3. Assume Matt's utility function is given by u(x1, x2) = (min {1,2})². The prices of goods 1 and 2 are p₁ and p2, respectively, and his income is m. (a) What kind of preference does this utility function represents? (b) Find the optimal levels of consumption for goods 1 and 2.

3. Assume Matt's utility function is given by u(x1, x2) = (min {1,2})². The prices of goods 1 and 2 are p₁ and p2, respectively, and his income is m. (a) What kind of preference does this utility function represents? (b) Find the optimal levels of consumption for goods 1 and 2.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.8P

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: Find the marginal utility oI X1, the marginal ty o and the marginal rate of substitution for the…

A: Marginal utility is the added satisfaction a consumer gets from having one more unit of a good or…

Q: 3. Suppose you consume two goods, whose prices are given by p₁ and p2, and your income is m. Solve…

A: The objective of the question is to find the demand functions for two goods given the prices of the…

Q: 3. A consumer's utility function is given by U(x, y) = min{x,y}. Initially px prices are pz = 1 and…

A: Compensating variation measures the change in income or wealth that would be necessary to keep an…

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: 2) A consumer’s utility function is: U(x,y) = sqrt(9xy). The price of each good is: (PX,PY) =…

A: Optimal consumption bundle: The optimal consumption bundle is such that at that bundle the…

Q: Consider the following utility function: U(x, y) = xy+x with MUx = y+1 and MUy = x. As the consumer…

A: For product x if (dMUx)/(dx)>0 marginal utility increases. (dMUx)/(dx)<0 marginal utility…

Q: Now suppose that Jason's utility is entirely based on number of hours of skiing (X) and skating (Y).…

A: Utility function : U (x ,y ) = max {aX, bY } Budget Constraint : Px (X) + Py (Y) = M Also its…

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 consumes two agricultural products: Red Meat, and Tomatoes according to the following…

A: Let y be the income of the consumer and let pR , pT be the prices of R and T. Then, given pR , pT ,…

Q: a) Write down Milo's budget equation and draw the corresponding budget line. Clearly label the axes…

A: Consumer M spends his income on stamps and maple candy.Symbolically,Income = I = 27Stamps = SMaple…

Q: I. You only consume two goods and your preferences are represented by utility function U(x1, x₂) =…

A: Monotonic preference refers to a preference ordering in which an individual's preference for one…

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: 4. If an individual's preferences are described by the utility function U(X1, X2 ) = X;? + X2?, a)…

Q: 1. Consider that an individual take utility from the consumption of good x and y according to the…

A: The study of consumer behavior focuses on how people and families choose what to buy while taking…

Q: Consider the following utility function for goods x1 and x2: u(x1,x2)=(x1+x2)2 What type of…

A: Utility function is a representation of individuals preferences for goods and services.

Q: 2) A consumer’s utility function is: U(x,y) = sqrt(9xy). The price of each good is: (PX,PY) =…

A: ***Since the student has asked to solve a specific part of the question, hence, the expert is…

Q: 13. Shawn likes to consume pineapple smoothies and hotdogs. His preferences are represented by the…

A: Consumer surplus is the economic benefit or value that consumers receive when they are able to…

Q: Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The…

A: An indifference curve depicts the combination of two products in several quantities that gives an…

Q: Suppose the utility function is given by U(1, 2) = 14 min{2z, 3y). Calculate the optimal consumption…

A: A utility function is a mathematical function that depicts the subjective satisfaction or value that…

Q: Consider an individual with the following utility function, U(x, x) = ax?x5. The current price of x,…

A: Utility Maximization is the condition where consumer spent the income in such a way that maximise…

Q: (c) What kind of preferences are represented by a utility function of the form u(21,72) = VE1+ 12?…

A: The utility is the want satisfying power of the commodity. The utility would result in the demand of…

Q: 21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be…

A: A utility function is a mathematical representation that quantifies an individual's or a…

Q: 4. Tim wants to maximise his utility given his utility function of U (A, B) = A² B¹. He faces 20; M…

A: Utility is maximised by consuming the bundle where ratio of marginal utilities is equal to ratio of…

Q: II. Your preferences are represented by the utility function U(x₁, x₂) = (x² − x²)⁰.5 for x₁ > 0, x₂…

A: Marginal utility is the additional satisfaction or benefit that a consumer derives from consuming…

Q: 6. Consider a consumer with the utility function u(x, x2) = In(x,) + x2 and the budget constraint p,…

A: A consumer maximizes utility by consuming at a point where slope of indifference curve, ratio of…

Q: 2. Vibha consumes three goods X, (shirts), X, (food in pounds), and X, (shelter in square feet).…

A: Rational consumer always consumes bundle of goods which provides him maximum utility. when law of…

Q: You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The…

A: Given Utility function: U(M,C)=M1/4C3/4 .....(1) Marginal…

Q: a. What is Julio's MRSFe (marginal rate of substiution of food for clothing) when utility is…

A: a) Utility Function = F0.5 C Budget constraint:- 3F + 5C = 100In order to maximise the utility , the…

Q: 6. Consider a consumer with the utility function u(x,, x2) = In(x,) + x, and the budget constraint…

A: Demand function is a mathematical function showing relationship between the quantity demanded of a…

Question

3. Assume Matt's utility function is given by u(x₁,x2) = (min {x₁, x2})². The prices of goods
1 and 2 are p₁ and p2, respectively, and his income is m.
(a) What kind of preference does this utility function represents?
(b) Find the optimal levels of consumption for goods 1 and 2.

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 1 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

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). =
2
VI. Utility Maximization 3. Consider an individual with the following utility function, U(x, x2) = ax5x95. The current price %3D of x, is 2 and the current price of x, is 4. 1. What is this consumer's budget constraint? 2. Calculate the optimal consumption of x, and x, if the consumer has income m.
14. Consider the following utility function: U(x, y) = xy+x with MUx = y+1 and MUy = x.As the consumer buys more x, the marginal utility of x:(a) Diminishes(b) Remains constant(c) Increases
please give answer step by step
5. Julio who consumes two goods Food (F) and clothing (C) has a utility function given by U(F,C)= sqrt(F)C. The price of food is $3 and the price of clothing is $5 and Julio's weekly budget for food and clothing is $100. a. What is Julio's MRSFe (marginal rate of substiution of food for clothing) when utility is maximized? Explain. b. If Julio is at point where MRSFC= 1, where is that point relative to the utility maximzing bundle (show this in a diagram)? c. Can Julio change his bundle so as to increase his satisfaction and if so in what way? Explain fully 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.