A consumer's preferences are represented by the following utility function: u(x, y) = 2/T+ Vg+7 1. Recall that for any two bundles A = (xA,YA) and B = (*B, YB) the following equivalence %3D then holds A - B u(A) > u (B) Which of the two bundles (r1, yı) = (9, 4) or (x2, Y2) = (4,9) does the consumer prefer? 2. Take as given for now that this utility function represents a consumer with strictly convex preferences. Also remember that preferences are strictly conver when for any three bundles A, B, and C, if BE A and C A then aB + (1 – a)C > A for any a E (0, 1). Use this information and your answer to part (1) to determine which of the two bundles (x3, Y3) = (7,6) or (*2, Y2) = (4, 9) the consumer prefers. Verify your answer. ||
A consumer's preferences are represented by the following utility function: u(x, y) = 2/T+ Vg+7 1. Recall that for any two bundles A = (xA,YA) and B = (*B, YB) the following equivalence %3D then holds A - B u(A) > u (B) Which of the two bundles (r1, yı) = (9, 4) or (x2, Y2) = (4,9) does the consumer prefer? 2. Take as given for now that this utility function represents a consumer with strictly convex preferences. Also remember that preferences are strictly conver when for any three bundles A, B, and C, if BE A and C A then aB + (1 – a)C > A for any a E (0, 1). Use this information and your answer to part (1) to determine which of the two bundles (x3, Y3) = (7,6) or (*2, Y2) = (4, 9) the consumer prefers. Verify your answer. ||
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Part 2 only
Transcribed Image Text:A consumer's preferences are represented by the following utility function:
u(x, y) = 2 T+ Vỹ +7
1. Recall that for any two bundles A =
(TA, YA) and B
(TB, YB) the following equivalence
then holds
AEB u(A)> u (B)
Which of the two bundles (x1,Yı) = (9,4) or (x2, Y2) = (4,9) does the consumer prefer?
2. Take as given for now that this utility function represents a consumer with strictly convex
preferences. Also remember that preferences are strictly convex when for any three bundles
A, B, and C, if B E A and C E A then aB +(1 – a)C > A for any a E (0, 1).
Use this information and your answer to
(1) to determine which of the two bundles
(03, Y3) = (7,6) or (x2, Y2) = (4, 9) the consumer prefers. Verify your answer.
3. Derive an expression for the marginal rate of substitution. Interpret the MRS. What is the
MRS at the point (x3, Y3) = (7,6)?
4. Derive an equation for the indifference curve through the bundle (x2,Y2) = (4,9). With an
equation it is meant: y as a function of x, y(x), such that (x, y(x)) lies on the indifference
curve passing through bundle (4,9).
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!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
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.Recommended textbooks for you
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 (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