Consider the consumer problem with two goods, apples and oranges. Let x be the amount of apples and y be the amount of oranges, and let u(x, y) = 2√x + y be the utility function of the consumer. Let på be the price of apples, py be price of oranges, and I be the income of the consumer. (a) Using the condition that the MRS is equal to the relative prices, that is, Px ди/дх ди/ду Py derive the demand functions of apples and oranges.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question
1. Consider the consumer problem
with two goods, apples
and oranges. Let x be the amount of apples and y be the amount of oranges, and
let u(x, y) = 2√x + y be the utility function of the consumer. Let på be the price
of apples, py be price of oranges, and I be the income of the consumer.
(a) Using the condition that the MRS is equal to the relative prices, that is,
Px
ди/дх
ди/ду Py
2
derive the demand functions of apples and oranges.
(b) Even though the demand function of apples does not explicitly contain I, it is
assumed that I cannot be too small. Explain why this assumption is necessary.
=
(c) Let I
90 and suppose that py = 6. Consider a price increase of apples
from 2 to 3 that leaves the price of oranges unchanged at 6. Calculate the
substitution effect and the income effect from this price change regarding the
demand for apples.
Transcribed Image Text:1. Consider the consumer problem with two goods, apples and oranges. Let x be the amount of apples and y be the amount of oranges, and let u(x, y) = 2√x + y be the utility function of the consumer. Let på be the price of apples, py be price of oranges, and I be the income of the consumer. (a) Using the condition that the MRS is equal to the relative prices, that is, Px ди/дх ди/ду Py 2 derive the demand functions of apples and oranges. (b) Even though the demand function of apples does not explicitly contain I, it is assumed that I cannot be too small. Explain why this assumption is necessary. = (c) Let I 90 and suppose that py = 6. Consider a price increase of apples from 2 to 3 that leaves the price of oranges unchanged at 6. Calculate the substitution effect and the income effect from this price change regarding the demand for apples.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Utility Function
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