Consider the following indirect utility function: V(p, 1) = II ₁(ail Jai Pi where 1 ai = 1, and ai #0, Vi 1. What's the demand function for x? (Hint: Take logarithm to both sides of the equation) 2. What's the original utility function? (Hint: If n is too abstract, let n = 2)

Consider the following indirect utility function: V(p, 1) = II ₁(ail Jai Pi where 1 ai = 1, and ai #0, Vi 1. What's the demand function for x? (Hint: Take logarithm to both sides of the equation) 2. What's the original utility function? (Hint: If n is too abstract, let n = 2)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: From economic theory, the willingness of a consumer to give up consumption of one commodity (X) in…

A: Consumer equilibrium refer to that situation of quantity consume where consumer receives maximum…

Q: If Sally's utility function is U= 12 (41) 0.5 + + 92. what is her Engel curve for g,? Let the price…

A: When goods and services are consumed by an individual, he/she derived benefits and satisfaction from…

Q: If u(x. y) is a utility function, then v(u) = u is a function that fulfills the monotonic…

A: Utility is an essential concept in economics which means the capability to satisfy various wants and…

Q: Derive the Marginal utility function from the following Total Utility function: TU = 200Q – 25Q² +…

A: Microeconomics studies the economic behavior of the individual unit such as a firm, a market, a…

Q: Calculate the marginal utility of the 4th scoop of ice cream. Express your answer without units…

A: Utility refers to the total amount of satisfaction derived from the consumption of a good or…

Q: Consider a consumer with a utility function U(X,Y) = 4vX + vỸ a) Explain what marginal utility is.…

A: Utility refers to the amount of satisfaction gained by an individual by consuming a good. Marginal…

Q: 2. Let your utility function be U (X, Y) = VX + VY. M This will give a demand function for X, X (Px,…

A: a. The demand function for Y is given by,…

Q: marginal utility for custard (U.). What is Amelia's marginal rate of substitution (MRS)? Give a…

A: Different utility levels of consumers are taken to be independent. This means that utility obtained…

Q: Kevin's utility function is given by U=3x+2y. Kevin's demand functions for X and Y graphically…

A: Substitute goods are used for each other. When price of one good increases, the consumer tends to…

Q: For the following utility function, u(x, y) =Vxy, (a) Verify that Shephard's Lemma:…

A: We are going to use marginal rate of substitution to find marshallian demand for both goods. Income…

Q: The following utility function is known as CES (constant elasticity of substitution) function: U (x,…

A: The utility function of an individual shows the level of satisfaction which can be derived from the…

Q: Given the assumptions of the law of diminishing marginal utility (exactly the same product consumed…

A: Marginal utility (MU) is defined as the extra utility or benefit a consumer gets by consuming an…

Q: Sarge's utility function is U(X1,X2)= X1*X2. If his marginal rate of substitution (MRS) is 3 and he…

A: The Marginal Rate of Substitution (MRS) determines the rate at which a consumer is willing to…

Q: QUESTION 3 Consider an individual who has a utility function U(X,Y) = 2x1/2)+ y(/2), the prices of…

Q: mer's utility function be f(q1,42,93) = 91q293, and her E 12+ P343. Consider qı + (p/pı)q2 =…

A: *Answer:

Q: Mr. Abdulah enjoys Coffee (K) and Tea (T), with the utility function U (K, T) = 3K + 4T. Question: -…

A: This is a perfect substitute case, as tea and coffee both are substitutes for each other and can…

Q: 1. A consumer has m dollars. The price of ₁ is p₁ dollars, and the price of P2 dollars. The consumer…

A: Utility function represents the relationship between utility and commodities or goods that are…

Q: todd is a cattle rancher in june and july he spent his clothing budget on jeans and cowboy hats.…

A: Utility means satisfaction.Marginal utility is the utility derived from the consumption of an…

Q: A utility function is called separable if it can be written as U(x, y) = U,(x) + U,(y), where U; >0,…

A: a) A separable utility function is given below: The calculation for the cross price derivative is…

Q: Given the following utility function and budget contraints: U(X,Y)= XY I= Px (X) + Py(Y) and given…

A: Utility refers to the satisfaction that is derived from consumption of goods. The utility function…

Q: Select the function that represents the marginal utility of X for the utility function: U = X³Y².

