A consumer has the utility functionU=x0.2 y0.8The price of xis $2, price of y is $4 and she a budget of $100 to spend on the twocommodities.a. Solve the constrained maximization problem for the consumer (use theLagrange approach)b. Establish that the solution is a true maximum

utility function refers that it is a function by which we measure the utility or satisfaction of the…

A consumer has the utility function U=x0.2 y0.8 he price of xis $2, price of y is $4 and she a budget of $100 to spend on the two mmodities. a. Solve the constrained maximization problem for the consumer (use the Lagrange approach) b. Establish that the solution is a true maximum

A consumer has the utility function U=x0.2 y0.8 he price of xis $2, price of y is $4 and she a budget of $100 to spend on the two mmodities. a. Solve the constrained maximization problem for the consumer (use the Lagrange approach) b. Establish that the solution is a true maximum

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.4P

See similar textbooks

Related questions

Q: Move the appropriate curve or curves in each graph to illustrate the effect of each of the four…

A: In the loanable fund market, interest rate is determined by the intersection of demand for loanable…

Q: 2. Discuss the factors that contribute to economic growth. 3. List and briefly describe the 17…

A: As per student's demand, I have provided the answers of the mentioned two questions. 2. Answer:…

Q: 1. Using the following table (hypothetical Irish National Income and Product Accounts Data), choose…

A: Gross domestic product(GDP) measures the money value of all final goods and services produced in an…

Q: Consumption expenditures are a function of disposable income the real interest rate autonomous…

A: Consumption is the total amount of products and services that a person utilises to fulfil their…

Q: Explain the comparative advantage based on illustration below

A: Meaning of Opportunity Cost: The term opportunity cost refers to the situation under which the…

Q: Which of the following is NOT one of three major principles of the World Trade Organization: A.…

A: The World Trade Organization (WTO) is an intergovernmental organization that regulates and…

Q: Some Caribbean countries give tax credits to homeowners who wish to install solar panels in their…

A: When Caribbean countries provide tax credits to homeowners who wish to install solar panels is a…

Q: Match the term with the definition: [?] is the rate you pay on the last dollars you earned…

A: Marginal value is the value from the last unit. Average value is the value per unit.

Q: plain the meaning of internal balance or government balanced budge

A: Budget refers to the financial statement which contains the government expenditure and revenue. The…

Q: If the Fed decides to conduct contractionary monetary policy by selling $250 million in UST bonds,…

A: Under the contractionary monetary policy the central bank sells bonds and hence take back money from…

Q: What is a two-part tariff? Why do firms sometimes use them? What is an example of a firm that uses a…

A: A two-part tariff (TPT) is a method of valuing where the price of a good or service is divided into…

Q: Examine the role of health as an input to and an output from a production function and discuss the…

A: Introduction The production function of health defines the relationship between health and the…

Q: YOUR GRANDMA WISHES TO PROVIDE P40,000.00 TO YOUR YOUNGEST BROTHER ON HIS 21st BIRTHDAY. HOW MUCH…

Q: Amy considers two investment opportunities (Stock A and Stock B) with the same price per unit in the…

A: A theory in economics called expected utility calculates the utility of an action taken when the…

Q: For an interest rate of 12% per year compounded continuously, find the effective interest rate…

A: Given that, Interest rate(i ) = 12% or 0.12

Q: ate the const mer's max zation problem and express this in words. ow let Px = 10, Py=20 and income M…

Q: 100 P Find the Elasticity of Demand at a price of $39 Given the demand function D(p) At this price,…

A: D(p) = 100p

Q: 5. A consumer dislikes good 1, and dislikes good 2. Show these preferences on a suitably labelled…

A: Indifference curves are the locus of points which provide same level of utility to the consumer .

Q: An industrial plant bought a set of equipment for 90,000. Miscellaneous expenses including…

A: Salvage value is the amount that company expects to get at end of useful life asset. Company…

Q: Investment is: A. Education, any new plant, equipment, additional inventory, computer software,…

A: Businesses invest while generating revenue through the provision of products and services. The…

Q: A decision-maker with initial wealth w faces a probability of incurring a loss. If the loss occurs,…

A: Risk aversion is the tendency to avoid risk. Risk-averse investors prioritize capital preservation…

Q: The graph below represents the market for sugar in the U.S. The domestic supply and demand curves…

A: * SOLUTION :- From the given information the calculation is given as below as No trade The…

