A farmer's tomato crop is wilting and he must decide whether to water it. If he waters the tomatoes or if it rains, the crop will yield $1000 in profits; but if the tomatoes get no water, they will yield only $500 in profits. The operation of the farmer's irrigation system costs $100. The farmer's goal is to maximize expected profits from tomato sales.
(a) If the farmer believes that there is a 50% chance it might rain, should he water his tomatoes?
(b) What is the maximum amount the farmer would be willing to pay a weather forecaster that predicts rain with 100% accuracy?
(c) How would your answer to part (b) change if the forecaster is only 90% accurate?