Consider a project of constructing a dam. The only person affected by this project is a farmer, with utility U(I) where $I is his income. There are two possible contingencies: it rains a lot (wet) or it does not rain a lot (dry). With the dam, his income is $200 if wet and $180 if dry. Without the dam, his income is $150 if Wet and $50 if dry. The probability of raining a lot is 50%.

(a) What is the expected surplus of the farmer?

(b) What is the standard deviation of income with the dam and without it?

(c) Assume U(I) = ln I. What is his expected utility in case the dam is not constructed? What is his option price? Compare its option price to its expected surplus.

(d) Assume U(I) = I² . What is his expected utility in case the Dam is not constructed? What is his option price? Compare its option price to its expected surplus.

(e) Calculate the option value for each case above. Compare them. How would you explain their difference?