A: Marginal utility ,it may be defined as the satisfaction that is derived from the consumption of an…

Q: ?? =

A: Given : u=x1/2y1/2 M=120 Px=4 Py=1

Q: Is the utility function u = min{3x, 2y + 1} a monotonic transfor- mation of u = min {3x, 2y}? True…

A: A monotonic transformation of a utility function is a transformation that preserves the order of…

Q: %3D Ollie's utility function for Apples (A) and Bananas (B) is Cobb-Douglas: U = AB/6 a. Find…

A: MRS = (MUA/MUB) We have the utility function : U = AB/6 MUA = dU/dA = differentiate the utility…

Q: g. Suppose you are told that after the price increase, the highest level of utility Alex can enjoy…

A: The utility function is the mathematical relationship between the utility and different bundles of…

Q: Denver Bluff High School has $60,000 to spend on computers and other goods so its budget equation is…

A: We are going to find optimal bundle and marginal rate of substitution using utility maximisation…

Q: For a utility function for two goods, U(x,y), to have a strictly diminishing MRS (1.e., to be…

A: We are given that for a utility function to have a strictly diminishing MRS, the following condition…

Q: a) Choose X, and X, to max the utility fxn, U(X,X)=chX;+Q-a)h.X, st: M = P, X, + P,X; a) Consider a…

A: U( X1 , X2 ) = a ln X1 + (1-a) ln X2 M = P1X1 + P2X2 a.) Demand functions are derived by…

Q: At the local ski resort, the rates for a day on the slopes are as follows: 4-hour pass =$23…

A: Marginal utility is the additional benefit derived from consuming an additional unit of a good. The…

Q: Show whether or not the following utility functions are monotonic transformation of each other u =…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: For the Cobb-Douglas utility function the optimal choice of good i is independent of the price…

A: To check whether the statement is true or false, we will solve the utility maximization problem…

Q: briefly discuss and explain the two major approches for the analysis of utility

A: In economics, utility is a term referring to the overall satisfaction obtained from consuming a good…

Q: Please answer this question with steps thank you

A: Approach to solving the question: Detailed explanation: Examples: Key references:

Q: 1. Find the MRS (marginal rate of substitution) for the following Utility functions: 1. U(x, y)= 2.…

A: INTRODUCTION: The marginal rate of substitution (MRS) is the quantity of one good that a consumer…

Q: When John maximizes his utility, his consumption bundle is (2 burgers, 3 burritos) and his marginal…

Q: Refer to the following table. Suppose strawberries cost $1 and apples cost $2. SHow all the formulas…

A: Marginal utility is the change in utility with an additional unit of consumption. MU per dollar is…

Q: der a consumer with the utility function Ur.v) = xy where x is the quantity of good X and y is the…

Q: Sarge's utility function is U(X1,X2)= X1*X2. If his marginal rate of substitution (MRS) is 3 and he…

A: An utility function represents the preferences of a set of goods and services that give the consumer…

Q: Consider the following utility function: U(x, y) = = xy x-y (a) Derive the MRS of x to y. Show your…

A: The utility function is the mathematical relationship between the utility and different bundles of…

Q: When do we differentiate between using the formula MU(x) = TU(x) – TU(x – 1) and Marginal Utility =…

A: Utility means satisfaction. It is derived from the consumption of goods and services. The total…

Q: Suppose a consumer's utility function is: u(x1,x2) x1 + In (x2). The price of x2 is 2 and the ngel…

A: The curve that shows the consumption pattern of a good by a consumer as his/her income changes is…

Q: A KU student maximizes his sporting utility by playing Golf (G) and Tennis (T). His function is…

A: The maximum utility that a person can possibly experience given a certain price, quantity, and…

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

Consider the following indirect utility function:
V(p,I) = II,(
Pi
where E-1 a; = 1, and a; + 0 , Vi
1. What's the demand function for x;? (Hint: Take logarithm to both sides of the equation)
2. What's the original utility function? (Hint: If n is too abstract, let n =
= 2)

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: State the given information

VIEW

Step 2: Find the demand function for Xi

VIEW

Step 3: The original utility function

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 17 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

