Let u(x₁, x₂) = 4x₁ + x₂ be the utility function. 1. Sketch the indifference curves corresponding to utility levels 2 and 4. Clearly label your graph. 2. What is the marginal rate of substitution for good 1 (state the unit of measurement)?

Let u(x₁, x₂) = 4x₁ + x₂ be the utility function. 1. Sketch the indifference curves corresponding to utility levels 2 and 4. Clearly label your graph. 2. What is the marginal rate of substitution for good 1 (state the unit of measurement)?

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: Find the marginal utility (MU) and marginal rate of substitution (MRS) of following utility…

A: Marginal Utility (MU) and Marginal Rate of Substitution (MRS) are two important concepts in…

Q: 1 Marginal utility and marginal rate of substitution Suppose an individual who derives utility u(x,…

Q: Total utility is 0 when marginal utility is 0 True/False

A: # Utility is a concept which helps us calculate the satisfaction a consumer gets when a good or…

Q: It is known that the indifference curve is convex. What does this tell you about the relationship…

A: The indifference curve refers to the graphical representation of different combinations of two goods…

Q: 1. Prove if the indirect utility function is quasiconvex The indirect utility function: V(p,w) =…

A: Indirect utility capacity is gotten from direct utility capacity with boundaries of use and cost of…

Q: 3. Consumer Optimization Utility Function: U = In (x) + 2*In (y) Budget Constraint: 50 = x + 2y Find…

A: A budget constraint addresses every one of the mixes of goods and services that a buyer might buy…

Q: Help!

A: Now, we will examine each component more thoroughly: (a) Budget Constraint: The budget constraint…

Q: if there are 2 products, milk and yoghurt, how can we understand the satisfaction maximization…

A: In the context of consumer choice and satisfaction maximization, a budget line represents all…

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: explain law of diminishing marginal utility concept with example.

A: According to the law of diminishing marginal utility, as we consume more of a good, the amount of…

Q: PROBLEM (7) A consumer with I dollars budget has the utility u(x,y) = x(y+1) over amounts of cake…

A: A person's preferences and level of satisfaction from consuming various products and services are…

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: Using the concept of consumer choices, draw a graphical representation of utility maximization. Your…

A: The diagram is shown in the next step.

Q: PROBLEM (5) A consumer with I dollars budget has the utility u(x,y) = x(y+1) over amounts of cake…

A: This can be described as the concept that shows the effect of change in the price of one good on the…

Q: Marginal utility can be: decreasing, but not negative. positive, but not…

A: 1. Marginal utility can be C.Positive, negative or zero Marginal utility is an important concept…

Q: Consider the utility function U(r, g) = r+ Iny. (a) Find the marginal rate of substitution, MRS of…

A: The marginal rate of substitution (MRS) is the amount of a good that a consumer is willing to…

Q: Explain the difference between the following concepts: Cardinal and ordinal measures of utility…

A: The utility is the wants satisfying power of a product. A consumer uses goods or services because…

Q: (Review Question) Sarah consumes both wine (x) and cheese y) and considers them perfect substitutes.…

A: Utility: Utility for a consumer can simply be defined as the want-satisfying power that a good…

Q: Law of equi marginal utility is an important law of cardinal utility analysis. Explain this law with…

A: Cardinal Utility analysis is one of the oldest demand theory. It explains the law of demand that…

Q: Abigail, Bernard, Cornwallis, and Douglas each derive a distinct amount of utility from consuming…

A: Utility theory is a positive theory. that looks to make sense of the people's noticed way of…

Q: t is known that the indifference curve is convex.

A: GIVEN It is known that the indifference curve is convex. What does this tell you about the…

Q: Consider a consumer with a utility function U(X,Y) = 4√x + √Y a) Evaluate whether marginal utilities…

A: To get whether the marginal utility is diminishing we need to differentiate marginal utility with…

Q: Greg has the following utility function:u=x63x937. He has an income of $66.00, and he faces these…

A: Compensating variation is the additional money that the consumer would need to reach its initial…

Q: commodity. In other words, It is the utility derived from each additional unit. Marginal Utility…

A: Option A Marginal Utility It is the change in total utility which is attained when an additional…

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

Q: x0.5 y0.5, A consumer has a Cobb-Douglas utility function u = and she has a bundle of goods (x, y) =…

A: The Cobb-Douglas utility function is a widely used form of utility function in economics that…

Q: additive utility O ignoring sunk cost rational optimization diminishing marginal utility

A: Utility, in the context of economics, describes the satisfaction, happiness, or well-being that an…

Q: explain law of diminishing marginal utility concept with exampl

A: The additional pleasure or benefit (utility) a customer obtains by acquiring an extra unit of a…

Q: Consider the utility function U(x, y) = xy + x. Which of the following bundles is not on the same…

A: We have to calculate the value of U for all (x,y). The bundle which gives the different result will…

Q: For each of the following utility functions get the marginal utility of consumption of each of the…

