Question

A certain household possesses R160000 worth of valuables with a 20% probability that there will be burglary that results in R70000 loss of valuables. the household can buy insurance for R15000 to fully cover against the loss from burglary. the utility function is given by U(X)=4X^0.5. what is the fair price of the insurance policy and what is the utility with insurance?

Answer 1

If there is a 20% probability that there will be burglary that results in R70000 loss of valuables, then the probable amount that can be lost is:

$70,000×0.2 = 14,000,$

which is the fair price of the insurance.

The utility with insurance is:

$U(X)=4×14,000^{0.5} = 473.29.$