Final answer:
The expected utility for an individual with actuarially fair full insurance and a utility function U = C^2/5 is derived from the certainty of consumption after paying an insurance premium that equals the expected loss. This calculation removes the uncertainty of accidents and provides a single utility value based on the post-premium income.
Step-by-step explanation:
The student is asking about the concept of actuarially fair insurance and the calculation of expected utility when such insurance is purchased, given a utility function. With an income of $200,000, the individual faces a 20% chance of a $75,000 accident and a 20% chance of a $10,000 accident, with a 60% chance of no accident. The utility function U = C2/5 specifies how the individual derives satisfaction (utility) from consumption (C).To calculate the expected utility, we must consider each possible outcome. With actuarially fair full insurance, the insurance premium will equal the expected loss. Therefore, the premium would be 0.2 x $75,000 (for the first accident type) + 0.2 x $10,000 (for the second accident type), which totals $17,000. The individual's consumption with insurance would then be $200,000 - $17,000 = $183,000, regardless of any accidents.The expected utility with insurance is therefore U = ($183,000)2/5. Since no probabilities are applied in this case (because the consumption is certain with full insurance), there is no need for a weighted average. This single number represents the utility level when the individual is fully insured at actuarially fair rates.To conclude, when the individual buys actuarially fair full insurance, the uncertainty of accidents is eliminated, and the utility is based on the certain consumption after paying the insurance premium.