Final answer:
The expected utility of Billy the soccer player, given a utility function of U(c) = c^1/2 and injury probabilities, is calculated in utils, not monetary values. The answer options provided in the question are incorrect as they are currencies, while the correct expected utility should be represented in utils.
Step-by-step explanation:
The student is asking about calculating the expected utility of a soccer player with a given utility function and probabilities of income based on injury status. The utility function given is U(c) = c1/2, where c represents income. With a 0.9 probability of earning $25 million (not injured) and a 0.1 probability of earning only $10,000 (injured), the expected utility can be computed using the formula:
Expected Utility = Probability(not injured) * Utility(income not injured) + Probability(injured) * Utility(income injured)
In Billy's case:
Expected Utility = 0.9 * U($25,000,0001/2) + 0.1 * U($10,0001/2)
Expected Utility = 0.9 * ($25,000,000)1/2 + 0.1 * ($10,000)1/2
Such calculations usually yield a utility level in utils, which is a hypothetical unit of satisfaction. We do not convert expected utility to monetary values, like dollars, because utilities only reflect the level of satisfaction or preferences and are intrinsically subjective and non-transferable. As such, none of the answer options provided (a to e) are in the correct format of expected utility, as they are presented as currency values rather than utils.