Consider a society consisting of two individuals, Prude (7) and Lewd (A), and a book, Lady Chatterley's Lover. At most one individual may hold the book, so the only three available alternatives are that nobody reads the book (Ø), only Prude reads it ({a}), or only Lewd does ({A}). Lewd prefers to read the book than to not read it, but would prefer it even more if Prude read it instead. Prude, however, believes that nobody ought to read the book, but, if somebody must, he would be the better

Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter22: Frontiers Of Microeconomics
Section: Chapter Questions
Problem 6PA
icon
Related questions
Question

help

5. Consider a society consisting of two individuals, Prude (7) and Lewd (A), and a
book, Lady Chatterley's Lover. At most one individual may hold the book, so the
only three available alternatives are that nobody reads the book (Ø), only Prude reads
it ({7}), or only Lewd does ({A}). Lewd prefers to read the book than to not read
it, but would prefer it even more if Prude read it instead. Prude, however, believes
that nobody ought to read the book, but, if somebody must, he would be the better
choice of reader. Formally, {T}Px{\}P,Ø and ØPr{T}Pr{A}.
A social welfare function is liberal if, assuming that the book is given to Prude or
Lewd, society's preference over whether Prude or Lewd reads it agrees with the book
recipient's preference. Show that no social welfare function can be liberal, unanimous,
complete and quasi-transitive. (A binary relation is quasi-transitive if its asymmetric
part is transitive; its symmetric part need not be.)
Transcribed Image Text:5. Consider a society consisting of two individuals, Prude (7) and Lewd (A), and a book, Lady Chatterley's Lover. At most one individual may hold the book, so the only three available alternatives are that nobody reads the book (Ø), only Prude reads it ({7}), or only Lewd does ({A}). Lewd prefers to read the book than to not read it, but would prefer it even more if Prude read it instead. Prude, however, believes that nobody ought to read the book, but, if somebody must, he would be the better choice of reader. Formally, {T}Px{\}P,Ø and ØPr{T}Pr{A}. A social welfare function is liberal if, assuming that the book is given to Prude or Lewd, society's preference over whether Prude or Lewd reads it agrees with the book recipient's preference. Show that no social welfare function can be liberal, unanimous, complete and quasi-transitive. (A binary relation is quasi-transitive if its asymmetric part is transitive; its symmetric part need not be.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

Blurred answer
Knowledge Booster
Comparative Advantage
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
  • SEE MORE QUESTIONS
Recommended textbooks for you
Principles of Microeconomics
Principles of Microeconomics
Economics
ISBN:
9781305156050
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Microeconomics (MindTap Course List)
Principles of Microeconomics (MindTap Course List)
Economics
ISBN:
9781305971493
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Economics, 7th Edition (MindTap Cou…
Principles of Economics, 7th Edition (MindTap Cou…
Economics
ISBN:
9781285165875
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning