Let ₁ and 2 be the amounts of two goods whose joint utility function is U (x1, x2) = 9x₁ + 3x2 − 4x² − x². - (a) Compute the partial derivatives au Əx₁' au 2² U Əx₂' dx²¹ 2² U dx²2 (b) Does the law of diminishing marginal utility hold for this utility function? Justify your answer. (c) Find the marginal rate of commodity substitution (MRCS) when x₁ = 1 and x₂ = 1/2.
Let ₁ and 2 be the amounts of two goods whose joint utility function is U (x1, x2) = 9x₁ + 3x2 − 4x² − x². - (a) Compute the partial derivatives au Əx₁' au 2² U Əx₂' dx²¹ 2² U dx²2 (b) Does the law of diminishing marginal utility hold for this utility function? Justify your answer. (c) Find the marginal rate of commodity substitution (MRCS) when x₁ = 1 and x₂ = 1/2.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
can you clearly show your working, thanks

Transcribed Image Text:Let ₁ and 2 be the amounts of two goods whose joint utility function is
U (x1, x2) = 9x₁ + 3x2 − 4x² − x².
-
(a) Compute the partial derivatives
au
Əx₁'
au 2² U
Əx₂' dx²¹
2² U
dx²2
(b) Does the law of diminishing marginal utility hold for this utility function?
Justify your answer.
(c) Find the marginal rate of commodity substitution (MRCS) when x₁ = 1
and x₂ = 1/2.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 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