Question

Consider a household that possesses $100,000 worth of valuables (computers, stereo equipment, jewellery, and so forth). This household faces a 0.10 probability of a burglary. If a burglary were to occur, the household would have to spend $20,000 to replace the stolen items. Suppose it can buy an insurance policy for $500 that would fully reimburse it for the amount of the loss. a) Should the household buy this insurance policy? b) Should it buy the insurance policy if it cost $1,500?

Answer 1

Answer:-

(A) If you remain uninsured then you face lottery in which you have 10% chance of $80,000 in valuables and a 90% chance of $100,000 in valuables.so The expected value of valuables is $98,000.

If you purchase the insurance policy for $500 then with no burglary you have( $100,000- $500) = $99,500 and with a burglary you have ($100,000 -$500-$20,000+$20,000) = $99,500. The expected value if you purchase the policy is therefore $99500. so the expected value at year end with insurance exceeds the expected value at year end without insurance then you should buy the insurance for $500.

(B) we should set up a table that shows the possible outcomes. The values in the table represent the value of valuables at year end depending on the corresponding row and column situations. so for $1500 cost

	Burglary	No burglary	Expected value
No insurance	$80000	$100000	$98000
Insurance	$98500	$98500	$98500
Probability	0.10	0.90

so if you have cost $1500 then you have $500 better off with the insurance policy