A farmer believes there is a 50-50 chance that the next growing season will be abnormally rainy.His expected utility function has the form
Expected utility=1/2lnYnr+1/2lnYr,
where Ynr and Yr represent the farmer's income in the states of normal rain and rainy respectively.
a)suppose the farmer must choose between two crops that promise the following income prospects.
Crop:
Wheat Ynr=$28000 Yr=$10000
Corn Ynr=19000 Yr=15000
Which of the crops will he plant?
b)suppose the farmer can plant half his field with each crop.Would he choose to do so?
c)What mix of wheat and corn would provide maximum expected utility to this farmer?
d)Would wheat crop insurance-which is available to farmers who grow only wheat and which costs $4000 and pays off $8000 in the event of a rainy growing season-cause this farmer to change what he plants?