A farmer believes there is an equal chance that the next growing season will be abnormally rainy. His expected return function has the form Expected return = 0.5lnYNR + 0.5lnYR where YNR and YR represent the farmer’s income in the states of “normal rain” and “rainy,” respectively. Suppose the farmer must choose between two crops that promise the following income prospects: Crop YNR YR Maize $14,000 $5,000 Cotton $9,500 $7,500 a) 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 Maize and Cotton would provide maximum expected utility to this farmer? d) Would Maize crop insurance, available to farmers who grow only Maize, which costs $2,000 and pays off $4,000 in the event of a rainy growing season, cause this farmer to change what he plants?
A farmer believes there is an equal chance that the next growing season will be abnormally
rainy. His expected return function has the form
Expected return = 0.5lnYNR + 0.5lnYR
where YNR and YR represent the farmer’s income in the states of “normal rain”
and “rainy,” respectively.
Suppose the farmer must choose between two crops that promise the following income
prospects:
Crop YNR YR
Maize $14,000 $5,000
Cotton $9,500 $7,500
a) 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 Maize and Cotton would provide maximum expected utility to this farmer?
d) Would Maize crop insurance, available to farmers who grow only Maize, which costs
$2,000 and pays off $4,000 in the event of a rainy growing season, cause this farmer to
change what he plants?
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