A farmer's payoff matrix per plot is:
Good Rain Year Bad Rain Year
Coffee 140 27
Corn 64 50
Probability 1/4 3/4
Assume that the farmer has no access to insurance and has to make the planting decision before she knows the outcome of the rain. The farmers utility for income is given by U(I)=I^(1/3).
Question 1. Which crop does the farmer plant? I know it has something do with expected value being higher.
Question 2. A device is invented that gives the farmer perfect information on the weather, how much would the farmer be willing to pay for the device? Is this similar to what value the farmer would be willing to pay for the information (which would be the difference)? Does it have to do with expected payoff again?
Question 3. Assume, the farmer receives less than a payoff of 50, but her son will send her enough money to ensure that her payoff is equal to 50, this should make her chose the more risky coffee shouldn't it?