There two goods, X and Y , available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are strongly monotone, strictly convex, and represented by the following (di erentiable) utility function: u(x; y) = x + xy + y; where x is the quantity of good X and y is the quantity of good Y . The consumer has wealth w > 0. The price for good X is p > 0, and the price for good Y is q > 0. (a) In an appropriate diagram, illustrate the consumers map of indi erence curves. Make sure you label the diagram clearly, and include as part of your answer any calculations about the slopes of the indi erence curves and where the indi erence curves intersect either of the axes. (b) Formulate and solve the consumer's utility maximization problem. Your  nal answer should describe the consumer's demand for goods X and Y as a function of w, p, and q, as well as the consumer's indi- rect utility function.

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

There two goods, X and Y , available in arbitrary non-negative quantities
(so the consumption set is R2+). A consumer has preferences over consumption bundles that are strongly monotone, strictly convex, and represented by the following (di erentiable) utility function:
u(x; y) = x + xy + y;
where x is the quantity of good X and y is the quantity of good Y .
The consumer has wealth w > 0. The price for good X is p > 0, and the price for good Y is q > 0.

(a) In an appropriate diagram, illustrate the consumers map of indi erence
curves. Make sure you label the diagram clearly, and include as part
of your answer any calculations about the slopes of the indi erence
curves and where the indi erence curves intersect either of the axes.
(b) Formulate and solve the consumer's utility maximization problem.
Your  nal answer should describe the consumer's demand for goods
X and Y as a function of w, p, and q, as well as the consumer's indi-
rect utility function.
(c) Now assume that w = 100 and p = 10.
(i) Illustrate the consumer's demand function for good Y in an appro-
priate diagram.
(ii) Illustrate the consumer's cross-price demand function for good X
in an appropriate diagram.

Expert Solution
steps

Step by step

Solved in 2 steps with 5 images

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.
Similar questions
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