The question is in the attached image. Thank you! 3) Consider a consumer who has preferences given by U(¤1, x2) = x2 +2/%1(quasilinear utility), with%3D1MUzMU¤2 = 1,where MU1 and MU-2 are the marginal utility of x1 and x2, respectively.Normalizing the price of good 2 to 1, the budget constraint is given byy = P1X1+x2.a) What is the marginal rate of substitution in this case?b) What is the next step that we need to do to solve this problem?c) Given your answer to b) solve for x1 and x2.d) What are the (unrealistic) implications of quasilinear utility?e) Suppose y = 10 and p1 = {1,2, 3}, what is the value of your utility in eachcase?f) Plot your indifference curves for each value labeling the graph, includingeach axis, correctly.How do the indifference curves shift with changes in the utility functions?Does the consumer ever not consume good 1?How about good 2?What assumptions on income are required to ensure an interior solution (i.e.both goods are consumed)?

In microeconomics theory of utility maximization, a consumer attains his equilibrium where the…

Answered: a) What is the marginal rate of…

a) What is the marginal rate of substitution in this case? b) What is the next step that we need to do to solve this problem? c) Given your answer to b) solve for x1 and x2.

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 6QFR

See similar textbooks

Related questions

Q: 1) a) Given the following typical utility curves determine whether they have convex indifference…

A: "Since you have posted multiple question, I can only answer the first question, rest you need to…

Q: Oil prices doubled in 2008, from $67.49 per barrel in June 2007 to $133.88 per barrel in June 2008.…

A: The substitution effect occurs when the quantity of one good increases while the quantity of another…

Q: Decreasing rate of marginal substitution between two inputs occur when the input being added replace…

A: MRTS or marginal rate of substitution refers to the rate at which one input is substituted for other…

Q: 200 100 0.5 flyers 1 flyer 25 50 75 100 125 150 175 200 225 250 COLOR FLYERS 2 flyers 6 flyers t the…

A: Given Budget = 25 $ Black and white flyer cost= 0.05 Total consumption = 25 / 0.05 = 500 Flyer…

Q: Suppose the marginal rate of substitution is constant at 6 for all possible consumption bundles.…

Q: Briefly explain and graphically illustrate the property of diminishing margincal rate of…

A: The willingness of a consumer to substitute one good for another as long as the new good is equally…

Q: complementary inputs occur where substitution is possible between the two * inputs True O False

A: Complementary inputs are inputs to production that a firm uses closely together. Hence if a firm has…

Q: For the typical Cobb-Douglas function, q=…

A: The function is given as follows: The MRTS (Marginal rate of technical substitution) refers to the…

Q: Define marginal rate of substitution.

A: The marginal rate of substitution(MRS) is a very technical word in economics, defined as the…

Q: What happen to the marginal rate of substitution as we move along the non linear indifference

A: Indifference Curve: This is the curve that shows the various combination of two goods that gives…

Q: It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label)…

A: The marginal rate of substitution (MRS) can be calculated as follows. The MRS is 0.5. Consumer…

Q: What is your marginal rate of substitution of $1 bills for $5 bills?

A: Definition : Marginal Rate Substitution is the rate at which some amount of one commodity…

Q: Let F be a function of two variables, defined by F(K, L) = 2 In K + 5 In L. (a) Find RLK= F₁'(K, L)…

A: Elasticity of substitution measures the ease with which one input can be substituted for other.

Q: Calculate your marginal rate of substitution as a function of B and C. U(B,C)= B^(1/4)C^(3/4)

A: The marginal rate of substitution denotes the slope of the indifference curve and is defined as the…

Q: fitness company offers online classes (x) for $10 per class. The typical customer has monthly…

A: a. Marginal rate of substitution (MRS) for x to m can be calculated as follows. Marginal rate of…

Q: The Pivot in the substitution Effect is

A: Suppose, a consumer has the choice of only two goods, in which if the price of good 1 changes, then…

Q: The marginal rate of technical substitution represents the slope of?

A: If there is two input goods x and y used in the production process, then the marginal rate of…

Q: Compute marginal utilities and marginal rate of substitution for each of the utility functions given…

Q: In industry, when the price of electricity goes up, the company employs more low-skilled workers.…

A: The decrease in the sales for a product that can be allocated to consumers switching to cheaper…

Q: Discuss the following statements : explain whether the statement is TRUE or FALSE, and provide…

A: Two utility functions that provide the same rank ordering of consumption bundles are positive…

Q: What is the marginal rate of substitution of x for y when x = 16 and y = 54?

