Q 12 1) A consumer has the utility functionU (x1, x2) = x1.5x2.5E(a) In the same graph, draw the indifference curve {(x₁, x₂) € R² |U (x₁, x2) = 2}.(b) Are these preferences strictly monotone?(c) Are these preferences convex? Is U quasiconcave? Justify your answers formally.

We are given the utility function as: U(x1, x2) = x10.5x20.5

1) A consumer has the utility function U (x1, x₂) = x1.5x2.5 (a) In the same graph, draw the indifference curve {(x1, x2) € R²|U (x1, x2) = 2}. (b) Are these preferences strictly monotone? (c) Are these preferences convex? Is U quasiconcave? Justify your answers formally.

1) A consumer has the utility function U (x1, x₂) = x1.5x2.5 (a) In the same graph, draw the indifference curve {(x1, x2) € R²|U (x1, x2) = 2}. (b) Are these preferences strictly monotone? (c) Are these preferences convex? Is U quasiconcave? Justify your answers formally.

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

ChapterE: Budget Constraint And Indifference Curve Analysis

Section: Chapter Questions

Problem 3QP

See similar textbooks

Related questions

Q: c. demand is likely to fall d. imports are likely to fall 9. In consumer behavior the culture,…

A: 8. Economic growth refers to a rise in the real per capita gross domestic product of an economy. An…

Q: 8. In a potential economic growth rate: a. unemployment is likely to fall b. prices are likely to…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: The Philippines has the highest Gini coefficient among ASEAN's six largest economies at 41.58%.…

A: Given information Gini coefficient of Philippines=41.58%=0.4158 Gini coefficient=area of A/Area of…

Q: Thanks to a (hopefully) long sequence of great decision by their ruler, the population feels…

A: You have posted multiple questions. As per our policy, we can answer just 1 question per post.…

Q: f ... 3 D JM 83% i 9:35 a.m. Units 4 and 5 Worksheet Question 3b The government in your country is…

A: Answer - "Thank you for submitting the question . But we are authorized to solve one question at a…

Q: Facebook is the biggest seller of advertising space in the social media market (Instagram is also a…

A: A monopolist earns maximum profit by producing at level of output where MR = MC. Total Profit =…

Q: It measures of the rate at which a consumer can give up some amount of one good in exchange for…

A: As per the guidelines answer is given to the first question: "Indifference curves represents…

Q: 24 28 30 Mobile phones (1 000s) 10 18 a) Mobile phones by 6 000 is 1 000 laptops b) Laptops by 1 000…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: 5. Given the demand for a product as Qd = 100 – 5p and the supply as Qs = -20 + 3p, you are told…

A: 5) The quantity demanded of a good or a service is the total demand for a good or a service by…

Q: $40 $35 MC ATC $30 AVC $25 P = MR $20 $15 $10 $5 $0 20 40 60 80 100 120 Output (Q) The diagram above…

A: Perfectly competitive market: - it is a market condition where there are many buyers and many…

Q: gure 5.1: Solow Diagram NVESTMENT, EPRECIATION dk

A: The solow model explains the short run and long run growth of economy through the capital…

Q: a. If the nominal interest rate is 0.05% and the inflation rate is 1%, what is the real interest…

A: ***Since the student has posted multiple questions, the expert is required to solve only the first…

Q: A firm produces its product using only labor. Its production function is Q = 20L-L², where Q is the…

A: Since you have posted multiple independent questions, according to the guidelines, only the first…

Q: Table 13-17 Consider the following table of long-run total cost for four different firms: Quantity…

A: Constant returns to scale refers to situation when output increases in the same amount as the cost…

Q: 5. The coach of a high school football team decides to allow girls to play football on the same team…

A: The problem relates to the subject of economic ethics and behavioural economics.

Q: Suppose you invest $2000 today, another $200 one year from now, and still another $800 two years…

A: Given the invested amount = $2000 After one year invested amount = $200 After two year invested…

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: Suppose now that the previous subsidy for schooling is removed, and the government instead…

A: We are solving question 11 (as per the policy we are only allowed to provide answer of one question)…

Q: pronts 4. A market that generates a negative externality that has not been internalized generates an…

Q: QUANTITY Refer to Figure. Assume that the above market is for plastic water bottles. Which of the…

A: 7. A shift in the supply curve occurs when there is more than one factor other than price involved…

Q: c. How does the ratio p,x/p,y depend on the value of ö? Explain your results intuitively. (For…

Q: Answer question 6C only

A: Equilibrium Point:The equilibrium point refers to the point where the demand is equal to supply, and…

Q: 29. Money demand is a decreasing; real a. b. function of the increasing; real increasing: nominal…

