Question

b. Becky is deciding whether to purchase an insurance for her home against burglary. The payoff table for her is shown as follow:

The insurance would cover all the loss from burglary and the insurance fee is $1,500. Her utility function is given as follow:

	With burglary (10%)	Without burglary (90%)
Net worth of her home	$40,000	$50,000

u = w0.4

Should Becky purchase the insurance? Explain.

Answer 1

First we take the case without insurance

Probability of burglary=p=0.1

Utility with burglary=U(40000)=40000^0.4=69.314484 utils

Probability of no burglary=1-p=1-0.1=0.9

Utility with no burglary=U(50000)=50000^0.4=75.785828 utils

Expected utility without insurance=p*U(40000)+(1-p)*U(56000)

Expected utility without insurance=0.1*69.314484+0.9*75.785828=75.138694 utils

Now we take the case with insurance

Probability of burglary=p=0.1

Wealth in case of burglary=50000-1500-10000+10000=$48500

Utility with burglary=U(48500)=48500^0.4=74.868080 utils

Probability of no burglary=1-p=1-0.1=0.9

Wealth in case of no burglary=50000-1500=$48500

Utility with no burglary=U(48500)=48500^0.4=74.868080 utils

Expected utility with insurance=p*U(48500)+(1-p)*U(48500)=U(48500)=74.868080 utils

We find that expected utility is lower in case of insurance. So, Becky should not go for this offer.