# Economics

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A person must decide whether or not to proceed with a particular investment project. If the project succeeds, She will gain \$15 million. If the project fails, she will lose \$3 million. She estimates there is a 20% chance that the project will succeed and an 80% chance it will fail.

There is a consultant that could tell her with certainty if the project succeed or fail, but only for a fee. What is the most that she should be willing to pay the consultant for the information? Explain. Assume that she correctly estimated the probabilities of the projectâ€™s likely success and failure.

• Economics - ,

First, lets assume the person is RISK NEUTRAL -- where the change in utility from an expected dollar loss is equal to the change in utility from an expected dollar gain.

That said, this is simply a comparison of the expected return on the person's investment. Without the consultant, there is a 20% chance she gets 15M and an 80% chance she loses 3M.
E(return) = .2*15 - .8*3 = 0.6

If she hires the consultant, she will only make the investment if its a win. However, taking into account of the fee, her expected return must greater than what she could do without the consultant. So:
E(return) = .2*(15 - F) - .8*F - 0.6

I get the Fee=2.4