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= X?Y, derive the Hicksian demand function for good Y.

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= X?Y, derive the Hicksian demand function for good Y.

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 17SQ

See similar textbooks

Related questions

Q: Suppose a consumer has income m = 50 and p, = 11. U(x,x) = min {x, + 10, 2x, + 2x,} Find the…

A: Given information U(X1,X2)=min{X1+10,2X1+2X2) Where m=50 P1=11 P2=3 P2=8

Q: For each of the following, sketch a curve with the appropriate shape given the assumptions: a. An…

A: Indifference curve is the curve that shows a consumer’s satisfaction level or utility level in the…

Q: Bob enjoys cookies (x) according to the utility function U(x)=20x- 2 tx , where t is a parameter…

A: According to the envelope theory, if the exogenous variable changes, the direct effects of that…

Q: Katalin has the utility of U(x 1, x 2 ) = max{3x 1, 4x 2 } of purchasing products 1 and 2. Katalin…

A: According to the income effect, when the price of an item falls, it appears as though the buyer's…

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

Q: Utility maximization under constraint Lucas gets utility (satisfaction) from two goods, A and B,…

A: Given information Utility function of Lucas U=25[C-3+4D-3]-4+25 Lets take Price of C=P1 Price of…

Q: Suppose we know that the marginal utility of good 1 is: 4x1?x2?, from this we can conclude that: The…

A: If the individual really likes the good 1, then good 1 can any one type of good out of the following…

Q: Consider an endowment setting where (@1, 2) = (1, 1). Assume that x₁, x₂ are ordinary goods. x₁ is…

A: Inferior goods refers to the type of goods which has inverse relation with income of the consumer.…

Q: For the utility u(x1, 82) = x} +x} 3 verify the Slutsky equation

A: Utility function : U(x1 , x2 ) = x11/3 + x21/3 Let the prices be p1 & p2 Income be (m) Budget…

Q: A consumer’s preferences over two goods x and y are given by the utility function U(x, y) = min{αx,…

A: Consumption: It refers to the intake of goods and services in the economy. The more the consumption…

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: For the utility u(x1, 2) = xf + x verify the Slutsky equation

A: Utility function : U(x1 , x2 ) = x11/3 + x21/3 Let the prices be p1 & p2 Income be (m) Budget…

Q: How can I analyze and find the Marshallian Demands of the following Utility function?…

A: The perfect complements x1 and x2 would result in the perfect complements which would be consumed…

Q: Assuming a linear budget constraint, consider the following utility maximization problem: U (x1, x2)…

Q: ider the indirect utility function: V(P;» P2, m) = (m + p,+ p,)} - 4p;P, 2 4p;P2 Derive the…

Q: Cobb-Douglas utility maximization Given the two-good Cobb-Douglas utility function: и(х, у) %3…

A: Thank you for question. Since you have posted multiple sub parts in question. As per BNED policy we…

Q: Suppose that the consumer has a utility function u(a, b) = min (2a, b). The price of both goods is…

A: Recall that the utility function of the form u(a, b) = min(2a, b) represents goods which are perfect…

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: Suppose a consumer has utility function u(r1, r2) = + x. (a) Compute the Marginal Rate of…

A: (a) MRS = MUx1MUx2 = 12x112x2= x2x1 (b) To find: Optimal bundle: x(p, w) Equating MRS to price…

Q: Consider the following indirect utility function: v(P1, P2, m) = m(p,+ pz°)} Find the expenditure…

A: The indirect utility function shows us the maximum utility that can be derived when the consumer is…

Q: An economy described in an edgeworth box consists of 2 goods, namely X and Y and two consumers,…

A: Given, a two good and two-person economy: Utility functions: A: UA = XAYA B: UB = XBYB Endowments:…

Q: Given the indirect utility function: V(P,M)= MP¯ª P;, where P, and P, are the prices of two goods X,…

A: Given, Indirect utility function : V(P,M)=MP1-aP2a-1Where, P1 and P2 are the prices of two goods X1…

Q: Suppose a consumer in a competitive market maximises utility subject to a standard budget…

A: a) The assumptions required for the given conclusion is that: The law of demand is being followed,…

Q: Consider the following function describing the utility of a consumer: U(x1, x2, x3) = a1*ln(x1) +…

A: Consumer theory studies the behaviors of consumers, how consumer spends their limited income given…

Q: Utility maximization under constraint Lucas gets utility (satisfaction) from two goods, A and B,…

A: Given; Lucas's utility function:- U(A,B)=10A-2+B-2-2 Let; Price of good A=…

Q: A consumer is faced with the following utility function, U(x1 x2)=(xp1 1+xp2)1/p, where 0<p<1. The…

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 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: Suppose the consumer solves the following UMP: max (x1)^2 + (x2)^2 , s.t. p1x1 + p2x2 ≤ w where…

A: U(x1,x2) = max (x1)^2 + (x2)^2 Budget line is given as p1x1 + p2x2 ≤ w where p1,p2 > 0