Q: Your retirement account has a current balance of $56,500. What interest rate would you need to be…

A: Given that, Present value = $56,500 Future Value = $1,500,000 Numbers of Years = 40 Annual Deposit…

Q: 15. The firm's profit maximization problem is: max n = F(r, w)-rk-wL {r, w} a. maxx=rK + wL-F(K, L)…

A: Note:- My dear student,As per Bartleby guidelines I have done only one answering at a time, because…

Q: Examine the Labour Laws in Montserrat relating to termination of the employment contract. Do you…

A: Labour Law in Montserrat that related to the termination of the employment contract are follows: A.…

Q: Briefly compare and contrast the demand curve for a monopolistically competitive firm and a…

A: * A market that is monopolistically competitive is one where firms sell goods that are imperfect…

Q: Economists often will advocate an employment subsidy instead of a minimum wage as a better solution…

A: Here we are considering the market for the low skilled workers. Where the demand for the low skilled…

Q: The estimated monthly sales of Mona Lisa paint-by-number sets is given by the formula q = 97e-3p/2,…

A: given that, monthly sales of Mona Lisa is given by the formula q = 97ep-3p2/2

Q: Which of the following are Adam Smith's Dos? A. Protect society from violence and invasion of…

A: Smith's three basic principles of economics: People follow the law of self-interest. Competition…

Q: You are planning to prepare your child to have a withdrawal of P 20,000 each on his 18th, 19th, 20th…

Q: (d) Suppose Krakozhia is open to trade and the world price is 150. Determine the domestic quantity…

Q: Consider the nature of unemployment and inflation and predict whether or not they should have some…

A: Inflation is the term used to describe price increases for almost all goods and services in the…

Q: In your own words, describe what the difference is between an error term and a residual. How does…

A: When a statistical or mathematical model fails to accurately capture the real connection between the…

Q: Hint: label and the relevant points on the graph (like we did in class). Suppose now the "T-shirt"…

Q: A shift in the demand curve for bonds occurs when the quantity demanded changes at each given…

A: The bond demand curve shows the relationship between bond price and the quantity demanded of the…

Q: An asset is purchased for P9,000,000. Its estimated economic life is 10 years after which it will be…

A: The sum of the years' digits is a quick method for calculating the predicted depreciation of an…

Q: The market supply curve for a product is derived from the individual firm supply curves by B…

A: The individual supply curve tell us the quantity supplied at each price. Now the market supply curve…

Q: Label the graph in Figure 1 with all of the parts of the business cycle.

A: A business cycle will be reflecting the fluctuations in the Gross Domestic Product (GDP) around its…

Q: 2. Discuss the factors that contribute to economic growth.

A: Please check the step 2 for solution

Q: In traveling about a city, most people use either subway or bus. Suppose all subway fares were…

A: It has been noticed that when a commodity becomes more expensive, people's willingness to buy it…

Q: i need this in words not handwritten just Rewrite this

A: As asked, wil be typing the solution.

Q: Nations can increase their productivity by specializing and trading with countries that are more…

A: Absolute advantage refers to the ability of a single person, company, region, or country to produce…

Q: 5. Motorcycle shop A sells brand new motor bikes at Php42,250 less 10%. Shop B, on the other hand,…

Q: 2. If a higher inflation is expected, what would you expect to happen to the shape of the yield…

A: The theory of pure expectation:Market expectation theory is another name for it. According to this…

Q: (g) Suppose Krakozhia is open to trade and the world price is 80. Determine the domestic quantity…

A: Here we are given the demand and supply curve for coffee in the domestic economy. Where there is an…

Q: The figure shows the total product curve for different levels of a variable input, labor. O A OB ос…

A: The total product is the output through the production process. Marginal product is the change in…

Q: Find a government regulation imposed by the Commonwealth of Virginia that addresses a market…

A: Demand and supply are unable to balance when there is market failure.. Demand and supply may not…

Q: Advantages of Globalization(at least 5), 2 exsample

A: DISCLAIMER “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Royalty receipts from your patented project are expected to begin five years from now. The…

A: Given information Amount at year 1=$50000 Annual increase=$2000 till 20 years Value at 0 year=$0…

Q: Explain how competitive advantage play a role as one of the globalization driver ?