1. Jan has the following utility function for broccoli: U(B) = 54B - 0.5B³ a) What is Jan's marginal utility function?
Can you help me answer this macroeconomics theory question
Imagine that when MattPat gets to Hope there are 27 Hardcore theorist and 9 others (i.e. Everyone else), what is the (inverse) demand curve for t- shirts here? What does the graph look like? 2. Suppose you have the following utility function: U(qx, y) = x 1/3 2/3 x qy is m (instead of specific prices/income given in the example video posted: mp4). a) What is the optimal consumption choice of good x and good y (i.e. q and q)? b) Show that if you double the income and prices that the choice of outcome (i.e. optimal quantity) does not change. c) Suppose there are 20 consumers in the market with the same preferences and income, what is the market demand for good a given m= $54 and Py = $6? The the price of good x is Pr, the price of good y is Py, and income
Ronald consumes two goods, X and Y. He has a utility function given by the expression: U = 4X0.75y0.25. So, MUX y0.25 and MUY = x0.75 The current prices of X and Y are y0.75 3. X0.25 24 and 48, respectively. Ronald currently has an income of 960 per time period. a. Calculate the optimal quantities of X and Y that Ronald should choose, given his budget constraint.
Typed answer.
4. Consider the following two-good utility function: u(x1, x2) xi+ Vx2. Answer the questions set out below. 'Tip: Go back to the definition of monotonic transformations on page 17 (theorem 1.2) to confirm that the transformation is effected by a strictly increasing function, in other words if v(x, u) = f(u(x, y)), ƒ is a strictly increasing function on the set of values taken on by u. 1 (a) What information is contained in the marginal rate of substitution of a utility function (apart from the fact that it represents the slope of the indifference curves)? Derive the marginal rate of substitution for the utility function u(x1, x2) above. (b) Explain why Hicksian demand functions are often referred to as "compensated demand functions". (c) If the corresponding budget constraint is given by y = P1x1 + P2x2, show that the con- sumer's Hicksian demand functions are x† (p, u) = („)´u² and x (p, u) = „) u? P2 pi+p2, Pi+p2 respectively. (d) What is the degree of homogeneity in prices of the…
Explain through the optimal choice of a person how their individual demand function arises. Use an example.
Derive Ryan's demand function for q₁, given his utility function is where o = = (9₁) P + (9₂)P, 1 1-p The demand curve for q₁ as a function of P₁, P2, and Y is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ 9₁ = character.) U= Let the price of q₁ be p₁, let the price of q2 be p2, and let income be Y.
21:45 Sat 7 Aug 26% O Screenshot_20210807-213016_Office.jpg 21:30 a) Choose X, and X, to max the utility fxn, U(X,X) =ahX;+(l-a)\n X, st: M = P, X 1 + P,X , a) Consider a price decrease for good 1 from P, toP . Write down the Demand functions for good 1 when prices are P, and when prices drop from PtoP b) What is the compensating income, M° associated with the price change? C) Obtain the SE and IE associated with the price change II
4.13 CES indirect utility and expenditure functions In this problem, we will use a more standard form of the CES utility function to derive indirect utility and expenditure functions. Suppose utility is given by U(x, y) = (x° +y®)'/8 [in this function the elasticity of substitution o = 1/(1 – 6)]. a. Show that the indirect utility function for the utility function just given is V = I(p, + p,)¬/", where r = 8/(ò – 1) = 1 – 0. b. Show that the function derived in part (a) is homogeneous of degree zero in prices and income. c. Show that this function is strictly increasing in income. d. Show that this function is strictly decreasing in any price. e. Show that the expenditure function for this case of CES utility is given by E = V(p', + p,)''". f. Show that the function derived in part (e) is homogeneous of degree one in the goods' prices. g. Show that this expenditure function is increasing in each of the prices. h. Show that the function is concave in each price.
Please answer all the questions below Leonidas has a utility function u(x, y) = x + 3y, an income of 12 and works in Sparta, where the prices of x and y are both 2.(a) What is Leonidas’ current utility?(b) Leonidas’ boss is thinking of sending him to Athens where the price of x is 1 and the price of y is 4. Leonidas says this is as bad as a cut in pay of γ. What is γ equal to?(b) He also says that he wouldn’t mind moving if his pay was increased by δ when he moved. What is δ equal to?
Question 4 Naomi's expenditure function defined for a month for two commodities, Cassava (Q₁) and Banana (Q₂) is given by: 1. 11. Where P₁ is the price of Cassava (P₁>0), P2 is the price of banana (P₂ >0) and U is the fixed utility. The income of Naomi is m, where m > 0. Derive the indirect utility function for Naomi (Hint: Use the duality conditions) Using the Shephard's Lemma condition, derive Naomi's Hicksian demand function for Cassava (Q₁). iii. H IV. [125P,PU3 8 Using the Roy's identity, derive Naomi's Marshallian demand function for Banana (Q₂). Using the answer in (i), evaluate Naomi's maximum utility level when the price per tuber of Cassava is 5 cedis, the price per finger of banana is 10 cedis and her income is 250 cedis.