Question

you currently have $10,000 in total wealth and rate your current utility at 4.25. you are deciding if you should invest your money in your friend's automotive restoration business. there is a 50% probability that you will double your money, in which case your total utility will be 6. there is a 50% probability that your friend's business will fail and you will lose the entire $10,000 and your total utility will be 2.5. macmillan learning decisions involving uncertainty - end of chapter problem a. what is the expected utility of investing in your friend's company? expected utility: you b. if you are risk averse, should you take the gamble and invest in your friend's company? invest in your friend's company. c. would your answer to part b be different if there was a 75% chance that you would double your money by investing in your friend's businese?

Answer 1

The expected utility of investing in your friend's company can be calculated by multiplying the probabilities and utilities of each outcome. If you are risk averse, you should not invest if the expected utility is lower than your current utility. If the chance of doubling money increases to 75%, the expected utility may become higher than your current utility, making investment worthwhile.

Step-by-step explanation:

The expected utility of investing in your friend's company can be calculated by multiplying the probability of each outcome by its corresponding utility, and summing up the results. For this case:

1. 50% chance of doubling money and having a utility of 6 (0.5 × 6 = 3)
2. 50% chance of losing entire money and having a utility of 2.5 (0.5 × 2.5 = 1.25)

Adding up the results, the expected utility of investing in your friend's company is 3 + 1.25 = 4.25.

If you are risk averse, you would not take the gamble and invest in your friend's company because the expected utility (4.25) is lower than your current utility (4.25).

If there was a 75% chance of doubling your money by investing in your friend's business, the expected utility would be:

1. 75% chance of doubling money and having a utility of 6 (0.75 × 6 = 4.5)
2. 25% chance of losing entire money and having a utility of 2.5 (0.25 × 2.5 = 0.625)

The expected utility in this case would be 4.5 + 0.625 = 5.125. As it is higher than your current utility (4.25), you would consider investing in your friend's company.