A: The marginal rate of substitution is considered as the slope of the Indifference curve that provides…

Q: Determine the marginal rate of substitution of X for Y (MRSXY)(

A: Marginal rate of substitution m refers to the sacrifices made of good- Y due to consuming one…

Q: A college football coach says that given any two linemen A and B, he always prefers the one who is…

A: Hi Student, thanks for posting the question. As per the guideline we are providing answers for the…

Q: how to find the marginal rate of substitution for perfect complements

A: Marginal rate of substitution can be defined as the maximum amount of one good which a consumer is…

Q: Decreasing rate of marginal substitution between two inputs occur when the input being added replace…

A: Marginal Rate of substitution is the slope of isoquant which states that how much change in good Y…

Q: 3 1. A consumer has the utility function U(x,y) = 2x y where x and y represent the quantity consumed…

Q: The marginal rate of technical substitution is defined by: a. MRTS 2 = MP/P2 b. MRTS 2= MP,MP C.…

A: Economics is a branch of social science that describes and analyzes the behaviors and decisions…

Q: The elasticity of substitution between two perfect substitutions is

A: To find: The elasticity of substitution between two perfect substitutions is

Q: 100 84 75 15 16 19 20 24 Hours of free time per day The diagram shows a student's indifference…

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

Q: Write the technical rate of substitution expression for f(x1, x2) = (x1 - 1)0.25 x20.5

A: The marginal rate of technical substitution (MRTS) is an concept that explains the rate by which one…

Q: -1/e Consider the utility funetion 2 (x1.x, ) = ( ax" + (1- a)x,). Ifp= 0, the elasticity of…

Q: Discuss general framework of Alfred Marshall's analysis by taking the concept of "substitution" into…

A: Marshall's hypothesis of capital was intended to fill two fundamental needs: a coordination of the…

Q: U = 5x11/2 + 2x2. What is the marginal rate of substitution at (1, 4)? Round your answer to two…

Q: What does the marginal rate of substitution (MRS) measure? What is your MRS of $1 bills for $5…

A: In a market, when a consumer enters the market and purchase a product for consumption purposes, he…

Q: h) Giffen goods i) Marginal Rate of Substitution j) Suppose I have a function f(x1, x2) = provide…

A: According to the law of demand, the quantity demanded of a good is inversely related to the price.…

Q: a) For an output level of 40 units, calculate the marginal rate of technical substitution between…

A: The marginal rate of technical substitution (MRTS) is an economic theory that shows the rate at…

Q: Define and then derive the expression for the marginal rate of technical substitution.

A: Marginal rate of technical substitution (MRTS) measures the rate at which one factor must give up in…

Q: Suppose that the following utility function is given U(X,Y) = X//3y1/2, which of the following is…

A: Given Utility function U=x1/3y1/2 ......... (1)

Q: Find the marginal rate of substitution given the following utility functions for X and y: U(x) = 2xy…

A: Utility refers to the satisfaction derived from a consumption of the good. The aim of the consumer…

Q: Find the marginal rate of substitution given the following utility functions for x and y: U(x) = 2xy…

A: Consumer theory: It studies the behavior of consumers based on their consumption preferences given…

Q: Discuss general framework of Marshall's analysis by taking the concept of "substitution" into…

A: Alfred Marshall referred in his studies to demand as utility and supply as cost of production and…

Q: Question 11 Marcus spends his income on movies and concerts. At his optimum, Marcus’ Group of…

A: When a consumer consumes two goods, to achieve the maximum utility at the optimum he compares…

Q: Cost of living will become more expensive fuelled by increases in food and electricity bill. Suppose…

A: Total effect of price change is called Price effect and TE = SE + YE . SE = substitution effect YE =…

Q: 1) a) Given the following typical utility curves determine whether they have convex indifference…

A: MRS is how much of one good the consumer will give up to obtain extra units of another good while…

Q: It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label)…

A: Marginal rate of substitution (MRS) can be calculated as follows. The MRS is 0.5. Consumer is give…

Q: The production function is Q = K.6 L.4. The marginal rate of technical substitution is: 2/3 K-1 L.…

A: Marginal rate of technical substitution means the rate at which the firm substitutes one input in…

Q: Is the marginal rate of substitution is another way to mathematically expressing the opportunity for…

A: Marginal Rate of Substitution is the comparison between two products which the consumer chooses to…

Q: QUESTION 18 Which of the following best explains why isoquant curves have the "curved" shape that…

A: Isoquant refers to the curve that shows the different combinations of inputs that can produce the…

Question

100%

The question is in the attached image. Thank you!

