Principles of Economics, 7th Edition (MindTap Course List)
7th Edition
ISBN: 9781285165875
Author: N. Gregory Mankiw
Publisher: Cengage Learning
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Chapter 22, Problem 5PA
To determine
The validation of the statement based on Arrow's impossibility theorem.
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Suppose that 2 roommates, Andy and Bob, are trying to pick an apartment in Chicago. Locations can be chosen from set of alternatives A={ x: x exists [0,1]}. Andy and Bob both want to minimize their daily commute but they work at different locations: Andy at xA=0.3, while Bob at xB=0.6. Specifically, their utility functions are: ui(x)= -(x-xi)2.
Question: What is the set of all Pareto Efficient outcomes in A, assuming no money can be exchanged.
Tom and Jerry are room mates. They spend a total of 80 hours a week together in
their room. Tom likes loud music, even when he sleeps. His utility function is
UT(CT, M) = CT + M,
where CT is the number of cookies he eats per week and M is the number of hours of
loud music per week that is played while he is in their room. Jerry hates all kinds of
music. His utility function is
M²
12
UJ = CJ
Every week, Tom and Jerry each get 12 chocolate chip cookies sent from home. They
have no other source of cookies. We can describe this situation with a box that looks
like an Edgeworth box. The box has cookies on the horizontal axis and hours of music
on the vertical axis. Let the bottom-left corner be the origin for Tom, and the
bottom-right corner be the origin for Jerry.
Suppose the dorm's policy is "rock-n-roll is good for the soul." Thus, M=80 in the
initial endowment. Consider a trade between Tom and Jerry: Jerry gives Tom one
cookie for reducing one hour of music. Then the change in Jerry's…
You are considering going to a football game. However, the roads are cover in ice due to bad weather. Your ticket was a gift. You derive a value of z from attending the game, and a cost of D for driving on the icy roads. Your utility function is given by: ug(Z) + ui(D) = In(Z - 3) - In(2 - D). In your ultimate wisdom, you calculate that the cost of driving on the icy roads is 1 unit (So, D=1). What is the minimum value you must obtain from attending the game, so that you decide to go?
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Chapter 22 Solutions
Principles of Economics, 7th Edition (MindTap Course List)
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