**Utility Function and Elasticity of Substitution**Consider the utility function:\[ u(x_1, x_2) = \left( \alpha x_1^{-\rho} + (1-\alpha) x_2^{-\rho} \right)^{-1/\rho} \]If $\rho = 0$, the elasticity of substitution is equal to 1.The elasticity of substitution for CES (Constant Elasticity of Substitution) utility functions is given by:\[ \frac{1}{1+\rho} \]**Question:**Is the statement "The elasticity of substitution for CES utility functions is $\frac{1}{1+\rho}$" true or false?- ○ True- ● FalseThe correct answer is "False".

Answered: Image /qna-images/answer/a2e9bab4-04a2-4078-84f8-bedfb7a964af.jpg

Answered: -1/e Consider the utility funetion 2…

-1/e Consider the utility funetion 2 (x1.x, ) = ( ax" + (1- a)x,). Ifp= 0, the elasticity of substitution is equal to 1. 1 The elasticity of substitution for CES utility functions is 1+p True False

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: The following are correct statements about the Income Effect (IE) and Substitution Effect (SE)…

A: Due change in price quantity of goods is also changed and it is inversely related. This is called…

Q: 8/ A consumer has the following utility function: u (x, y) = 6xy + 10 a) Determine the marginal…

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

Q: Suppose that consumer has the following utility function: U(X,Y) = XªY® where 1 > a > 0 and 1 > b>0…

A: In economics, the marginal rate of substitution (MRS) is the quantity of one good that a customer is…

Q: Suppose that the following a quasi-linear utility function is given U(X,Y) = U(X,)=-x-²-y-,Find…

A: We are going to solve above question using Marginal Rate of Substitution formula.

Q: Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the…

A: The utility function for John is given as follows. The value of * lies between 0 and 1. The income…

Q: A utility maximising individual has utility function u(x, y) = x¹/2y3/4, income m = 100 and faces…

A: Utility function represents a mathematical illustration of a consumer's preferences over distinct…

Q: Consider the following 6 utility functions: U1 = /x + 2y U2 = v2x + Jy U3 = 2x2 + y? + Jy U5 =…

A: *Hi there as you have posted multiple sub parts , as per our guidelines we will only first three .…

Q: Question-3 (Finding optimal bundle) utility functions and budget constraints. 1. U (₁, ₂) = 3x₁ +2r2…

A: An optimal bundle is the combination of two goods that provide a consumer with the highest utility…

Q: 2. Given the utility function U = x0.5y0.5 calculate the utility of consuming bundle z:[25,49].…

A: Marginal rate of substitution is equal to the ratio of marginal utility of good 1 with respect to…

Q: Let u(x₁, x₂) = 4x₁ + x₂ be the utility function. 1. Sketch the indifference curves corresponding to…

A: The indifference curve shows the different combinations of two goods which can be consumed which…

Q: On separate graphs, draw indifference curves that would result in a total utility of 25 and 100 for…

A: Let's start by charting the indifference curves for utility values 25 and 100.

Q: Consider the following indirect utility function v(p1,P2,y) = a) Calculate the equivalent variation…

A: Equivalent Variation refers to the amount of income which is to be provided or taken from consumer…

Q: Determine the monotonicity and convexity of these preferences and briefly define what they mean.…

A: Utility refers to the level of satisfaction a consumer obtains from the consumption of goods or…

Q: meaning. 04.46 ← 2. Thus, given any one utility function, any monotonic transformation of it will…

A: The objective of the question is to understand the concept of monotonic transformations and their…

Q: Consider the utility function U(x, y) = xy + x. Which of the following bundles is not on the same…

A: We have to calculate the value of U for all (x,y). The bundle which gives the different result will…

Q: Utility = x1x2. P1 = 10 and P2 =5. Income (m) = $200. The original utility maximizing quantities…

A: This can be defined as a concept that shows from the available fixed resources to the consumer how…

Q: meaning. 04.46 ← 2. Thus, given any one utility function, any monotonic transformation of it will…

A: The objective of the question is to understand the concept of monotonic transformations and their…

Q: Xn) = 0 implicitly defines a utility func- 4. Assuming that the equation F(U, X1, X2, .- tian U =…

Q: 2. A consumer has a utility fuinction given by a) Derive an expression for the two marginal…

