ider the utility function U(r, y) = r + 2y. Derive the two Marshallian demand functions for goods x and y. Are the above demand functions homogeneous? Yes/no, justify your a Derive the two Hicksian demand functions for goods z and y.

ider the utility function U(r, y) = r + 2y. Derive the two Marshallian demand functions for goods x and y. Are the above demand functions homogeneous? Yes/no, justify your a Derive the two Hicksian demand functions for goods z and y.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.8P

See similar textbooks

Related questions

Q: Assume there is consumer, his utility function is u(x,y) = x0.5 + y, and his %3D budget constraint…

A: Given information U=X0.5+Y Px=$1, Py=$8, M=$40 After tax collection on good X price of good X…

Q: 3. Construct compensated demand functions for q and q2 for the utility function U = 2q,92 +91.…

A: Since the second part of the question asks for the elasticities for which we will need Marshallian…

Q: Suppose the utility function of a person consuming two commodities X and Y with income borr 600 is…

A: Given: Maximize U= 2XY Budget= Birr 600 PX = Birr 20 PY = Birr 40 The budget line of the person will…

Q: Consider the utility function U(x, y) = min{x, 2y} Find (a) the Marshallian demand functions for x…

Q: Given the utility function and budjet constraint. Z=3X1+X1X2+2X2 , M=P1X1 + P2X2. 1. Obtain…

A: Marshallian demand curve equations are attained by maximizing the utility with the budget(income) as…

Q: True or False: (a) If a consumer spends her entire income, then she has a strictly monotone utility…

A: NOTE: .We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Consider the indirect utility function: V(P1» P2, m) = (m +p, + p,)² - 4p,p2 4p,P2 Derive the…

Q: Let a1 and a2 denote the quantities consumed. The consumer's preferences are represented by the…

A: We have Utility function U(x1,x2)=x1+x2 ... (1) Consumer income m=100 Price of good 1:…

Q: Suppose that we can represent Pauline's preferences for cans of pop (the x-good) and pizza slices…

A: The Hicksian demand function or the compensated demand function is the quantity demanded of a good…

Q: Suppose that Obdulia reflects the following preferences: U(x, y)= ln(x) + y, if Obdulia's initial…

A: Given information U=ln(X)+Y M=15000 Px=100 Py=150 P'x=80

Q: Utility function of Mr. Haroon is given by Find the optimal quantities of the two commodities (X…

A: Given: Price of commodity X- Rs 5 per unit Price of commodity Y- Rs 10 per unit The income of Mr.…

Q: mand functions for the following preferences: 1. Perfect Substitutes 2. Perfect Complements…

A: x and y goods are the perfect substitutes for each other. so the demand curve will be sloping…

Q: Bonus: On homework 2 you found the Marshallian Demands for the utility function U(x,y) =0.5x + 5ln y…

A: We are going to find Marshallian and Hicksian demand to answer this question.

Q: 1. Assume you spend your entire income on two goods X & Y with prices given as Px & Py,…

A: Note: You have uploaded multiple question at a time. We shall answer only the first one. If you seek…

Q: Thirsty Ed drinks only pure spring water, but he can purchase it in two differentsized containers:…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: Consider the following expenditure function E(P,U) = p^ py Derive the Hicksian demand functions.…

Q: Let a consumer's preferences are reflected by a Cobb-Douglas utility function i.e., UXLX) = Xf x5 BM…

A: X1= αMP1 Question1: Price elasticity of good X1: = dX1dP1*P1X1 =-αMP12 * P1X1= -αMP1(αMP1) = -1…

Q: A consumer has the following indirect utility function: u (x1, x2) = − 1/ x1 − 1 /x2 1.…

A: 1. Walrasian Demand is also called Marshallian Demand. It depicts, given the prices of the goods and…

Q: The demand for video recorders has been estimated to be linear and given by the demand relation Qy =…

Q: Suppose david faces a new utility such as U(X, Y)=25x0.2 Y0.75 for consuming commodity X and Y, redo…

A: Since nothing is specified, we will answer only the first question E. Please resubmit the question…

Q: the Marshallian Demands for the utility function U(x,y) =0.5x + 5ln y a) For this utility function…

A: Utility function : U(x ,y) =0.5x + 5ln y Budget Constraint : Px(x) + Py(y) = M

Q: Consider a utility maximizing consumer who generates utility according to the following utility…

