8pts) For the following utility functions:1. U(X, Y) = XY2. U(X, Y) =XY+ 10Y%3D3. U(X, Y) = X² + Y?Write the general equation of the MRS for each utility function.а.b. Write the equation for the indifference curve where utility is equal to 100 for each utilityfunction.c. Determine whether these indifference curves for each of the utility functions are convex(that is, whether the MRS decreases as x increases) or are concave (and thus violate anassumption about preferences).

Since you have asked multiple questions with multiple subparts, so as per Bartleby's guideline we…

Answered: Write the general equation of the MRS…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Which of the following is not a property of the family of indifference curves representing a consumer's tastes between two goods? No two indifference curves can cross. The indifference curves are all concave. Each basket of goods is on one and only one indifference curve. The indifference curves are all downward sloping.
Emily is a utility maximizer. Her income is $100, which she can spend on cafeteria meals and on notepads. Each meal costs $5 and each notepad costs $2. At these prices Emily chooses to buy 16 cafeteria meals and 10 notepads. a) Draw a diagram that shows Emily’s choice using an indifference curve and her budget line, placing notepads on the vertical axis and cafeteria meals on the horizontal axis. Label the indifference curve, I1, and the budget line BL1. Make sure you calculate the endpoints of the budget constraint. b) The price of notepads falls to $1; the price of cafeteria meals remains the same. On the same diagram, draw Emily’s budget line with the new prices and label it BL2. c) Lastly, Emily’s income falls to $90. On the same diagram, draw his budget line with this income and the new prices and label it BL3. Is she worse off, better off, or equally as well off with these new prices and lower income than compared to the original prices and higher income?
List and briefly explain each of the four properties of indifference curves. Provide an example where you have made a buying decision based on one or more of these properties.
Amy consumes x and y and her preferences can be represented by the following utility function U(x,y) = 4x + y. 1. Are Amy's preferences transitive? 2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x? Explain. 6- 3. Can you use (2) to answer whether Amy's preferences are strictly monotonic? 4. What is MRS.y ? Is MRSx.y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? 5. On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve. Also indicate on your graph whether the indifference curve will intersect either or both axes. Label the curve U1. 6. Are Amy's preferences convex? Are they strictly convex? Explain
A consumer has the following utility function: U(x, y) = y + x1/2. Let px and py bt the corresponding prices and m her income. a). Write down the corresponding Lagrangian function and find the first order conditions (FOCs). b). Use these FOCs to find the expression for the marginal rate of substitution (MRS). Bearing in mind that the MRS is the slope of the indifference curve, what can you tell about the indifference curves of a quasilinear utility function?
Sketch indifference curve for the given utility levels. Use arrow to show the direction in which utility is increasing U(x,y) = 2y ; U=10 U(x.y) = (X+2Y)2 U = 9 U(x,y) = min(2X, X+Y) U = 6 U(x,y) = XY 2, U = 16 (hint: MUx=Y2 MUy =-2XY3 and slope of indifference curve = MRS = -MUx/MÜy) %3D
Suppose a consumer's utility function is given by u(x,y) = Min{0.5x , 2y}, where Min is the minimum function. What is the shape of the consumer's indifference curves? a) downward sloping and convex b) linear and downward sloping c) L-shaped (right angle) d) horizontal e) linear and upward sloping
Mrs. Griffiths earns $5000 a week and spends her entire income on dresses and handbags, since these are the only two items that provide her utility. Furthermore, Mrs. Griffiths insists that for every dress she buys, she must also buy a handbag. Draw an indifference curve showing the optimum choice. Label the optimum as point A. What would be the marginal rate of substitution at the point that corresponds to the optimal consumption choice? Interpret the marginal rate of substitution
1
Prove that the utility maximization conditions as suggested by the “marginal utility framework” are consistent with the “indifference curves approach”.
Could Figure 3.2 be a single indifference curve if preferences are monotonic?
Outline the four properties that apply to all indifference curves.

Recommended textbooks for you

ENGR.ECONOMIC ANALYSIS

Economics

ISBN:

9780190931919

Author:

NEWNAN

Publisher:

Oxford University Press

Principles of Economics (12th Edition)

Economics

ISBN:

9780134078779

Author:

Karl E. Case, Ray C. Fair, Sharon E. Oster

Publisher:

PEARSON

Engineering Economy (17th Edition)

Economics

ISBN:

9780134870069

Author:

William G. Sullivan, Elin M. Wicks, C. Patrick Koelling

Publisher:

PEARSON

ENGR.ECONOMIC ANALYSIS

Economics

ISBN:

9780190931919

Author:

NEWNAN

Publisher:

Oxford University Press

Principles of Economics (12th Edition)

Economics

ISBN:

9780134078779

Author:

Karl E. Case, Ray C. Fair, Sharon E. Oster

Publisher:

PEARSON

Engineering Economy (17th Edition)

Economics

ISBN:

9780134870069

Author:

William G. Sullivan, Elin M. Wicks, C. Patrick Koelling

Publisher:

PEARSON

Principles of Economics (MindTap Course List)

Economics

ISBN:

9781305585126

Author:

N. Gregory Mankiw

Publisher:

Cengage Learning

Managerial Economics: A Problem Solving Approach

Economics

ISBN:

9781337106665

Author:

Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:

Cengage Learning

Managerial Economics & Business Strategy (Mcgraw-…

Economics

ISBN:

9781259290619

Author:

Michael Baye, Jeff Prince

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS