A businessman is confronted with the following opportunity. He can invest $10,000 in a project that will either succeed wildly, fail miserably, or simply pay him back his $10,000. If wildly successful, the project will earn the businessman $110,000, but if it fails he will not get any money back.
i. If the businessman is risk neutral and he feels that there is a 1/2 chance of miserable failure, then what is the minimum probability of wild success required for him to want to invest in the project?
ii. Based on the probability that you derived in part i, explain what you know about the minimum probability that would be required by a risk averse businessman.
i. The expected payoff from the project is 0(0.5) + 10,000(1 - 0.5 - p) + 110,000p where p is the probability of wild success. Setting that equal to the $10,000 required investment gives a minimum probability of 0.05.
ii. The risk averse businessman would require a probability higher than 0.05, but exactly how much high cannot be derived without knowing his utility function.
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