A: Given Utility function: U = ln(k)+s .... (1) Price of good k is pk and price of good s is…

Q: If the price for good x1 is p1 = 2, the price for good x2 is p2 = 3, and Kramer’s available income…

A: Given; Price of x1; P1= 2 Price of x2; P2=3 Kramer's income; m= 16 Kramer's utility function;…

Q: sider the utility function U(r, y) = r +2y. Derive the two Marshallian demand functions for goods a…

Q: 10. Ken has a utility function for tennis rackets (X) and tennis balls (Y) of the form…

A: MACRO ECONOMICS- Macro economics is concerned with the problem of the economy at an aggregate level,…

Q: Please answer all (a) - (e), whether they are True or False:

A: Since you have posted multiple questions, we will answer the first three questions for you. If you…

Q: 2. Consider the following utility function, u (21, 22) = x{x", where y e (0, 1) %3D (a) Derive the…

A: u( x1,x2)=x1γ x21-γ, where γ∈(0,1) Hicksian Demand Function Through minimize expenditure function.…

Q: assume that both X and Y are goods s.) Consider a person whose preferences can be represented by the…

A: We first define the properties of each type of good in terms of price elasticity as well as income…

Q: Suppose the utility function for goods x and y is given by utility = U(x, y) = xy + y. a. Calculate…

A: Answer a) Uncompensated demand Function for the two goods. Utility Function U(x,y) = xy + y Budget…

Q: Question 2 There are two goods, apple and banana, whose quantities are denoted by X, and Xz and…

Q: sider the utility function U(r, y) +2y. %3D Derive the two Marshallian demand functions for goods a…

Q: Pankti consumes two goods, x and y. Her utility function is given by U(x, y) = ln(xy). (a) Suppose…

A: Pankti consumes two goods, x, and y. Let, the utility function be- U(x,y) = In(xy) a) If the income…

Q: Using one diagram, illustrate and explain the income and substitution effects of a price decrease of…

A: Law of demand in economics states that when price of any commodity change then keeping other factors…

Q: Assume you spend your entire income on two goods X & Y with prices given as Px & Py. respectively.…

A: Given that Marshallian demand function U = X2+Y2. Price of good X = Px and price of good Y = Py

Q: If the MRS is an increasing function of which of the following must be true. a. Preferences are…

A: IC (Indifference curve) shows the different agreement of two commodities between which a consumer is…

Q: If the demand function face by the consumer for good X is given by X=15+MP-120 Where X…

A: Total Effect = Substitution Effect + Income Effect Substitution Effect refers to that change in…

Q: A consumer has utility function U(21, 2) =4 +8 where z and zz are the two goods. Market prices are…

A: Since you have posted multiple questions, we will answer the first question for you. If you want any…

Q: Suppose i's preferences are represented by the following utility function: u=x-y.Which of the…

A: U = x-y

Q: Assume you spend your entire income on two goods X & Ywith prices given as Px & Py, respectively.…

A: Marshallian demand Function U = X2 + Y2 Budget line = Px+Py = m For Optimal Bundle MRSxy = Slope of…

Q: 3. Consider the following quasi-linear utility function U(x, y)=x+In y. Find the uncompensated…

A: Utility function: U(x,y) = x + ln y

Q: Let t = 3 The consumer has a preference relation defined by the utility function u(x, y) = −(t + 1 −…

A: The utility is the want the satisfying power of the commodity. It may differ from place to place or…

Q: Suppose a consumer’s utility from consuming the two goods x and y is given by: PHOTO a) Calculate…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 2. Find Hicksian demand by duality for utility function: u(x1,x2) = 2/x, + 4/x2

A: A consumer's Hicksian demand function or compensated demand function for a good is the quantity…

Q: Suppose a consumer’s utility from consuming the two goods x and y is given by: U(x,y)= x +…

A: (Q)Suppose a consumer’s utility from consuming the two goods x and y is given by: U(x,y)= x +…

Q: Consider the following Utility Function 1 3 U = q; q a) Derive the Hicksian demand functions. b)…

A: We are going to derive hicksian and marshallian demand function to answer this question. Note: Since…

Q: To calculate Hicksian demand (also compensated demand), income m" is used, which keeps the utility…

A: We need the new income, m', to be such that u(x(p1, m))=u(x(p1', m')) That is the new income should…

