Homework Help is Here – Start Your Trial Now!
Business
Economics
mer of two goods has utility U(X1, 2) = X1X2. She can purchase each good ce of p; dollars per unit. Alternatively, she can buy a discount card for fixed fee of c that allows her to purchase good 1 at a price of p₁/2 dollars per unit. (The discount s no effect on the price of good 2.) The discount card is of no value to the consumer nsofar as it reduces the price she pays for good 1. Find this consumer's Marshallian demand for each c> 0. lution: If w

mer of two goods has utility U(X1, 2) = X1X2. She can purchase each good ce of p; dollars per unit. Alternatively, she can buy a discount card for fixed fee of c that allows her to purchase good 1 at a price of p₁/2 dollars per unit. (The discount s no effect on the price of good 2.) The discount card is of no value to the consumer nsofar as it reduces the price she pays for good 1. Find this consumer's Marshallian demand for each c> 0. lution: If w

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

please  only do: if you can teach explain steps of how to solve each part: 

A consumer of two goods has utility u(#₁, #₂) = ₁22. She can purchase each good i = 1,2 at a price of p; dollars per unit. Alternatively, she can buy a discount card for fixed fee of c dollars that allows her to purchase good 1 at a price of p₁/2 dollars per unit. (The discount card has no effect on the price of good 2.) The discount card is of no value to the consumer except insofar as it reduces the price she pays for good 1. (0) Find this consumer's Marshallian demand for each c > 0. Solution: If w<c, then she cannot purchase the card. If w≥c, if she does not purchase the card, she obtains utility v(p, w) = w²/4p1p2, whereas if she purchases the card, she obtains utility v((p₁/2, p2), wc) = (w - c)2/2p1p2, where v(p, w) is the usual indirect utility function associated with u(x) = 12. Hence she prefers to purchase the card whenever (w - c)²/2p1p2 ≥ w²/4p1p2, or equivalently, w > √2c/(√2-1). Therefore, using the expression from class for the Marshallian demand with Cobb-Douglas utility, we have x(p, w) = 2(w-c) W-C pi "P2 W Using the identity v(p, e(p, u)) = 4 this consumer's expenditure function for each c > 0. Solution: From part (a), this consumer's indirect utility function is w² v(p, w) = max. w>√že √2-1 otherwise. =u, this corresponds to e(p, u) = min {2√/p1p2u, √2p₁p2u+c}.
Transcribed Image Text:A consumer of two goods has utility u(#₁, #₂) = ₁22. She can purchase each good i = 1,2 at a price of p; dollars per unit. Alternatively, she can buy a discount card for fixed fee of c dollars that allows her to purchase good 1 at a price of p₁/2 dollars per unit. (The discount card has no effect on the price of good 2.) The discount card is of no value to the consumer except insofar as it reduces the price she pays for good 1. (0) Find this consumer's Marshallian demand for each c > 0. Solution: If w<c, then she cannot purchase the card. If w≥c, if she does not purchase the card, she obtains utility v(p, w) = w²/4p1p2, whereas if she purchases the card, she obtains utility v((p₁/2, p2), wc) = (w - c)2/2p1p2, where v(p, w) is the usual indirect utility function associated with u(x) = 12. Hence she prefers to purchase the card whenever (w - c)²/2p1p2 ≥ w²/4p1p2, or equivalently, w > √2c/(√2-1). Therefore, using the expression from class for the Marshallian demand with Cobb-Douglas utility, we have x(p, w) = 2(w-c) W-C pi "P2 W Using the identity v(p, e(p, u)) = 4 this consumer's expenditure function for each c > 0. Solution: From part (a), this consumer's indirect utility function is w² v(p, w) = max. w>√že √2-1 otherwise. =u, this corresponds to e(p, u) = min {2√/p1p2u, √2p₁p2u+c}.
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Taxes And Equity
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
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
SEE MORE TEXTBOOKS