a) Show that the utility function is strictly increasing in x1 and x2. b) For a given level of utility U, derive the marginal rate of substitution between good 1 and good 2. c) Find the optimal choice of x1 and x2 when the consumer maximizes his/her utility.

a) Show that the utility function is strictly increasing in x1 and x2. b) For a given level of utility U, derive the marginal rate of substitution between good 1 and good 2. c) Find the optimal choice of x1 and x2 when the consumer maximizes his/her utility.

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: Q2. Suppose a consumer seeks to maximize the utility function U (x, y) = (x + 2) (y + 1), where and…

A: U(x,y) = (x+2)(y+1) Budget Constraint = Px*x + Py*y = I

Q: Jack and Jill live in the same village where they both face the same price. Jack has preferences…

Q: Assume that the consumer faces a price of $1 for y, and a total income of $120. The price of a…

A: Budget constraint: given the price of 2 goods and consumer’s income. The budget constraint shows…

Q: Mary can consume two goods X₁ and X2, where X₁ and X₂ are the quantities of two goods purchased.…

A: Mary's preferences are represented by the utility function: U(X1,X2)=X10.6X20.4Price of the good X1…

Q: Pete consumes goods 1 and 2. Pete thinks that 3 units of good 1 is always a perfect substitute for 4…

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

Q: A consumer has set a budget of $400 for the consumption of good X and Y. The price of Good X is…

A: Utility function : U (X, Y ) = x y Price of x : Px Price of y : 5 Budget Set = 400 Therefore ,…

Q: A consumer has a utility function 9*sqrt(x1)+x2 and a budget constraint of 8x1+6x2 ≤10000. How much…

A: Utility means satisfaction. Utility is maximized where the MRS is equal to the price ratio of two…

Q: A consumer with the following utility function U = xy2 faces two constraints. The first is the…

A: Consumer theory is important in economics because it investigates how consumers might maximize…

Q: 5) for y. U (x, y) = x0.5 + y Pxx+Pyy = I Use the above utility function and budget line to find the…

A: The notion of utility maximization and budget restrictions is important to consumer theory, which…

Q: Tom is a consumer with preferences over two goods represented by the quasilinear utility function…

A: Utility function : U (x, y ) = 2x0.5 + y Income = 120 Px = 2 Py = 4Hence , Budget Constraint : 2x…

Q: Consider the utility function: U(x,y)= -4(3x-12)² - (2y-10)² Determine the marginal utility for…

A: The marginal utility can be defined as the extra utility received from the consumption of one more…

Q: Which of the following utility functions represent preferences which do not satisfy monotonicity? U=…

A: Monotonic preferences refer to such consumer preferences towards the greater consumption of goods…

Q: Individual that consumes two goods (X and Y) and has a CES Utility Function of the form: U =…

A: "As per our policy, we can provide solutions to the first three subparts. Kindly raise the question…

Q: The marginal utility of the last unit of apples consumed is 12, and the marginal utility of the last…

A: Marginal utility is the utility derived by the consuming 1 additional unit of good.

Q: Let a1 and a2 denote the quantities consumed. The consumer's preferences are represented by the…

A: We have Utility function U(x1,x2)=x1+x2 ... (1) Consumer income m=100 Price of good 1:…

Q: Consider a consumer who has a direct utility function given as U(x₁, x2) = (x1+x25)² where ₁ > 0 and…

A: Utility Function: A utility function is the combination of all commodity bundles that gives a…

Q: A consumer derives utility from good A and B according to the following utility function: U(A, B) =…

A: Utility maximization problem: With the given prices and income, a consumer chooses his consumption…

Q: Assume that a person's utility function is given by the following function: TU = 2X/2y/2 Assume also…

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

Q: a)Assume that the typical consumer always spends a small share of her overall budget on Vietnamese…

A: Total customers = 120,000 Price of other products = Pm= $1 Price of Vietnamese Meals = Pv The…

Q: Assume a utility function U(x,y) = XY, where Px = $2, Py =$1 and Income = $100. a) Determine and…

A: Disclaimer: - since you asked multipart question, we are solving only first 3 parts as per the…

Q: PART A You must answer the question in this section. A.1 Individuals in a market each have a total…

Q: If the consumer's utility function is given by U(x, y) = 10x0.5 0.5, solve for the optimal quantity…

A: Consumer theory is important in economics because it investigates how people maximize their…

Q: 3. Tom's utility function is U (x; y) = 3x+4y: His budget constraint is ax + by = 1, a, b, I > 0 a)…

A: The perfect substitute utility function is a linear utility function. Under perfect substitute, the…

Q: sider the utility function U(x, y) = xy, which describes the enjoyment Emi gets from consuming s (x)…

A: Equilibrium condition: MRSxy = Px/Py

Q: uppose a consumer’s preferences for goods Y and X can be represented by the utility function,…

A: A rational consumer will consume where the MUx/MUy = Px/Py Here , MUx is the Marginal utility's of…

Q: Consumer satisfaction from consuming goods X and Y is as follows: U=10X+14Y-X2-Y2 and consumer…

A: Consumer equilibrium is the situation where he gets maximum satisfaction level of utility with given…

Q: A consumer has the following demand function for good 1: x1 = (1/4)(m/p1) The original price of the…

A: Individuals (consumers) directly concerned within the acquisition, use, and disposal of economic…

Q: 2. Cynthia has preferences represented by the utility function u(x) = x² + x2 (a) Calculate…

A: A utility function is a mathematical representation of a consumer's preferences over different…

Q: The utility function of a consumer regarding two goods x and y is given by U(x,y) = x^(7.9)y^(9).…

A: U(x,y) = x7.9y9 Price of x (Px) = 19 Price of y (Py) = 80 Total Income (M) = 10800

