Answer all parts (a)-(d) of this question.There are two goods in the economy: good x and good y with prices px and py, respectively.Alice has an income of m.Suppose first that her utility function isu(x, y) = √x +√y.(a) [10 marks] Derive and illustrate in a graph Alice’s indifferences curves.(b) [15 marks] Derive Alice’s optimal bundle when px = 2, py = 4 and m = 24.(c) [10 marks] Derive Alice’s optimal bundle when px = 8, py = 2 and m = 24.Suppose now instead that Alice had another utility function, namelyv(x, y) = x2 + y2. (1)(d) [15 marks] Derive Alice’s demand function with the utility function v, as specified inequation (1) above.
Answer all parts (a)-(d) of this question.There are two goods in the economy: good x and good y with prices px and py, respectively.Alice has an income of m.Suppose first that her utility function isu(x, y) = √x +√y.(a) [10 marks] Derive and illustrate in a graph Alice’s indifferences curves.(b) [15 marks] Derive Alice’s optimal bundle when px = 2, py = 4 and m = 24.(c) [10 marks] Derive Alice’s optimal bundle when px = 8, py = 2 and m = 24.Suppose now instead that Alice had another utility function, namelyv(x, y) = x2 + y2. (1)(d) [15 marks] Derive Alice’s demand function with the utility function v, as specified inequation (1) above.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Answer all parts (a)-(d) of this question.
There are two goods in the economy: good x and good y with prices px and py, respectively.
Alice has an income of m.
Suppose first that her utility function is
u(x, y) = √
x +
√
y.
(a) [10 marks] Derive and illustrate in a graph Alice’s indifferences
(b) [15 marks] Derive Alice’s optimal bundle when px = 2, py = 4 and m = 24.
(c) [10 marks] Derive Alice’s optimal bundle when px = 8, py = 2 and m = 24.
Suppose now instead that Alice had another utility function, namely
v(x, y) = x
2 + y
2
. (1)
(d) [15 marks] Derive Alice’s demand function with the utility function v, as specified in
equation (1) above.
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 2 steps with 17 images
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