In the first problem set, you solved the consumer problem for the utility function u(x₁, x₂) =₁+2√2. Throughout this question, assume that the consumer has the same utility function,and that wealth is high enough to ensure an interior solution to the utility maximizationproblem.(a) Verify that the Slutsky equation holds for cross-price changes (i.e. for Good 1 when p2changes, and for Good 2 when p₁ changes).(b) Suppose that the price of Good 1 increases from p₁ to p₁ while the price of Good 2remains unchanged. Let u and u¹ respectively denote the utilities before and after thischange. Using the Hicksian demand function from the first problem set, write expressionsfor the equivalent and compensating variations in terms of prices and utilities uº andu¹. How do they compare?(c) Instead of a change in p₁, suppose that the price of Good 2 increases from p2 to p2while the price of Good 1 remains unchanged. Write expressions for the equivalent andcompensating variations. How do they compare? Explain why the comparison does ordoes not differ from that in part (b).

Answered: Image /qna-images/answer/bf6d404c-8d59-426c-aaa3-e777aeadbc58.jpg

In the first problem set, you solved the consumer problem for the utility function u(x1, x₂) = ₁+2√2. Throughout this question, assume that the consumer has the same utility function, and that wealth is high enough to ensure an interior solution to the utility maximization problem. (a) Verify that the Slutsky equation holds for cross-price changes (i.e. for Good 1 when p2 changes, and for Good 2 when p₁ changes). (b) Suppose that the price of Good 1 increases from p₁ to p₁ while the price of Good 2 remains unchanged. Let uº and u¹ respectively denote the utilities before and after this change. Using the Hicksian demand function from the first problem set, write expressions for the equivalent and compensating variations in terms of prices and utilities uº and u¹. How do they compare? (c) Instead of a change in p₁, suppose that the price of Good 2 increases from p2 to p/2 while the price of Good 1 remains unchanged. Write expressions for the equivalent and compensating variations. How do they compare? Explain why the comparison does or does not differ from that in part (b).

In the first problem set, you solved the consumer problem for the utility function u(x1, x₂) = ₁+2√2. Throughout this question, assume that the consumer has the same utility function, and that wealth is high enough to ensure an interior solution to the utility maximization problem. (a) Verify that the Slutsky equation holds for cross-price changes (i.e. for Good 1 when p2 changes, and for Good 2 when p₁ changes). (b) Suppose that the price of Good 1 increases from p₁ to p₁ while the price of Good 2 remains unchanged. Let uº and u¹ respectively denote the utilities before and after this change. Using the Hicksian demand function from the first problem set, write expressions for the equivalent and compensating variations in terms of prices and utilities uº and u¹. How do they compare? (c) Instead of a change in p₁, suppose that the price of Good 2 increases from p2 to p/2 while the price of Good 1 remains unchanged. Write expressions for the equivalent and compensating variations. How do they compare? Explain why the comparison does or does not differ from that in part (b).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.11P

See similar textbooks

Similar questions

It is given that a typical consumer has a well-behaved preference structure for his consumption bundle, which includes only two goods, A and B. Further, assume that commodity A is normal and commodity B is Giffen. By keeping commodity A on the x-axis and commodity B on the y-axis, you are required to show the price decomposition for commodity B when $PB decreases exogenously relative to $PA.
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?
If we observe a consumer choosing (x1, x2) when (y1, y2) is available onetime, are we justified in concluding that (x1, x2) (y1, y2)?
1- A consumer who starts (i.e. has an endowment) at point B, and has preferences shown by IC1, will want to borrow. Select one: True False 2-Assuming a mix of present and future consumption is preferred, ANY consumer who starts (i.e. has an endowment) at point A will gain utility from a rise in interest rates. Select one: True False 3-A consumer who starts at point B will want to borrow, but as little as possible in order to minimise the cost of interest. Select one: True False 4-If a consumer starts at point A, and then receives extra income in the present, this would appear as an outward shift of the budget constraint. Select one: True False
Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8logx2+ 0.72logx3 incomes x1 , x2, x3 in the next three years. This is an example of (A) expected value; (B) quasi-hyperbolic utility function; (C) standard discounted utility; (D) none of the above.
For a > 0, consider a consumer whose utility function amounts to u(x1, x2) = − exp(−ax1x2). Can you take first order conditions to solve the utility maximization problem? Explain your argument. Next solve the utility maximization problem, and derive Marshallian demands and the indirect utility function. Given your calculations, state and use the duality theorem to find the expenditure function and Hicksian demand Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
A typical consumer has a well-behaved preference structure for his consumption bundle which includes only two goods, A and B. assume that commodity A is normal and commodity B is inferior. By keeping commodity A on the x-axis and commodity B on the y-axis you are required to show the price decomposition for commodity B when $PB increases exogenously relative to $PA. Please Answer the question by using well labelled diagrams
By using the expected utility theory approach with u(x)=x2, choose the optimal decision for three different possible outcomes with probabilities p(ω1)=1/2, p(ω2)=p(ω3)=1/4, rewards R(d1,ω1)=£49,R(d1,ω2)=R(d1,ω3)=£25, R(d2,ω1)=£36,R(d2,ω2)=£100,R(d2,ω3)=£0, R(d3,ω1)=£81,R(d3,ω2)=R(d3,ω3)=£0
If the consumer thinks that (x₁,x2) is at least as good as (y₁.42) and that (y₁y2) is at least as good as (x₁,x2), we can conclude that (look at the following options)
Show that a decision maker who has a linear utilityfunction will rank two lotteries according to their expectedvalue.
Consider two treatments. Treatment 1 saves one year of life at a cost of $10,000. Treatment 2 saves ten years of life at a cost of $1,000,000. Which treatment is more cost-effective? Why? Consider two treatments. Treatment 1 saves six years of quality adjusted life at a cost of $90,000. Treatment 2 saves three years of quality adjusted life at a cost of $60,000. Which treatment is preferred from a cost utility analysis perspective? Suppose Jay has been experiencing back pain and that there are two options for back pain: Treatment Regimen Total Cost Pain Reduction Do nothing $0 0 units Cortisone injections $600 30 units Calculate the ICER between cortisone injections and doing nothing. Jay says he is willing to pay $10 for a per unit of pain reduction. Should he choose cortisone injections? Another treatment is discovered. It costs $700 and reduces pain by 25 units. Should he choose the new treatment?
Emma has a utility function U(x1, x2, x3) = log x1 + 0.8 log x2 + 0.72 log x3 over her incomes x1, x2, x3 in the next three years. This is an example of (A) expected value; (B) quasi-hyperbolic utility function; (C) standard discounted utility; (D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns? (A) preference for flflexibility; (B) context effffects; (C) time inconsistency; (D) intransitivity.