A: utility function is an important concept that measures preferences over a set of goods and services.…

Q: (2) If a good is normal, then an increase in the price of the good will lead to which of the…

A: We are approached to consider the effect of a price increase on a normal good within a two-good…

Q: ate a table and graphs (a) Suppose we have preferer indifference curve through the bundle X = 30 and…

A: Utility function : U = 10 x2/3 y1/3 Budget Constraint : Px*x + Py*y = M Optimal consumption is…

Q: The individual's utility is given by the following function: 1 1 U(x,y) = - x y a) Calculate the…

A: A want satisfying power of a commodity or service is known as its utility. Utility is a significant…

Q: A) Suppose a quasilinear utility function is given by u(x₁, x₂) = 2√x₁ + 4x₂. 1. For this utility…

A: Utility function shows relationship between utility and inputs. The Engel curve exhibits…

Q: Suppose a consumer is indifferent of the bubdles (5,6 ) and (6,6) Are his preference monotonic?…

A: # A consumer is said to have a monotonic preference when more of a good is offering higher level of…

Q: can you clearly show your working, thanks

A: Utility is the satisfaction that one derives from the consumption of goods and services. The joint…

Q: Problem 3. Consider the Cobb-Douglas utility function u(x, y) = x²y². Let the budget constraint be…

A: ***Since the student has posted a question with multiple subparts, the expert is required to solve…

Q: Consider the following indirect utility function: V(p, 1) = II ₁(ail Jai Pi where 1 ai = 1, and ai…

A: Given,The indirect utility function -Where,

Question

**Utility Function and Elasticity of Substitution**

Consider the utility function:

\[ u(x_1, x_2) = \left( \alpha x_1^{-\rho} + (1-\alpha) x_2^{-\rho} \right)^{-1/\rho} \]

If $\rho = 0$, the elasticity of substitution is equal to 1.

The elasticity of substitution for CES (Constant Elasticity of Substitution) utility functions is given by:

\[ \frac{1}{1+\rho} \]

**Question:**

Is the statement "The elasticity of substitution for CES utility functions is $\frac{1}{1+\rho}$" true or false?

- ○ True
- ● False

The correct answer is "False".

Expert Solution

Step 1

Step by step

Solved in 2 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

Please solve with step and no reject thank u
which answer is correct among the provided ones the answer i got is provided on the image which is incorrect
meaning. 04.46 ← 2. Thus, given any one utility function, any monotonic transformation of it will represent the same preferences. e-books-MICRO-INTERMDE... 70 UTILITY (Ch. 4) 3. The marginal rate of substitution, MRS, can be calculated from the utility function via the formula MRS = Ax2/Ax₁ = -MU₁/MU2. REVIEW QUESTIONS 1. The text said that raising a number to an odd power was a monotonic transformation. What about raising a number to an even power? Is this a monotonic transformation? (Hint: consider the case f(u) = u².) 2. Which of the following are monotonic transformations? (1) u = 2v-13; (2) u = 1/v²; (3) u = 1/v²; (4) u = lnv; (5) u = −ev; (6) u = v²; (7) uv² for v> 0; (8) u = v² for v<0. 3. We claimed in the text that if preferences were monotonic, then a diag- onal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if it intersected some indifference curve twice?) 4. What kind of preferences are…
Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices på and på for the goods.) (b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and prices) using the Lagrangian method. = (c) Suppose a = . Suppose also that John has income I = 1 and pv 2. What is the value of John's optimal happens if John's income doubles to I = 400? 200 and faces prices p consumption bundle? What =
Please answer the all ,I will give instant upvote A) True or false: The marginal utility of good 1, that is, MU1, must be diminishing in x1. B) True or false: Two different indifference curves cannot intersect. C) If the marginal rate of substitution becomes more negative, then the indifference curves become a. flatter b. steeper c. flatter or steeper D) True or false: With a linear utility function and a linear budget set, the solution to the consumer's problem will generally be a corner solution, except in special knife-edge cases.
Subpart 7 only
Constant Elasticity of Substitution utility function U(x. y) = (x^a*y^ (1-a))^b + y. I am looking for a this form of CES utility function to derive demand functions. (Note = > a is alfa, b is lambda).