1. Uncertainty and Risk (40 points). Consider the project of constructing a dam. The only person affected by this project is a farmer, with utility U(I) where I is income. There are two possible contingencies: it rains a lot (\"wet\") or it does not rain a lot (\"dry\"). With the dam, income is $200 if \"wet\" and $150 if \"dry\". Without the dam, income is $180 if \"wet\" and $50 if \"dry\". The probability of raining a lot is 50%. (a) What is the change in the expected net benefits (e.g., the expected surplus) if the dam is constructed? (10 points). (b) Is the project risk-increasing or risk-reducing? Motivate your answer. (10 points). (c) Assume that the farmer is risk-neutral. What is the option price (OP) for the farmer? (10 points). (d) Assume that the farmer's utility is U(I) = In(/). What is the option price (OP) for the farmer? (10 points)