4. Consider the following two-good utility function: u(x1, x2) = VT1 + V#2. Answer the questions set out below. ITip: 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(r, u) = f(u(x, y)), f 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- %3D 2 sumer's Hicksian demand functions are x (p, u) = („)*u² and a (p, u) = („)* u² - Pi+p2 respectively. (d) What is the degree of homogeneity in prices of the Hicksian demand functions in (c) above? Provide an economic interpretation for this.

4. Consider the following two-good utility function: u(x1, x2) = VT1 + V#2. Answer the questions set out below. ITip: 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(r, u) = f(u(x, y)), f 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- %3D 2 sumer's Hicksian demand functions are x (p, u) = („)u² and a (p, u) = („) u² - Pi+p2 respectively. (d) What is the degree of homogeneity in prices of the Hicksian demand functions in (c) above? Provide an economic interpretation for this.

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: Q10. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. In Case 1, Total income is…

A: We are going to use Consumser decision theory to answer the question.

Q: (a) Suppose the indirect utility function v(p, m) is differentiable. Prove that dv(p, m) av (p, m)…

A: The indirect utility function refers to the maximum attainable utility when prices of concerned…

Q: Suppose the utility function of U(x1, x2) = x11/2x21/2 and the budget constraint of p1X1+p2x2=m.…

A: Utility means satisfaction. Higher the utility, higher is the satisfaction. The budget constraints…

Q: Consider a utility function given by u(x, y) = (ax² + by). It is called CES utility function.

A: Given utility function u(x,y)=axρ+byρ1ρGiven utility function is known as CES production…

Q: Question 1. Suppose Barry only drinks coffee with 1/2 teaspoon of sugar. That is, if he is consuming…

A: Indifference curve (IC) is a graphical representation that depicts the various combinations of two…

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: 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: ility representations = of the pairs of utility functions over X R2, state whether they erences. If…

Q: Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers…

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

Q: Milo spends £27 on stamps (S) and maple candy (C). His preferences for these goods are given by the…

A: Given , Milo income = 27 Utility function : U = min { S , 3C } Price of Stamps = 1.1 Price of…

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: 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: Suppose that the total utility (TU) from consuming (C) per consumption quantity is defined as: TU =…

A: Total utility is the measurement of satisfaction or happiness of a consumer upon consuming a…

Q: Assume there is consumer, his utility function is U(x,y)=y/(100-x). If px = 1, py = 1, please show…

A: Utility function U (x, y) = y/(100-x) .... 1) (MUx) / (MUy) = Px /Py.…

Q: Question 1 Consider an economy with two goods t = 1,2. Whenever an individual consumes ₁ units of…

A: As given utility function is u(x1,x2) = αlnx1 +lnx2 Where α>0

Q: Consider the following utility functions. G(x,y) = x² + 3y² H(x,y) = (x+1)¹/2 + y + 1 L(x,y) = x ey…

A: The function for which the MRS decreases as good x increases, have strictly convex preference.

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: For the utility function U = Qx0.58Qy(1-0.58) find the trade-off rate between good X and good Y at…

A: The marginal rate of substitution of X for Y measures the rate at which the consumer is ready to…

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: 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: With a high stress job that oversees the public health of a nation, Tony loves to eat pomegranate…

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

Q: 4. Consider the general multiplicatively separable utility function given by u (x1,x2) = pu1 (x1) u2…

A: Given Utility function U=μX1X2Budget consraint=P1X1+P2X2=WW= income of the consumerP1= price of good…

Q: Suppose Carlos has to choose between purchasing jewelry and water. Which of the following is the…

A: Marginal utility is the utility from the next unit consumed of the same good. MU per dollar=MU of…

Q: Ayana is pitching an idea for a startup company that makes and sells solar-powered phonechargers…

A: Let us understand this, with associating values in the equation, Let the income (I) be 1000; Let PC…

Q: Solve the following utility maximization problem, u (x1, x₂) subject to P1x1 + P2x₂ = I max meaning…

A: The utility maximization problem is a problem that seeks to find the quantities of two goods or…

Q: For the utility function U = Qx0.42Qy(1-0.42) find the trade-off rate between good X and good Y at…

A: To find the trade-off rate between good X and good Y for the given utility function , we need to…

Question

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

Introduction

VIEW

Answer & Approach for Part A)

VIEW

Answer & Approach for Part B)

VIEW

Answer & Approach for Part C)

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 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

1
Which of the following statement is TRUE based on this question : A utility function with 2 goods (X,Y) is given by U = X^1/2Y. If there’s 3 bundles, bundle A = (9,3); bundle B = (4,1); bundle C = (16, 4)
Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…
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.
Utility is a type of function that occurs in economics. When a consumer receives x units of a certain product, a certain amount of pleasure, or utility U, is derived. The graph represents a typical utility function. a) Find the average rate of change of U as x changes from 0 to 1; from 1 to 2; from 2 to 3; from 3 to 4. b) Why do the average rates of change decrease as x increases? a) The average rate of change of U as x changes from 0 to 1 is. (Type an integer or a decimal.) C Utility (pleasure units) AU 200- 150- 100- 50- 0 (1,67) (2,106) I (3,134) (4,156) 2 Number of units of product 4 X