Consider a household that possesses $200 comma 000 worth of valuables such as jewelry. This household faces a 0.02 probability of a burglary, where she would lose jewelry worth $70 comma 000. Suppose it can buy an insurance policy for $15 comma 000 that would fully reimburse the $70 comma 000. The household's utility function is U(X)equals2Upper X Superscript 0.5. Should the household buy this insurance policy? The household ▼ should should not buy this policy.

The household should not buy the insurance policy.

Data and Calculations:

Value of jewelry = $200,000

Probability of a burglary = 0.02

Probability of no burglary = 0.98 (1 - 0.02)

Loss from burglary = $70,000

Value of jewelry after burglary = $130,000 ($200,000 - $70,000)

Cost of insurance = $15,000

Expected value of jewelry after the burglary = $198,600 {($200,000 x 0.98) + ($130,000 x 0.02)}

Expected loss after burglary = $1,400 ($200,000 - $198,600)

Thus, the household should not buy the insurance policy.  It will pay more insurance premium ($15,000) than the expected value of loss ($1,400).

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The household should not buy this policy

Explanation:

The probability of burglary is

$200,000 * 0.02 = $4,000

The insurance policy costs $15,000

The loss probability is lower than the cost of insurance policy

E(U) = (Jewelry Worth - Jewelry loss due to burglary + Insurance cover - Insurance policy cost) * 0.5

E(U) $200,000 - $70,000 + $70,000 - $15,000

E(U) = $

E(U) $430.11