Q1. 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 = 0.5lnYNR + 0.5lnYR Where  and  represent the farmers income in the state of ‘normal rain’ and ‘rainy’ respectively. Suppose the farmer must choose between two crops that promise the following income prospects Crop YNR YR Wheat $83,000 $10,000 Maize $83,000 $15000 What mix of wheat and maize would provide maximum expected utility to this farmer?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.8P
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Q1. 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 = 0.5lnYNR + 0.5lnYR

Where  and  represent the farmers income in the state of ‘normal rain’ and ‘rainy’ respectively. Suppose the farmer must choose between two crops that promise the following income prospects

Crop

YNR YR

Wheat

$83,000

$10,000

Maize

$83,000

$15000

What mix of wheat and maize would provide maximum expected utility to this farmer?

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