Consider an economy with n consumers, one private good and one public good. We think of the private good as “all other goods,” and measure it in terms of money. There are n individuals in the economy with utility functions Ui(xi, y) = αi ln y + xi, where y is the public good, xi is the private good consumed by individual i = 1, . . . , n, and 0 < α1 < α2 < · · · < αn are parameters. Initial endowment of private good of each consumer is given by wi . We donote the aggregate endowment 1of the private good by w =Pi wi . The cost of producing the public good is c(y) = cy for some c > 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.
Consider an economy with n consumers, one private good and one public good. We think of the private good as “all other goods,” and measure it in terms of money. There are n individuals in the economy with utility functions Ui(xi, y) = αi ln y + xi, where y is the public good, xi is the private good consumed by individual i = 1, . . . , n, and 0 < α1 < α2 < · · · < αn are parameters. Initial endowment of private good of each consumer is given by wi . We donote the aggregate endowment 1of the private good by w =Pi wi . The cost of producing the public good is c(y) = cy for some c > 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Consider an economy with n consumers, one private
good and one public good. We think of the private good as “all other
goods,” and measure it in terms of money. There are n individuals in
the economy with utility functions Ui(xi, y) = αi ln y + xi, where y is the
public good, xi is the private good consumed by individual i = 1, . . . , n,
and 0 < α1 < α2 < · · · < αn are parameters. Initial endowment of private
good of each consumer is given by wi
. We donote the aggregate endowment 1of the private good by w =Pi wi
. The cost of producing the public good is c(y) = cy for some c > 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.
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 3 steps with 21 images
Knowledge Booster
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
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