Question

Willy’s only source of wealth is his chocolate factory. He has the utility function p(cf)1/2 + (1 − p)(cnf)1/2,where p is the probability of a flood, 1 − p is the probability of no flood, and cf and cnf are his wealth contingent on a flood and on no flood, respectively. The probability of a flood is p = 1/6. The value of Willy’s factory is $500,000 if there is no flood and $0 if there is a flood. Willy can buy insurance where if he buys $x worth of insurance, he must pay the insurance company $2x/17 whether there is a flood or not but he gets back $x from the company if there is a flood. Willy should buy:
a) no insurance since the cost per dollar of insurance exceeds the probability of a flood
b) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/4 of what it would be if there were no flood
c) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be the same whether there was a flood or not
d) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/3 of what it would be if there were no flood
e) enough insurance so that if there is a flood, after he collects his insurance, his wealth will be 1/5 of what it would be if there were no flood

Answer 1

Willy should buy(a) no insurance since the cost per dollar of insurance exceeds the probability of a flood

Explanation:

Willy's only source of wealth is his chocolate factory. He has the utility function  p(cf)1/2 + (1 − p)(cnf)1/2,, where p is the probability of a flood, 1 - p is the probability of no flood, and cf and in are his wealth contingent on a flood and on no flood, respectively. The probability of a flood is p = 1/6. The value of Willy's factory is $500,000 if there is no flood and $0 if there is a flood. Willy can buy insurance where if he buys $x worth of insurance, he must pay the insurance company $2x/17 whether there is a flood or not but he gets back $x from the company if there is a flood. Willy should buy

The answer for the above statement is option ( A.) no insurance since the cost per dollar of insurance exceeds the probability of a flood .

It is because the probability of flood as given in the question is  only 1/6, whereas the chances of no flood are 5/6. So that means that  he should not buy the insurance because the probability of the flood is comparatively less than the amount  Willy has to pay to the insurance company and  the  amount paid back to willy by the insurance company is $ x worth of insurance