Question

(Table: The Utility from Income for Alexandra) Use Table: The Utility from Income for Alexandra. Alexandra runs her own business, which generates an annual income of $40,000. Alexandra is considering developing a new product. The probability that the new product will increase Alexandra's income by $30,000 is 0.5, and the probability that it will reduce Alexandra's income by

1 pts
Tin
Atte
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$10.000 is 0.5. Alexandra's expected utility after developing her new product is _

The Utility from Income
for Alexandra
ncome
Total Utility
0
$10,000
200
$20,000
360
$30,000
500
$40.000
620
$50,000
720
$60,000
800
$70,000
860
• 500
• 1,360
• 860
• 680

Answer 1

The expected utility is calculated by weighting the utility of each outcome by its probability. In this case, the expected utility for developing a new product is 680.

Let's break down the calculation step by step:

1. Determine the Possible Outcomes:

- Successful new product: Income increases by $30,000.

- Unsuccessful new product: Income decreases by $10,000.

2. Calculate Utility for Each Outcome:

- For a successful new product (Income = $70,000): Refer to the table, and the corresponding utility is 860.

- For an unsuccessful new product (Income = $30,000): Refer to the table, and the corresponding utility is 500.

3. Assign Probabilities to Each Outcome:

- Probability of a successful new product: 0.5.

- Probability of an unsuccessful new product: 0.5.

4. Calculate the Weighted Utilities:

- Weighted utility for success:
`\(0.5 * 860 = 430\)`.

- Weighted utility for failure:
`\(0.5 * 500 = 250\).`

5. Calculate the Expected Utility:

-
`\(Expected \, Utility = Weighted \, Utility_(success) + Weighted \, Utility_(failure) = 430 + 250 = 680\).`

Therefore, the yields an expected utility of 680.