6- Consider a consumer with a utility function U(X,Y) = 4√x + √Y a) Evaluate whether marginal utilities of X and Y are diminishing or not. b) Compute marginal rate of substitution (MRS). What is the value of MRS when the consumer is consuming 4 units of X and 64 units of Y. d) c) Provide an interpretation of the value of MRS you found in part (c). Evaluate whether this consumer has diminishing marginal rate of substitution or not

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question

Please explain step by step

5-
6-
For this question, consider that the letter "A" denotes the last 4 digits of your
student number. That is, for example, if your student number is: 12345678, then
A = 5678.
Suppose that the consumer has a utility function given by U(X,Y) = X0,2 y0,8
The prices of goods X and Y are given by px=4 TL and py=2 TL. The total
budget the consumer has is given by I = A TL.
a. Write down the consumer's optimization problem (formally, as we wrote in the
lectures).
b. Apply the Lagrangian method. Find the necessary condition (NC) for the
consumer's optimization problem. Then find the values of X and Y that maximize
consumer's utility.
C. Illustrate your results by using a graph.
d. In the graph you drew for part (c), mark a consumption bundle that is not optimal
(i.e. does not satisfy the NC) and discuss why it is not optimal.
Consider a consumer with a utility function U(X,Y)= 4√x + √Y
a) Evaluate whether marginal utilities of X and Y are diminishing or not.
b) Compute marginal rate of substitution (MRS). What is the value of MRS
when the consumer is consuming 4 units of X and 64 units of Y.
c) Provide an interpretation of the value of MRS you found in part (c).
d) Evaluate whether this consumer has diminishing marginal rate of
substitution or not.
Transcribed Image Text:5- 6- For this question, consider that the letter "A" denotes the last 4 digits of your student number. That is, for example, if your student number is: 12345678, then A = 5678. Suppose that the consumer has a utility function given by U(X,Y) = X0,2 y0,8 The prices of goods X and Y are given by px=4 TL and py=2 TL. The total budget the consumer has is given by I = A TL. a. Write down the consumer's optimization problem (formally, as we wrote in the lectures). b. Apply the Lagrangian method. Find the necessary condition (NC) for the consumer's optimization problem. Then find the values of X and Y that maximize consumer's utility. C. Illustrate your results by using a graph. d. In the graph you drew for part (c), mark a consumption bundle that is not optimal (i.e. does not satisfy the NC) and discuss why it is not optimal. Consider a consumer with a utility function U(X,Y)= 4√x + √Y a) Evaluate whether marginal utilities of X and Y are diminishing or not. b) Compute marginal rate of substitution (MRS). What is the value of MRS when the consumer is consuming 4 units of X and 64 units of Y. c) Provide an interpretation of the value of MRS you found in part (c). d) Evaluate whether this consumer has diminishing marginal rate of substitution or not.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Utility Maximization
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
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
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)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
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-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education