Final answer:
To calculate the expected utility for an individual with actuarially fair and full insurance, we first find the fair premium based on expected losses. The premium is $17,000, making the consumption $183,000 after insurance. Thus, the expected utility is U = 183,000.
Step-by-step explanation:
The question presents a scenario of calculating expected utility for an individual with a probability of incurring accidents and a utility function U = C, where C represents consumption.
Since the individual has a 20% chance of a $75,000 accident, a 20% chance of a $10,000 accident, and a 60% chance of no accident, and the insurance is actuarially fair, the expected utility can be computed by multiplying the probability of each outcome by the utility that results from the income after the accident minus the insurance premium that exactly compensates for the expected loss.
Calculating Expected Utility with Actuarially Fair and Full Insurance:
Let's find the fair and full insurance premiums first. The individual faces an expected loss of [(0.20 * $75,000) + (0.20 * $10,000)] = $17,000. Therefore, an
actuarially fair premium
for full insurance would also be $17,000.
With full insurance, the individual's consumption will always be the income minus the premium: $200,000 - $17,000 = $183,000.
The expected utility with actuarially fair and full insurance would simply be U = 183,000 since there are no other uncertainties once the insurance is purchased.