A: Money demand refers to an individual's demand for money in the form of different assets like bonds,…

Q: $70 $60 $50 $40 $30 $20 LRATC LRMC $10 Demand = P MR $0 50 100 150 200 250 Output (Q) The diagram…

A: Q24AnswerThe firm produces at LRMC=MRwhereQ=100P=40 from the demand curveATC=20Profit…

Q: 9. In consumer behavior the culture, social class, and reference group influences have been related…

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

Q: QUESTION 19 When the demand of a product is elastic then an increase in the price of that good will…

A: In the market, the price elasticity of demand plays a significant role for a producer to determine…

Q: Q.4.1 Use the following information on economy X to answer the questions below. Consumption…

A: At equilibrium, Y = aggregate expenditure Y= consumption + investment + government + exports -…

Q: Current Account Balance = (Export Import) + net income from abroad + Net unilateral transfer Current…

A: Answer Explanation Current account +capital account+finanancial account=0 -100+[-10]+financial…

Q: Consider the five investment alternatives described below. Which alternatives can be eliminated from…

A: Dear learner you have posted multiple questions, as per our policy we have solved only first…

Q: 4. Now consider this policy: the government taxes oil producers $10,000, and uses the revenue to…

A: Ans 3 In this case, government taxes the oil producers by $10,000 that is government's income is…

Q: 4. Why does a change in elasticity of demand affect the monopoly? Discuss only using words. DO NOT…

A: 4. The elasticity refers to the responsiveness of the quantity demand due to change in the price. If…

Q: 10. Why does the government not set a minimum wage for corporate lawyers and airline pilots?

A: A minimum wage refers to the lowest wage a worker can be paid legally.

Q: Question 6 Which of the following examples represents convergence? O Lower income countries are…

A: Convergence is the tendency of countries to come to their respective steady states.

Q: 18. Calculate the gross domestic product for the economy with the following data: Indicators Amount…

A: Note:- Hi! Thank you for the question, As per the honor code, we are allowed to answer one question…

Q: (b) In period analysis, the dynamic stability of equilibrium depends on (the complementary…

A: Answer B The dynamic stability of equilibrium. Consider y''+ay'+b=0 be the differential equation of…

Q: The Federal Open Market Committee consists of O 12 members, each of which is the president of one of…

A: The Federal Open Market Committee (FOMC) is the monetary policymaking body of the Federal Reserve…

Q: Utilize the provided goal post of the United Nations. Based on the given information: a. Life…

A: Introduction data of Philippines has given as Life 67 years Adult literacy rate 68 %…

Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

Q 12

1) A consumer has the utility function
U (x1, x2) = x1.5x2.5
E
(a) In the same graph, draw the indifference curve {(x₁, x₂) € R² |U (x₁, x2) = 2}.
(b) Are these preferences strictly monotone?
(c) Are these preferences convex? Is U quasiconcave? Justify your answers formally.

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

Given

Part A

Part B

Part C

Step by step

Solved in 4 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

U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.
II. Your preferences are represented by the utility function U(x₁, x₂) = (x² − x²)0.5 for x₁ > 0, x₂ > 0, and x² > x². 1. Find your marginal utility function for each good.
2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current in come is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?
21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, Py = 5 and m = 100. Suppose that px increases to px = 15, how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =
A5
You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.
please give answer step by step
6
2. Maria likes to have one cup of coffee (x) and two slices of bread (y) each morning. Which of the following utility functions represents Maria's preference for (x, y)? (a) U(x, y) = min(8x, 2y) (b) U(x, y) = min (4x, 2y) - RIGHT ANSWER (c) U(x, y) = min(x, 2y) (d) U(x, y) = min(x, 2y)
2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current income is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X, Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?
(2) Consider the utility function u(x, y) = Vx+ay. Your budget constraint is P1x+p2y = М. (a) Find the marginal utilities for these goods. (b) Show that these preferences are quasilinicar. (c) Solve the consumer's optimization problem.
2) A consumer’s utility function is: U(x,y) = sqrt(9xy). The price of each good is: (PX,PY) = (15,20). The monthly budget is: M = 600, answer the following:a. What is the optimal bundle (X, Y) that maximizes the consumer’s utility?b. What is the optimal utility given your answer from part a?c. If the desired level of utility the consumer is U = 400, what would be the optimal bundle (X, Y) to minimize consumer expenses?d. Given U = 400 from part c, what would be the new optimal bundle for both goods if PX increases to 25?e. Given the price increase in good X from part d, what would be the optimal bundle for this consumer wishing to maximize its utility with an income, M = 600?f.: Graph the budget line and utility curve from part a i need help on part c