Consider two insurance companies. Insurance Company A insures homes in Florida against hurricane damage. Insurance Company B insures homes in Oklahoma against tornado damage. Suppose that in the next year, there is a 20 percent chance that Florida will be hit by a devastating hurricane. If it does, Company A will lose $3 million. If no hurricane hits Florida, Company A will earn $5 million in profits. Suppose that also in the next year, there is a 10 percent chance that Oklahoma will be hit by a devastating tornado. If it does, Company B will lose $2 million. If there is no tornado, Company B will earn $4 million in profits.Now suppose that these two companies are considering a merger. If they merge, they will split their profits or losses equally. The potential outcomes and their probabilities are as follows:72 percent chance of neither a hurricane nor a tornado occurring;18 percent chance of a hurricane occurring, but not a tornado;8 percent chance of a tornado occurring, but not a hurricane;2 percent chance of both a tornado and a hurricane occurring.Which of the following statements is true?The expected value of Company A's earnings is the same whether or not the companies merge.If Company A is risk averse, the company would prefer to merge.The expected value of Company B's earnings is $3,400,000 if there is no merger.

Question

Quizplus · Accepted Answer

The expected value of Company A's earnings remains the same with or without the merger due to the averaging effect of sharing profits and losses, which also makes the merger appealing to a risk-averse company. The calculation for Company B's expected earnings without a merger, considering the given probabilities and outcomes, indeed results in $3,400,000.

Consider Two Insurance Companies