4. P4: Functions of two or more independent variables a. An individual's utility function has the Cobb-Douglas form: U=X0.5y² where U is an index of her utility and X and Y are the weekly quantities of the two goods consumed. Find the marginal utilities of the two goods. Does the consumer ever experience satiation with respect to either good? b. How does the marginal utility of each good vary as consumption of it increases with consumption of the other good held constant? What is the economic significance of the signs of these partial derivatives? c. By differentiation, show that the indifference curve is negatively sloped and convex in the KL plane. Give an economic interpretation to the slope and curvature of the indifference curve. Sketch the graph of the indifference curve.

4. P4: Functions of two or more independent variables a. An individual's utility function has the Cobb-Douglas form: U=X0.5y² where U is an index of her utility and X and Y are the weekly quantities of the two goods consumed. Find the marginal utilities of the two goods. Does the consumer ever experience satiation with respect to either good? b. How does the marginal utility of each good vary as consumption of it increases with consumption of the other good held constant? What is the economic significance of the signs of these partial derivatives? c. By differentiation, show that the indifference curve is negatively sloped and convex in the KL plane. Give an economic interpretation to the slope and curvature of the indifference curve. Sketch the graph of the indifference curve.

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: 6. The law of diminishing marginal utility can be stated as follows: a. as the amount of a good…

A: We will answer the first question since the exact one was not specified. Please submit a new…

Q: 4. Show that the two utility functions given below generate identical demand functions for goods X…

A: Utility refers to the economic concept where individuals or consumers aim to make choices that…

Q: 3. Susan has the following utility function U(x,y) = xy, where x represents food and y represents…

A: *SOLUTION :- * (3)

Q: True or false with reasoning 1)_______When an extra glass of wine is consumed, the total utility…

A: Sol:- since, marginal utility is simply the change in total utility per unit change in the…

Q: Suppose consumer consume two goods. Can both goods be inferior? Can one of the goods be inferior?…

Q: s Dr. Gonzalez drinks five beers, his total utility rises from 5 to 45 when he drinks one beer. His…

A: Marginal utility is the utility gained by consuming one extra unit of a good. Given Dr. Gonzalez's…

Q: 2. Consider these three utility functions: u1 = 2122 U2 = In z1 + In a2 Which of these functions can…

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

Q: Suppose Joe's utility for lobster (L) and soda (S) can be represented as U = L0.5 S0.5. Joe…

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

Q: 1.There are two goods F and C. Let MU and P denote marginal utility and price of each good.…

A: Price effect consists of income effect and substitution effect. Substitution effect is always…

Q: Consider a consumer with the utility function U (x, y) = x" y where x is the quantity of good X and…

A: Optimal consumption bundle is where MUx / MUy = Px / Py Where MUx = Marginal utility from good x MUy…

Q: 1. Suppose that a consumer with the utility function U = X0.25 y0.75 chooses a consumption bundle…

Q: Carefully write down the consumer's utility maximization problem and find Marshallian demand…

A: A utility function refers to the willingness of a consumer to consume a particular consumption…

Q: 4. The CES utility function is given by U (x, y) = * (i). Show that the first-order conditions for a…

A: Hey champ, Welcome to this platform. Here you will get the answer with better quality in minimum…

Q: Utility Maximisation and Non-negativity Constraints. Suppose the consumer wants to maximise utility…

A: Condition for optimal consumption is given as

Q: A consumer has preferences for coffee and pancakes that are complete, continuous, transitive,…

A: Preferences refer to an individual's or a group's subjective ranking or ordering of various goods,…

Q: The law of diminishing marginal utility says that... A. as a person consumes more and more of a…

A: The marginal utility is the satisfaction derived from the consumption of an additional unit. The…

Q: Utility is a type of function that occurs in economics. When a consumer receives x unils of a…

A: The utility function provides a measure of the overall satisfaction (denoted by 'U') that an…

Q: A consumer has to choose the optimal number of slices of pizza and bottles of water to purchase.…

A: Optimal decisions will be reached at the margin. The main approach on making the best decision on…

Q: Suppose you are thirsty and you want to quench your thirst with water. You observe that the first…

A: Marginal utility refers to change in total utility due to the consumption of one additional unit of…

