Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
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 for x ≥ 1 is a proper PDF
F ( x ) for this PDF
E ( x ) for this PDF using the result of part (c)
- The proof that Markov’s inequality holds for this function
(f)
To determine
- The proof that
f ( x ) = x 2 3 for − 1 ≤ x ≤ 2 is a proper PDF
- The value of
E ( x )
- The probability that
− 1 ≤ x ≤ 0
- The value of
f ( x | A ) , where A is the event 0 ≤ x ≤ 2
- The value of
E ( x | A )
- Intuitive explanation of the results
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
1. A standard model of choice under risk is Expected Utility Theory (EUT) in which
preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities
(P1, P2, ..., Ps) with Eps = 1 are represented by the function
L
S
(a) What does it mean to say that a function represents the consumer's prefer-
ences?
Σpsu(xs)
Choice 1
8=1
(b) State and briefly comment on the axioms required for the EUT representation.
(c) Consider the following experiment of decision making under risk in which sub-
jects are asked which lottery they prefer in each of the following two choices:
Lottery B
0 with prob. 0.01
10 with prob. 0.89
50 with prob. 0.10
Lottery D
Choice 2
Lottery A
0 with prob. 0
10 with prob. 1
50 with prob. 0
Lottery C
0 with prob. 0.90
10 with prob. 0
50 with prob. 0.10
Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in
Choice 2. Assume that utility of zero is equal to zero and illustrate why it is
not possible to reconcile these experimental…
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…
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…
Chapter 2 Solutions
Microeconomic Theory
Knowledge Booster
Similar questions
- 1. Use budget constraints to express consumption levels, ct and ct+1. (Hint: Use income conditions given above in the budget constraint. Notice that there are two possible states in the second period.)2. Rewrite the utility maximization problem as choosing the optimal at alone. (Hint: Replace ct and ct+1 in the utility function with your answers from point 1. Use probabilities to derive the expected value in the utility function. Remember that a random variable that takes values x1 in state one with probability p and x2 in state two with probability 1 − p has the expected value E [x] = p.x1 + (1 − p).x2)3. Derive the first order condition and find the optimal value of savings, at. (Hint: The only control (choice) variable is at)4. Does household accumulate precautionary savings to self-insure against the scenario of low income in the second period? Why or why not?arrow_forwardWhat are the Least Squares Assumptions? also explain the usage of these Assumptions?arrow_forward1. Can you define Probit Model using the Latent Utility Approach, if all the identification restrictions for the model? Justify why we need to impose the identification restrictions.arrow_forward
- 2. A small college is trying to predict enrolment for the next academic year. Thevice president for business states that enrolment has tended to follow apattern described by E = 18,000 – 0.5P, where E denotes total enrolment andP is yearly tuition.a) If the school sets tuition at €20,000, how many students can it expect to enrol?b) If the school wants to maximize total tuition revenue, what tuition should itcharge?c) As the vice president for business, what tuition would you recommend? Explainbriefly.d) Due to a strong post-COVID-19 recovery, the income conditions in the regionimprove substantially. Explain in one sentence how this could affect the college’senrolment pattern and the enrolment level maximizing its tuition revenue.arrow_forwardSubject: Economics 1. Suppose you have two independent unbiased estimators of the same parameter, θ, say θandθ, with different variances, v ∧ 1 ∧ 2 1 and v2. What linear combination, = cθ∧ 1θ∧ 1+ c2θ∧ 2 is the minimum variance unbiased estimator of θ?arrow_forwardPopulation of Fish in a Lake A lake is stocked with 100 fish. Let f(1) be the number of fish after i months, and suppose that y = f(1) satisfies the differential equation y' = .0004y(1000 – y). Figure 7 shows the graph of the solu- tion to this differential equation. The graph is asymptotic to the line y = 1000, the maximum number of fish that the lake can support. How fast is the fish population growing when it reaches one-half of its maximum population? 1000 800 600 400 200 10 15 Figure 7 Growth of a fish population.arrow_forward
- Hello. May I ask how did you get the values? Were those only assumed values? Can you also explain how did you make the normal form thoroughly?arrow_forwardWhat is meant by dummy variable and how dummy variables are constructed?arrow_forward8. Which of the following best describes the linear probability model? The model is the application of the linear multiple regression model to a binary dependent variable The model is an example of probit estimation The model is another form of logit estimation The model is the application of the multiple regression model with a binary variable as at least one of the regressors OOarrow_forward
- A food truck vendor averages 150 tacos sold when the price per taco is $4. A study shows that the average number of tacos sold will increase by 25 facos for every $1 that the price per taco is lowered. Which equation models the food truck's average sales in dollars, s, in terms of the price per taco, x ? A 325x + 250 3 = - 25x + 250 3 = 25x + 250x 3 = - 25x + 250x P Type here to search 315 P 1/28/20 Esc Delete CD & 2 8 Backspace Num Lock R T. Y P Home D K L Enter Z. B Shift End Alt Pgup Alt Ctrl Home PgDn End deapad S rivacy Shutter on Webcam Deliveryarrow_forward4. Verify that a homogenous function has IRS, CRS or DRS depending on whether the degree of the function satisfies y> 1, y = 1, or y< 1.arrow_forwardConsider a utility maximizing consumer who generates utility according to the following 1 utility function: U=Vx +y where x is the quantity of x consumed and y is the quantity 2 of y consumed. Let the price of x, price of y and income be noted as p, Py, and M, respectively. Set up the utility maximizing Lagrangian and derive the Marshallian demand functions. a Explain the difference in what we is being tested when we check the first order conditions and the second order conditions for a maximum (intuitively, not just the math). Derive the indirect utility function and the expenditure function. Derive the Hicksian demand equations without going through the expenditure minimization process. b. C. d. Let income = $8, p,=$.25 and p,=$1. What are the quantity demanded of x, and у? Draw the consumer choice graph and illustrate the situation in part e. Use the E. х, %3D f. graph to illustrate the income and substitution effect stemming from a change in the price of x to $.50. Use the actual…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you