Ronald has $18,000.But he is forced to bet it on the flip of a fair coin.If he wins he has $36,000.If he loses he has nothing.Ronald's expected utility function is .5x^.5  .5y^.5, where x is his wealth if heads comes up and y is his wealth if tails comes up.Since he must make this bet, he is exactly as well off as if he had a perfectly safe income of

A) $16,000.
B) $15,000.
C) $12,000.
D) $11,000.
E) $9,000.

Ronald's expected utility from the bet can be calculated using the given utility function, which simplifies to 0.5 * utility(wealth if win) + 0.5 * utility(wealth if lose). Given the outcomes, if he wins, he has $36,000 (x = 36,000), and if he loses, he has $0 (y = 0). The question implies that the utility of this risky situation is equivalent to the utility of having a certain income, which we are trying to find. Since the utility function is not explicitly given, we infer from the context that the certain income providing the same utility as the expected utility from the bet must be $9,000. This is because, in a fair coin flip with a 50% chance of doubling your money and a 50% chance of losing everything, the expected monetary value is the average of the two outcomes, but the utility of wealth typically increases at a decreasing rate. Therefore, the certain equivalent is less than the expected value of $18,000 due to risk aversion, making $9,000 the correct answer as it represents a level of wealth that Ronald would be indifferent to when compared to taking the bet, under the assumption of diminishing marginal utility of wealth.