A: In recent decades, the primary idea of globalization has taken centre stage in economic life. Almost…

Question

A consumer has the utility function
U=x0.2 y0.8
The price of xis $2, price of y is $4 and she a budget of $100 to spend on the two
commodities.
a. Solve the constrained maximization problem for the consumer (use the
Lagrange approach)
b. Establish that the solution is a true maximum

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 3

VIEW

Step by step

Solved in 3 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

Is it possible for total utility to increase while marginal utility diminishes? Explain.
The primary goal of very consumer is to maximize satisfaction. Explain, how a consumer achievesequilibrium using:a) Indifference curve analysisb) Marginal Utility theory
In ordinal Utility approach, let a consumer's utility function is given by TU X³Y. If price of X is 2 birr and price of Y is 3 birr and if budget of the consumer is 100 birr for consumption of X and Y. then what are the utility maximization X and Y?
Vani eats only green eggs and ham. He has an income of $36. Green eggs have a price of Priceof Green eggs = $2 and ham has a price of Price of Ham = $6. Sam’s preferences are represented bythe utility functionUtility = 10Eggs + 40Hama) Draw vani's budget constraint
Suppose that MUx = 10 and MUy = 20. Further suppose that the consumer’s budgetconstraint can be expressed as 20x + 10y = 400. For this consumer, the optimal amount of good x to buy would be a) 5. b) 0. c) 20. d) 40.
(a) A consumer has utility u(x,y,z) = ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pz=1. Optimally she consumes 30 units of z. What is her income? How much money does she spend on x? (HINT: MUx = 1/x, MUy= 2/y, MUz = 3/z and remeber the "equivalent bang for the buck" condition). (b) Forget about (a). Suppose you have t= 29 hours in total to spend on 3 projects X,Y and Z to make some money. If you spend x hours on project X, you make 2 sqrt(x) dollars; If you spend y hours on project Y, you make 3 sqrt(y) dollars; If you spend z hours on project Z, you make 4sqrt(z) dollars; Writing down your "utility function" u(x,y,z) and the constraint, solve the utility maximization problem; what is the optimal amount of time to spend on x? on y? on z?
Suppose an individual has the following utility function: U(x,y)=−4(x−5.5)^2 −2(y−3.5)^2 Further assume that the price of good x, px = $6, the price of good y, py = $8 and the individual has an income m = $65 a) Draw an indifference curve (one IC is enough) that represents this person’s prefer- ences. Please label the graph properly including values for x and y. b) Intuitively, and without formally solving, can you guess the maximized values x* and y*for the above utility function. Explain your answer. c) Derive the optimal values x*and y*by formally solving the above utility function subject to the above constraint. You can use any of the utility maximization techniques we learned in class. d) Compare your answers in parts b) and c). Based on the utility function that is given in this problem as well as the budget constraint, can you explain the differences between the answers you found in parts b) and c) (if any). Be as detailed as possible with your explanation.
Suppose, a glass of lemonade (x) sell for10 taka each and a cupcake (y) cost 60taka. Total income of a particular consumer is200 taka. Utility of consumer 1 from consuming lemonades and cupcakes is given by: U(X,Y) = X0.15Y0.85. Find the utility maximizing choice of the consumer and the total utility.
a. Suppose Fiona’s income is $100 per week, which she allocates between chocolates and books. Chocolates cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to $5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Fiona might have more than one utility-maximizing solution? b. Confirm that if a consumer’s utility function is described by U = 2X + Y, and prices are px = 2 and py = 1, there is no unique utility maximizing solution regardless of income level. What does this tell you about X and Y as commodities? (Hint: draw a graph showing a budget constraint and indifference curve using the information provided.)
Consider the following utility function belonging to “Consumer A”. UA(x,y,z,v) = x0.1y0.2z0.3v0.4. Suppose that prices of x, y, z and v are 1$, 2$, 3$ and 4$. The consumer’s income is 10$. a. Find the values of x, y,z and v that maximize the consumer’s utility subject to his/her budget constraint. b. Suppose that “Consumer B” has a utility function which is a logarithmic transformation of the consumer A’s utility function, i.e. UB =ln UA. Suppose that prices and income are the same. Would the amounts of x, y, z and v consumed by “Consumer B” be the same as the amounts consumed by “Consumer A”?
a. Define a budget line. b. Ilustrate and explain why indifference curves cannot intersect. c. With the use of a diagram, describe a consumer equilibrium.
Suppose a consumer has utility function U(X, Y) = X2/3Y1/3. Suppose the consumer has M =$90 to spend and the prices of goods X and Y are PX = $15 and PY = $6 . a. Carefully express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the…