8.7 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
ln YNR ln YR, 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 YNR YR Wheat $28,000 $10,000 Corn 19,000 15,000 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?

Explain your result.

c. What mix of wheat and corn would provide maximum expected utility to this farmer?

d. Would wheat crop insurance, available to farmers who grow only wheat, which costs

$4000 and pays off $8000 in the event of a rainy growing season, cause this farmer to change what he plants?