3) Consider a consumer who has preferences given by U(¤1, x2) = x2 +2/%1
(quasilinear utility), with
%3D
1
MUz
MU¤2 = 1,
where MU1 and MU-2 are the marginal utility of x1 and x2, respectively.
Normalizing the price of good 2 to 1, the budget constraint is given by
y = P1X1+x2.
a) What is the marginal rate of substitution in this case?
b) What is the next step that we need to do to solve this problem?
c) Given your answer to b) solve for x1 and x2.
d) What are the (unrealistic) implications of quasilinear utility?
e) Suppose y = 10 and p1 = {1,2, 3}, what is the value of your utility in each
case?
f) Plot your indifference curves for each value labeling the graph, including
each axis, correctly.
How do the indifference curves shift with changes in the utility functions?
Does the consumer ever not consume good 1?
How about good 2?
What assumptions on income are required to ensure an interior solution (i.e.
both goods are consumed)?

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 by step

Solved in 2 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

You are given the following utility function and price of commodities q1 and q2: U = 3q1+q1q2-5q2-15 P1=3 and p2=2 If the corresponding bugdet is 20. i. Write the consumer's budget equation,augmented objective function, ii.construct a constrained utility maximization problem out of the information given above, Is the second order condition for a maximum satisfied? Iii. Find the optimum level of U and the levels of q1 and q2 that will satisfy the first order condition for a maximum.
The preferences of a typical Californian can be represented by the following utility function: U (x1 , x2 ) = α ln(x1) + (1 − α) ln(x2) Here, x1 and x2 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by p1 and p2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x1 ≤ 50). Call this restriction a rationing constraint. (a) If α=0.25, m=100,and p1 =p2 =1, find the optimal consumption bundle of gasoline and electricity. Is the electricity rationing constraint binding (meaning does x1∗ = 50)? (b) Suppose that α = 0.75, but the other parameters are the same. What is the optimal consumption bundle? Is the rationing constraint on electricity consumption binding? (c) Now, assume that there is no rationing constraint. Assume m = 100 and p1 = p2 = 1, but α remains as a generic parameter. Solve for the optimal quantity…
A consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 15 and the marginal utility of Y is 8. The unit price of X is $3 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should Multiple Choice a. decrease consumption of product X and increase consumption of product Y. b. increase consumption of product X and increase consumption of product Y. c. decrease consumption of product Y and increase consumption of product X. d. stick with the current consumption mix because it yields maximum utility.
Suppose the market demand curve for pizza can be expressed as QD = 100 - 2P + 3Pb, where QD is the quantity of pizza demanded, P is the price of a pizza, and Pb is the price of a burrito. What is the slope of this demand function, and what information does the slope provide?..
Suppose the utility function is represented by the following equation: U (X, Y) = XY + X + 2Y + 2 and the budget constraint (I = PxX + PyY) is represented by (I = 95; PX = 10 and PY = 5): 95 = 10X + 5Y a. Determine the optimal quantity to buy of X and Z subject to the budget constraint. b. What is the total profit under the optimal combination? c. By how much will total profit increase if income increases by one dollar?
1.a Assume that a person’s utility function is given by the following function: ??=3?^(2/3)?^(1/3) Assume also that the price of X is £3, and the price of Y is £3 and that the budget is £45. What is the optimal amount of goods X and Y that should be purchased with this budget? b) Assume now that the price of good X is PD, while all other conditions remain the same. Find the optimal amount of good X that should be purchased for a generic price PD. In other words, find the individual demand function for good X. 1.b Assume now that the price of good X is PD, while all other conditions remain the same. Find the optimal amount of good X that should be purchased for a generic price PD. In other words, find the individual demand function for good X.
Q1-Select the true or false for the following statement also give the explanation and support your answer with graphical presentation where necessary. Explanation is compulsory 3 to 6 line. If total utility at optimum level marginal utility is negative.
1. Consider a consumer who chooses bundles consisting of two commodities, x and y. Suppose that, regardless of the prices px and py (which are always positive), the consumer chooses to consume x and y in a ratio of 2:1. This behavior is consistent with: a. A consumer having Cobb-Douglas utility function. b. The consumer’s utility function exhibiting perfect complements. c. The consumer’s utility function exhibiting perfect substitutes. d. Any of the above could be correct.
For the utility function U = Qx0.22Qy(1-0.22) find the trade-off rate between good X and good Y at Qx= 9 and Qy=19 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
A consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 10 and the marginal utility of Y is 8. The unit price of X is $5 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should
Assuming, there are two goods: coffee and tea. Your budget is 18000 KRW per day. The price of coffee pc ranges between 0 KRW to 6000 KRW The price of tea pt ranges between 0 and 5000 KRW a) Specify your indifference map of your preference relation b) Specify your utility function c) Specify a budget constraint based on the assumption above d) specify your own-price offer curves for coffee e) specify your curve Engel curve for coffee
A consumer has a perfect complements utility function, where she prefers to have one unit of H with each unit of G. Also, she has an income of $210. Assume that the price of H is $8 and the price of G is $6. What is the consumer's optimal choice for good G*? Group of answer choices 11 12 15 16