In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/463/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is .
In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/463/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is .
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.9P
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![In class discussions about uncertainty we assumed that the utility levels in each
state of nature depends on c, which we might interpret as some aggregate con-
sumption and we expressed utility as U(c). Now, let's extend this to a case
where the utility level depends on consumption of two goods (this was the type
of utility we used mainly in this course).
Ben is a farmer who grows wheat and barley. However, his harvest is uncertain.
If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather
is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each
state of nature is U(w, b) = w¹/4b³/4, where w and b represent his consumption
of wheat and barley, respectively. Prices of wheat and barley are $1 in both
state of nature. The probability of good weather is T.
Question 3 Part a
Express Ben's expected utility function. (Hint: find Ben's optimal consumption
in each state of nature first)
Question 3 Part b
Let's assume = 0.5. Knowing that bad weather reduces his harvest, Ben
contemplates to purchase an insurance. He can purchase an insurance at a cost
of 20 cents for each $1 worth of coverage. So, for each $1 of insurance premium
he will receive $5 in bad weather. How much insurance would Ben purchase?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54045ccc-9971-4f02-985f-92b37937c185%2Fffa0f4bc-c157-4c2d-9252-051ee131052f%2Fg45bj9e_processed.png&w=3840&q=75)
Transcribed Image Text:In class discussions about uncertainty we assumed that the utility levels in each
state of nature depends on c, which we might interpret as some aggregate con-
sumption and we expressed utility as U(c). Now, let's extend this to a case
where the utility level depends on consumption of two goods (this was the type
of utility we used mainly in this course).
Ben is a farmer who grows wheat and barley. However, his harvest is uncertain.
If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather
is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each
state of nature is U(w, b) = w¹/4b³/4, where w and b represent his consumption
of wheat and barley, respectively. Prices of wheat and barley are $1 in both
state of nature. The probability of good weather is T.
Question 3 Part a
Express Ben's expected utility function. (Hint: find Ben's optimal consumption
in each state of nature first)
Question 3 Part b
Let's assume = 0.5. Knowing that bad weather reduces his harvest, Ben
contemplates to purchase an insurance. He can purchase an insurance at a cost
of 20 cents for each $1 worth of coverage. So, for each $1 of insurance premium
he will receive $5 in bad weather. How much insurance would Ben purchase?
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