A farmer believes there is a 50–50 chance that the next growing season will be abnormally rainy.His expected utility function has the formexpected utility =;In Y NR +;In 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 incomeprospects:CropYNRYRWheat$28,000$10,000$15,000Corn$19,000Which of the crops will he plant?b. Suppose the farmer can plant half his field with each crop. Would he choose to do so? Explainyour result.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 whichcosts $4,000 and pays off $8,000 in the event of a rainy growing season-cause this farmer tochange what he plants?

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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 1. expected utility ==In Y NR +5! In YR, 2 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-which is available to farmers who grow only wheat and which costs $4,000 and pays off $8,000 in the event of a rainy growing season-cause this farmer to change what he plants?

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 1. expected utility ==In Y NR +5! In YR, 2 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-which is available to farmers who grow only wheat and which costs $4,000 and pays off $8,000 in the event of a rainy growing season-cause this farmer to change what he plants?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

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