(Solution) - Vicky N Vestor is considering investing some of her money -(2025 Original AI-Free Solution)

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Vicky N. Vestor is considering investing some of her money in a startup company. She currently has income of $4,000, and she is considering investing $2,000 of that in the company. There is a 0.5 probability that the company will succeed and will pay out $8,000 to Vicky (her original investment of $2,000 plus $6,000 of the company's profits). And there is a 0.5 probability that the company will fail and Vicky will get nothing (and lose her investment). The accompanying table illustrates Vicky's utility function.
Income Total utility (utils)
$0???????????.. 0
1,000??????????. 50
2,000??????????. 85
3,000??????????. 115
4,000??????????. 140
5,000??????????. 163
6,000??????????. 183
7,000??????????. 200
8,000??????????. 215
9,000??????????. 229
10,000??????????. 241
a. Calculate Vicky's marginal utility of income for each income level. Is Vicky riskaverse?
b. Calculate the expected value of Vicky's income if she makes this investment.
c. Calculate Vicky's expected utility from making the investment.
d. What is Vicky's utility from not making the investment? Will Vicky therefore invest in the company?