Q: Anna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are…

A: Budget Constraint:A budget constraint represents the limit on the consumption of goods and services…

Q: 8) When Marginal Utility = 0, Total Utility is A) Maximum B) Constant C) Minimum D) None of the…

A: Total Utility:- The overall amount of contentment achieved by a consumer as a result of consuming a…

Q: A consumer derives his utility from two goods, the amounts of which are x and y, according to the…

A: Given Utility function U=2lnx+lny .......(1) Px=$2 and Py=$4 Consumer income =$48 We have…

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: Consider an individual with preferences over two goods. This consumer is maximising utility when:…

A: The problem of estimating consumer equilibrium, that is, the combination of products and services…

Q: Q1. Bob has a utility function defined over goods 1 and 2: u(x1; x2) = min{6*x1 + x2, x1 + 2*x2}…

A: u(x1; x2) = min{6*x1 + x2, x1 + 2*x2}

Q: (a) What are the effects of an increase in the price of good A on a consumer’s demand if i) good A…

A: The fluctuations that happen between demand and also the supply-side decides the levels of prices…

Q: A consumer has preferences over two goods, coconuts and fish. The consumer prefers more of each good…

A: Indifference curve represents the combinations of two goods between which the cunsumers are…

Q: (A) Suppose an individual who derives utility u(x, y) from consuming a units of the good X and y…

Q: 3. A consumer is faced with a utility function u(x, y) = 4x² + 3xy + y² And his budget constraint is…

A: Thank You for the question. According to Bartleby's answering guidelines, we answer only the first 3…

Q: For each of the following utility functions answer the following questions (i-iv): i) Calculate the…

Q: Consider a market with two goods, x and z. The consumer’s utility function is U = x^0.2z^0.8 A.…

A: Utility denotes the want satisfying power of a commodity. A consumer maximizes his/her utility when…

Q: Consider a consumer with the utility function u(x1,x2) = x11/3 x22/3. a. Find the Marginal Utility…

A: Dear student, you have asked multiple sub-part questions in a single post. In such a case, I will be…

Q: Suppose your income is 200, the price of good x is 2, and the price of good y is 3. You know that…

A: For optimal consumer choices, equate ratio of prices with Marginal Rate of Substitution

Question

ilable
Paragraph
H
AaBbCсD AabbCcDc AaBbC, AaBbCcE
Normal 1 No Spac... Heading 1 Heading 2
Consider a consumer with the following utility function:
U(x1, x2)=(x1+4) (x2 + 6) for x1, x2 20
with the accompanying budget constraint:
p1x1 +p2x2=Y where p1, p2, Y>0
Styles
b)
c)
For
Replace
Select-
Editing
a) Show that the utility function is strictly increasing in x1 and x2.
For a given level of utility U, derive the marginal rate of substitution between good 1 and good 2.
Find the optimal choice of x1 and x2 when the consumer maximizes his/her utility.
Create and Share Request
Adobe PDF Signatures
Adobe Acrobat
A
ENG
Add-ins
Add-i
9:56 PM
12/15/2023
1009

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: Introduce the concepts

VIEW

Step 2: Analyse whether the utility function is Increasing

VIEW

Step 3: Analyse the marginal rate of substitution

VIEW

Step 4: Analyse utility maximising bundle

VIEW

Solution

VIEW

Step by step

Solved in 5 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

An individual’s utility function is given byU = x1√x2where x1 and x2 denote the monthly consumption of two goods. Unit prices of these goodsare $2 and $4 respectively, and the total monthly expenditure on these goods is $300.(a) Write down the budgetary constraint.(b) Find the optimal quantities of x1 and x2 the maximize U.(c) Verify that the stationary point is a maximum.
Consumer has the following utility function U(x,y) = x1/2y1/2 , where the price of good x is 1$ per unit, the price of good y is 4$ per unit, and the consumer’s income is 800$. Find the utility maximizing consumption levels of x and y.
Show clear and step by step solutions.
The total utility from two products is maximized at the optimal consumption bundle. True or False?
Question 7 The law of diminishing marginal utility states that: Utility derived from the additional unit of the good consumed falls as the consumption of the good increases. Total Utility derived from consumption of a good falls as consumption increases. None of the suggested options. Ratio of the MU to P for luxuries is lower than that for necessities. Ratio of MU to P will be the same for all goods
Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.
The utility function of a consumer is u = √x + 2y. (a) Calculate how much MRS of that consumer when x = 4. (b) If the consumer currently consumes 4 units of goods x and the price ratio of Px / Py = 1/4, then the consumer should increase or decrease the consumption of goods x?
Ricky has utility function u=x'y. This implies that MUx=2xy. MUy=x². His income is 100. The price of y is 10. (a) Find his demand for x at price 20. (b) Find his demand for x at price 30. (c) Write down his demand function for x: that is, write down his demand for x as a function of the price of x.
A consumer consumption bundle contains good X and Y. Suppose the price of good X goes up and a consumer goes on consuming the exact same amount of X as before. Check the correct statement(s).A) Both X and Y are inferior. B) X is an inferior good.C) In the special case where X is Leisure, and Y is "all other goods", X is an inferior good.D) The consumption of Y decreases.E) It is impossible that the consumption of X remains unchanged when the price of × goes up.F) The substitution effect is negative
A consumer’s utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A, B) = A1/4 B 3/4. The price of goods A and B are $20 and $40, respectively. The consumer has a budget of $1200 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. A new tax of $10 is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax? d. Show that the consumer would prefer a lump sum income tax that raises the same revenue as the tax on good B. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
The price of good "a" is $5 and the price of good "b" is $15. If the marginal utility of good "a" is 20 then the marginal utility of good "b" must be ________ to have an optimum combination of goods purchased. 80 20 60 4
True, false, or undetermined?