Principles of Economics 2e
2nd Edition
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
Chapter6: Consumer Choices
Section: Chapter Questions
Problem 10RQ: What is the rule relating the ratio of marginal utility to prices of two goods at the optimal...
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Question
![2. [This question describes a class of preferences that combine aspects of perfect
complements and perfect substitutes.]
Suppose u(x) = min{arı + ßr2, yz₁+z2}, for some parameters a, ß, 7, 6 > 0.
Assume that > 7.
(a) Will this consumer will spend all their money (i.e. choose z so that
p·x* = m)? Why or why not?
(b) If r¡ > 0 and î; > 0, what is z*? In this case, what is u(z)?
(c) Name an example for (a, ß, 7, 8, P₁, P2, m) such that the consumer will only
buy good 1. Justify your answer.
(d) Name an example for (a, 6, 7, 8, P₁, P₂, m) such that the consumer will only
buy good 2. Justify your answer.
(e) Name an example for (a, ß, y, d, P1, P2, m) such that the consumer will buy
both goods. Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd86cda1-af2d-4585-b012-7ab18b7ef9b3%2F74ed459c-497d-430c-9d06-383516a4c993%2Facc3ies_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. [This question describes a class of preferences that combine aspects of perfect
complements and perfect substitutes.]
Suppose u(x) = min{arı + ßr2, yz₁+z2}, for some parameters a, ß, 7, 6 > 0.
Assume that > 7.
(a) Will this consumer will spend all their money (i.e. choose z so that
p·x* = m)? Why or why not?
(b) If r¡ > 0 and î; > 0, what is z*? In this case, what is u(z)?
(c) Name an example for (a, ß, 7, 8, P₁, P2, m) such that the consumer will only
buy good 1. Justify your answer.
(d) Name an example for (a, 6, 7, 8, P₁, P₂, m) such that the consumer will only
buy good 2. Justify your answer.
(e) Name an example for (a, ß, y, d, P1, P2, m) such that the consumer will buy
both goods. Justify your answer.
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Given:
Utility function:
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