A: This can be defined as a concept that shows that when a purchaser purchases an extra unit of any…

Q: (2) Consider the utility function u(x, y) = Vx+ay. Your budget constraint is P1x+p2y = М. (a) Find…

A: Since you have not mentioned which question you require an answer for, as per our standard procedure…

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: Utility functions are simply mathematical representations of preferences. (a) True (b) False

A: Utility is defined as the total amount of satisfaction received by an individual by consumping a…

Q: ate a table and graphs (a) Suppose we have preferer indifference curve through the bundle X = 30 and…

A: Utility function : U = 10 x2/3 y1/3 Budget Constraint : Px*x + Py*y = M Optimal consumption is…

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: Is it possible for marginal utility to be negative while total utility is positive

A: The total utility (TU) can be understood as the total satisfaction that is derived from consumption…

Q: Please answer this question with steps thank you

A: Approach to solving the question: Detailed explanation: Examples: Key references:

Q: Consumer utility function is, U(XY) = X 75 Y 0.5. The price of X good 2 AZN and Y good 4 AZN. If…

A: A consumer maximizes utility by consuming at the point where slope of indifference curve given by…

Q: At last time you have answered my question ,but I still have some problems want to ask you and there…

A: To understand the concepts of the Indifference Curve and Budget Line, let us first understand the…

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…

Concept explainers

Marginal Rate of Technical Substitution

MRTS reaches a manufacturer when a part of the product is lowered to sustain the manufacturing level when the other part is extended. It is the level of the quantity that is lowered when one extra volume is used, and the output is unchanged.

Preferences and Utility Analysis

Before understanding what is preference and utility analysis, it is very important to understand the terms preference and utility separately.

Question

Let u(x₁, x₂) = 4x₁ + x₂ be the utility function.
2
1. Sketch the indifference curves corresponding to utility levels 2 and 4. Clearly label your
graph.
2. What is the marginal rate of substitution for good 1 (state the unit of measurement)?

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: Define indifference curve.

VIEW

Step 2: Draw the individual curve.

VIEW

Step 3: Calculate MRS.

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 5 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

Questions 1. Will's utility from vacations (91) and meals (92) is given by the function U(V, M) = 91 x 92. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, while the price of vacations remained the same. Both years, Will had an income of $1500. (a) What is the compensating variation for the price change in meals? (b) What is the equivalent variation for the price change in meals?
(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curve through the bundle (X = 30, Y = 30). What is the utility of (30, 30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? < (c) Why is the Marginal Rate of Substitution not applicable in this example? < (d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain.< (e) State the consumer's maximization problem and express this in words.< (f) Now let Px = 10, Px= 20 and income M = 2000. Find optimal X*, Y*, and the resulting Utility (U*). Show your work. < (g) Now let Py = 15. How does optimal consumption (X*.Y*) and utility (U*) change relative to (e)? Explain in simple terms and show in a diagram.<
4
In a monetary economy with flexible prices, a temporary contraction of the quantity of money will cause Select one: O a. An increase in the nominal interest rate O b. O c. A proportional fall in the price level More inflation in the future, unless it is accompanied by fiscal adjustment O d. two of the other
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?
Suppose a consumer's utility function is U(x₁,x₂)=x₁x₂. The price of Good 1 is 1, the price of Good 2 is 2, and his income is 40. 1st Question 3 On a graph, use blue ink to draw the consumer's budget line. (Use a ruler and try to make this line accurate.) Plot a few points on the indifference curve that gives him a utility of 150 and sketch this curve with red ink. Now plot a few points on the indifference curve that gives him a utility of 300 and sketch this curve with black ink or pencil.
solve g, h please Thank you
2. Donald derives utility from only two goods, carrots (X) and donuts (Y). His utility function is as follows: U(X, Y) = XY. Donald has an income (M) of S120 and the price of carrots (Px) and donuts (PY) are both $1. a) Find the marginal utility that Donald receives from carrots (MUx) and from donuts(MUY) )
4. Let u(z) be a utility function that represents the preferences of a household. We say that the function v(r) is a monotonic transformation of u if f(-) is a strictly increasing function and v(z) = f(u(z)). (a) Show that if v(z) is a monotonic transformation of u, it represents the same preforences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are reprosented by a utility function of the form u(a1, 12) = VEi +#2? What about the function v(z1, r2) = 13z + 13r2? (d) Consider the function u(r1, 2) = VE1#2. What kind of preferences does it represent? Is the function (11, r2) jz a monotonic transformation of 1 u(r1, 12)? Is the function w(r1, 12) u(r1, 12)? = zfr a monotonic transformation of
solve d,e,f please Thank you
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.
A decrease in the price of good Y will have what effect on the budget line on a normal X-Y graph? Select one: OA. Parallel outward shift of the line OB. Parallel inward shift of the line OC. Decrease the horizontal intercept COD. Increase the vertical intercept