Consider a household that possesses $$200,000$ worth of valuables such as jewelry. This household faces a $0\mathrm{.}02$ probability of a burglary, where she would lose jewelry worth $$50,000.$ Suppose it can buy an insurance policy for $$15,000$ that would fully reimburse the $$50,000.$ The household's utility function is

$U(x)=2x^{0\mathrm{.}5}$

Should the household buy this insurance policy?

The household should not buy this policy.

What is the actuarially fair price for the insurance policy?

If the insurance is fair, then the cost of the insurance policy is $$1000\mathrm{.}00.($Enter your response rounded to two decimal places.$)$

What is the most the household is willing to pay for an insurance policy that fully covers it against loss?

The most the household would pay for such a policy $($p$)$ is $$.($Enter your response rounded to two decimal places.$)$