Q: Suppose that you have the following utility for 1-). Apples (A) and Toys (T): U(A,T)=A"T". Suppose…

A: In microeconomics, a consumer's Hicksian demand function or compensated demand function for a good…

Q: Suppose there are 2,000 potential consumers in the Chestnut Hill market for tablet computers. All…

Q: uppose a person is endowed with Bundle A and the price of X is $10 and the price of Y is $1 on the…

A: When a person is endowed with Bundle A and the price of X is $10 and the price of Y is $1 on the…

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: Suppose that an individual receives utility from two goods X and Y and his utility function is given…

A: Let the budget constraint be; Pxx+Pyy=MU=-1x-1yMRS=1x21y2=y2x2At equilibrium;MRS=PxPyy2x2=PxPy

Q: A consumer is faced with the following utility function, U(x1 x2)=(xp1 1+xp2)1/p, where 0<p<1. The…

A: Utility function : U(x1 , x2 ) = (xp1 1+xp2)1/p Budget Constraint : p1x1 + p2x2 = m Firstly we…

Q: For example, the economy of a country can be explained by several models as follows: Consumer: The…

A: Macroeconomics is a sub-part of economics that is used to understand, the policies and fiscal…

Q: A consumer has the following indirect utility function: U∗(Px, Py, M) = M2/2PxPy 1. What is the…

A: We have given the indirect utility function U* (Px, Py, M) = (M2 / 2*Px*Py) Where Px is the price of…

Q: Consider the following indirect utility function: ʋ(P,y) = y(P1r + P2r)-1/r Where r = ρ/(ρ-1, Pi…

A: Roys's Identity states that : dϑdp1dϑdy= x1* where : ϑ = Inverse Utility function x* =…

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

Q: In a 2-good model, where the goods are denoted X, and x2, the consumer's utility 1 1 function is as…

A: A consumer's Hicksian demand function, also known as a compensated demand function, is the quantity…

Q: c. Please derive the expenditure function. If originally m = 8, px=1, py=4. d. Now px has increased…

A: Optimal consumption bundle is where MUx / MUy = Px / Py Where MUx = Marginal utility from good x and…

Q: Consider the figure above, which shows the budget constraint and the indifference curves of good…

A: A budget constraint is a term used in economics to describe all different combinations of goods and…

Q: 8. In a 2-good model, where the goods are denoted X1 and x2, the consumer's utility 1 1 function is…

A: We are going to find the Marshallian demand function to answer the part d) of this question.

Q: Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his…

A: As per the policy , since you have posted a question with multiple parts , I have solved the first…

Q: Problem 2 Joan has the following utility function: u(x, y) = 5x + 3y. (a) Find Jane's marshallian…

A: Answer in step 2. Mention D part separately.

Q: TRUE or FALSE. If the statement is correct, write TRUE on your answer sheet. If the statement is…

A: Indifference curve refers to the curve which shows different combinations of two goods which provide…

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: 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…

Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

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= X²Y², derive the Hicksian demand function for good Y.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 2 images

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

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 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)
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
Suppose U = 2X + Y, I = 20, Px = 2, and Py = 2. (a) Find Marshallian demand for X and Y . (b) What is Marshallian demand for X and Y if the price of X increases to 5? How much of the change in demand for X is the income effect and how much is the substitution effect? (c) How much is compensating variation for the price change described in part (b)? (d) How much is equivalent variation for the price change described in part (b)? ( Please solve all the subparts ASAP I will give you thumbs up . )
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.
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.
A consumers utility function is given by U(X1, X2)=Xa1X21-a where A>0, 0<a<1 A consumer also faces the prices p1 and p2 and has income level m. Equivalent variation and compensation variation are equivalent ways of evaluating welfare. Discuss
Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.
Suppose that the consumer has a utility function u(a, b) = min (2a, b). The price of both goods is equal to 1 and income is equal to 24.a. Find the optimal consumption bundle.Suppose price of the first good increases to 2.b. Find the Slutsky substitution and income effects for the first good.c. Find the Hicks substitution and income effects for the first good.
A consumer consumes two goods and her utility is form by Cobb-Douglas utility function. Her MRS is 0.9 * (q2/q1) Using these information find Marginal utility levels of first amd second goods
True or False:(a) If a consumer spends her entire income, then she has a strictly monotone utility function. (b)The condition that ‘the marginal rates of substitution equal the ratio of prices’ is necessary but not sufficient for a given bundle to be a Walrasian demand. (c) If U, V: R2 → R are such that U is a strictly increasing transformation of V then U and V must represent the same preferences. (d) If the substitution effect is negative (in response to a price increase) then we know the Walrasian demand for the good in question (in response to the same price increase) will also be negative. (e) A consumer’s utility is continuous and strictly monotone and when prices are given by p and income is I her Walrasian demand yields a utility of 7. Then, any bundle that yields a utility of at least 8 must cost more than I.