actuarially Fair price for an Insurance Policy?
3). What is the maximum amount that the baseball pitcher is willing to pay for the Insurance Policy?

Answer 1

Probability of making $1,000,000 = 0.9

Probability of earning 0 = 0.1

Utility, U = W^W1/2, where W = wealth earned

1) Expected utility for the beneficiary = 0.9,(1,000,000^1/2) + 0.1(0^1/2)

= 900

2) Actuarially fair price of the insurance= probability of loss*size of the loss = 0.1*1000,000 = $100,000

3) willingness to pay is calculated as follows:

Expected utility= 900

U=W^W1/2

900= W^W1/2

W= 810,000

Expected wealth is 810,000

So maximum willingness to pay is 1000,000 - 810000 = 190,000 dollars.