Question

you currently have a wealth of $70,000 and are offered a chance to invest in a risky company when there's a 30% chance that you'll gain $30,000 next year and a 70% chance that the company will fail and you'll lose $20,000. your rates for the utility level are as follows: 2.0 for $20,000 wealth, 3.0 for $30,000 wealth, 6.0 for $50,000 wealth, and 9.0 for $100,000 wealth. what is your expected utility? 6.9 1.6 2.4 8.1

Answer 1

The expected utility in this case is 5.1, which is the sum of the expected utilities for gaining and losing money.

Step-by-step explanation:

To calculate the expected utility, we need to multiply each possible outcome by its probability and the corresponding utility level, and then sum them up. In this case, we have two possible outcomes: gaining $30,000 with a 30% chance, and losing $20,000 with a 70% chance.

The expected utility for gaining $30,000 is: 0.3 * 3.0 (utility level for $30,000 wealth) = 0.9

The expected utility for losing $20,000 is: 0.7 * 6.0 (utility level for $50,000 wealth) = 4.2

Adding the expected utilities together: 0.9 + 4.2 = 5.1
The expected utility in this case is 5.1.