Question: Certainty Equivalents. The certainty equivalent concept can be widely employed in the analysis of personal and business decision making. Indicate whether each of the following statements is true or false and explain why:

1. The appropriate certainty equivalent adjustment factor, \(\alpha\), indicates the minimum price in certain dollars that an individual should be willing to pay per risky dollar of expected return.
2. If \(\alpha \neq 1\), a certain sum and a risky expected return of different dollar amounts provide equivalent utility to a given decision maker.
3. If previously accepted projects with similar risk have \(\alpha\) in a range from \(\alpha=0.4\) to \(\alpha=0.5\), an investment with an expected return of $150,000 is acceptable at a cost of $50,000.
4. A project for which \(\mathrm{NPV}>0\) using an appropriate risk-adjusted discount rate has an implied \(\alpha\) factor that is too large to allow project acceptance.
5. State-run lotteries that pay out 50 percent of the revenues that they generate require players who place at least a certain $2 value on each $1 of expected risky return.

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