Q: Carefully write down the consumer's utility maximization proble and find Marshallian demand…

A: A consumer maximizes the utility subject to a budget constraint. The utility function is the…

Q: 9. Refer to the following table to ANSWER the following question: The marginal utility of the third…

A: Utility refers to the satisfaction or happiness that a consumer get form the consumption of a goods…

Q: 2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferences…

A: Given Utility function U=0.5X+5logY where X=Soda Y=Juice Budget constraint M=Px.X+Py.Y

Q: der a consumer with the utility function Ur.v) = xy where x is the quantity of good X and y is the…

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

4. P4: Functions of two or more independent variables
a. An individual's utility function has the Cobb-Douglas form: U=X0.5y2 where U
is an index of her utility and X and Y are the weekly quantities of the two goods
consumed. Find the marginal utilities of the two goods. Does the consumer ever
experience satiation with respect to either good?
b. How does the marginal utility of each good vary as consumption of it increases
with consumption of the other good held constant? What is the economic
significance of the signs of these partial derivatives?
c. By differentiation, show that the indifference curve is negatively sloped and
convex in the KL plane. Give an economic interpretation to the slope and
curvature of the indifference curve. Sketch the graph of the indifference curve.
5. P5: Lagrange Multiplier Method
a. Consider the following utility function: U=X¹Y4, x, y> 0. Let Px = 2 and
Py = 3 and M = 100. Find the utility-maximizing consumption bundle.
b. Find the marginal utilities of the goods, x and y. Are they always positive?
c. Sketch their graphs.
d. By implicit differentiation, find the slope of any difference curve and show that it is
given by the ratio of marginal utilities of the two goods.Are the indifference curves
always negatively sloped? Sketch their graphs.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 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

. Consider an economy with the following features. . There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, s) = 4c¹/4g¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium?
True or false with reasoning: 1) _______When we claim that utility can be ordinally measured, we assume that the consumer is able to measure the total and marginal utility received when one extra unit of a commodity is consumed. 2)_______If MRS between two goods is constant, then having more of one good without having more of the other does not increase utility. 3)_______Marginal Utility increases until total utility is at a maximum and then marginal utility decreases.
When diminishing returns are present in consumption, the relationship between total utility and marginal utility is as follows: O Total utility increases at a decreasing rate while marginal utility decreases Total utility increases at an increasing rate while marginal utility increases Total utility increases at an increasing rate while marginal utility decreases Total utility decreases at a decreasing rate while marginal utility increases
6. A consumer has an expenditure function given by E = Ū(P+). When the consumer has an income of 100, it can reach a maximum utility of 20. The price of x increases by 3 and the consumer's income increases by 25. Are they better off or worse off than before the changes? Explain how you know. Full solution please
3.5 Marginal Utility and Consumer Choice Participation Question 7: • A consumer derives utility from consuming integer units of Good X and Good Y. See the table below for a total utility level at different consumption levels. What is the marginal utility of the second unit of Good X when the consumption of Good Y is at 3? Total Utility 1 Good X 2 Good X 3 Good X 1 Good Y 1 8. 2 Good Y 8 10 3 Good Y 10 11 A. 10 В. 5 С. 3 D. 2
Please tell me which of the multiple choices in question 1.6)1.7)1.8) are correct.State only the correct ones please. 1.6) The marginal rate of substitution (MRS) can be defined as: Select one or more: a. The amount of one good that the consumer is willing to trade for one unit of the other. b. The ratio of the amounts of two goods. c. The change in the consumer’s utility when one good is substituted for another. d. The absolute value of the slope of the indifference curve. 1.7) (SEE ATTACHED PICTURE) The diagram shows that: Select one or more: a. If Angela works 24 hours a day she can still survive. b. There is a technically feasible allocation where Angela does not work. c. A new technology that produced more grain would give a larger technically feasible set. d. If Angela needed less grain to survive the technically feasible set would be smaller.
4. Suppose that a consumer with the utility function U =X0.25 Y0.75 choses a bundle where X=5 and Y=10. If the prices of the two goods are Px= $1, and Py = $3. Calculate marginal utility per dollar spent on each good. Can this consumer increase utility without increasing expenditure and if so how?