Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 2, Problem 2.14P
(a)
To determine
The proof of
(b)
To determine
The proof of
(c)
To determine
The proof of
(d)
To determine
The proof of
(e)
To determine
- The proof that
f ( x ) = 2 x − 3 x ≥ 1
F ( x ) E ( x ) - The proof that Markov’s inequality holds for this function
(f)
To determine
- The proof that
f ( x ) = x 2 3 − 1 ≤ x ≤ 2
- The value of
E ( x )
- The probability that
− 1 ≤ x ≤ 0
- The value of
f ( x | A ) A 0 ≤ x ≤ 2
- The value of
E ( x | A )
- Intuitive explanation of the results
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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) = w¹/46³/4, 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 π.
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 π = 0.5. Knowing that bad weather…
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…
Chapter 2 Solutions
Microeconomic Theory
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