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Farmers face uncertainty over their earnings because rain is random. Let a farmer's yield be Y= 0 in the dry outcome and Y = 1 in the wet outcome. However, not all farmers are the same:   Probability(Y= 1) = p1= 2/ 3 if type = 1 p0= 1/ 3 if type = 0 All farmers are risk averse, with utility U(Y) = √Y as th

Farmers face uncertainty over their earnings because rain is random. Let a farmer's yield be Y= 0 in the dry outcome and Y = 1 in the wet outcome. However, not all farmers are the same:   Probability(Y= 1) = p1= 2/ 3 if type = 1 p0= 1/ 3 if type = 0 All farmers are risk averse, with utility U(Y) = √Y as th

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Farmers face uncertainty over their earnings because rain is random. Let a farmer's yield be Y= 0 in the dry outcome and

Y = 1 in the wet outcome. However, not all farmers are the same:

 

Probability(Y= 1) = p1= 2/ 3 if type = 1

p0= 1/ 3 if type = 0

All farmers are risk averse, with utility U(Y) = √Y as their utility function. Farmers know their type.

(a) Calculate each farmer's expected yield, E(Yi) =pI1 + (1- pi)0, expected utility ,E(Ui) =piU(1) + (1 - pi)U(0), and calculate the utility at E(Yi), U(E(Yi)), for i= 0, 1. Show these all on a graph with utility on the vertical axis and yield on the horizontal axis.

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