Alvin's utility function is U = W. Barry's utility function is U = W2. Carl's utility function is U = W0.5. Each has wealth of only $100. An investment of that $100 has a 10% chance of netting $1,000 and a 90% chance of netting a loss of that $100. Who among the three will make the investment?
What will be an ideal response?
Carl's expected utility is (0.1 ? 1,0000.5 ) + (0.9 ? 00.5 ) = 3.16. This is less than his current utility of 10. He will not make the investment. Alvin's expected utility is(0.1 ? 1,000 ) + (0.9 * 0 ) = 100. This equals his current utility of 100. Barry's expected utility is (0.1 ? 1,0002 ) + (0.9 ? 02 ) = 100,000. This exceeds his current utility of 10,000. Barry is risk loving and will make the investment. Carl is risk averse; he will not. Alvin is risk neutral; the investment is a fair game, and he is indifferent about making the investment.
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