1.2. 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.

a. Calculate Vicky’s marginal utility of income for each income level. Is Vicky risk-averse?

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?

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Income $0 Total utility (utils) 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