Q: wo goods X, and X2 and has a function given as: U = 0xfx% where 0 < a<1 and 0 is a constant. Assume…

A: In consumer theory, the expenditure (EMP) minimization problem is the dual of utility (UMP)…

Q: "Two goods, A and B are perfect substitutes with prices $PA and $PB respectively. The income of an…

A: In ordinary cases when indifference (IC) curve is convex to the origin, the consumer’s equilibrium…

Q: 3.1 Slutsky's equation relates the Marshallian demand function to the Hicksian demand func- tion,…

A: Note :- Since you have posted a question with multiple sub parts we will here Answer 3.1 part of…

Question

PT.
sider the utility function
U(r, y) = x3 + 2y.
Derive the two Marshallian demand functions for goods x and y.
Are the above demand functions homogeneous? Yes/no, justify your ansv
Derive the two Hicksian demand functions for goods a and y.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?
The consumer has an incom Mand a utility function of the form u (x1; x2) = aInx1 + (1 - a)Inx2 If the prices of the two goods are given by p1 and p2, derive the Hicksian demand functions for a given utility level U: Derive the expenditure function. Using the concept of duality, derive the indirect utility function.
Consider an individual with the following utility function: Derive step-by-step both corresponding Hicksian demand functions depending on the different prices (P₁, P2) and a fixed utility level u. The equation given In picture.do This in 10 minutes.
Consider the following indirect utility function:ʋ(P,y) = y(P1r + P2r)-1/r Wherer = ρ/(ρ-1, Pi are parametric prices, and y is the consumer’s budget a) Solve for the Marshallian demand functions xi (P, y) and verify that these functions are homogenous of degree zero (Hint: you can also use Roy’s Identity). b) Derive the Hicksian demand functions xih (P,u)
the Marshallian Demands for the utility function U(x,y) =0.5x + 5ln ya) For this utility function calculate the Hicksian demand functions for x and y.b) Use your Marshallian and Hicksian demand functions to calculate the partial derivative of both Marshallian and Hicksian demand for x with respect to px and the partial derivative of Marshallian demand with respect to income.c) Use your answers for (b) to verify the Slutsky equation
Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y 2 , derive the Hicksian demand function for good Y.
Consider a consumer with utility function u(x1, x2) = α_1x_1^( 2) + α_2x_2^( 2) where α1 > 0 and α2 > 0. Assume that p1, p2 > 0.? (a) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (b) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utility
Suppose a consumer’s utility from consuming the two goods x and y is given by: PHOTO a) Calculate the uncompensated (Marshallian) demand functions for x and y respectively. b) Calculate the consumer’s indirect utility function for x and y c) Compute the compensated (Hicksian) demand functions for x and y d) Determine the uncompensated own- and cross-price elasticities. e) Determine the compensated own- and cross-price elasticities.
Consider an individual whose preferences are represented by the utility function U(x1,x2) = min {3x1+x2 , x1+3x2}. For this individual, Calculate her demand function X1* (P1, P2,m) Calculate her own price, cross price, and income elasticities at X1*(1, 2, 24) and at X1*(1, 4, 24). Based on these, can you say the goods 1 and 2 are (gross, or Marshallian) complements or substitutes?
Amy chooses between two goods, x and y, with prices px and py, respectively. She has an income I and her preferences are represented by the utility function U(x, y) = √x + y. 1. Assuming that an interior solution exists to the constrained utility maximization problem, derive Amy ’s Marshallian demand function for each of the two goods. Are both goodsnormal? Explain 2. Find the indirect utility function, V (px, py, I). 3. Derive Amy’s Hicksian demand function for each of the two goods and the expenditure function. Compare the Marshallian demand for good x and the Hicksian demand for good x. Arethese different functions? If so, why? If not, why not? 4. Suppose that I = 100, px = 1 and py = 2. How much of good x and good y will Amy optimally choose? 5. Now the price of good x rises to px = 2, while income (I = 100) and the price of good y, py = 1, remain unchanged. What quantities does Amy buy and what is her resulting utility?Illustrate graphically 6. Find the income and substitution…
The individual's utility is given by the following function: ?(?,?)=−1/?−1/? a) Calculate the Marshallian demand functions for both goods.b) Determine whether x and y are gross substitutes or gross complements. Is there any asymmetry in the gross definitions?c) Without actually doing so, determine whether x and y are net substitutes or net complements. Please explain.
Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand Functions