Player 1 and Player 2 have formed a partnership (e.g., a law firm). Suppose both players simultaneously invest some effort and split the joint return equally. Let x and y denote the amounts of effort that Player 1 and Player 2, respectively, invest. This will result in a disutility of x²/2 for Player 1 and a disutility of y/2 for player 2. However, it will result in a joint return of (x+y) which the players split evenly. a) Left to their own devices, what effort levels will the players' choose? Show calculations.
Player 1 and Player 2 have formed a partnership (e.g., a law firm). Suppose both players simultaneously invest some effort and split the joint return equally. Let x and y denote the amounts of effort that Player 1 and Player 2, respectively, invest. This will result in a disutility of x²/2 for Player 1 and a disutility of y/2 for player 2. However, it will result in a joint return of (x+y) which the players split evenly. a) Left to their own devices, what effort levels will the players' choose? Show calculations.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
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![Player 1 and Player 2 have formed a partnership (e.g., a law firm). Suppose both players
simultaneously invest some effort and split the joint return equally. Let x and y denote the
amounts of effort that Player 1 and Player 2, respectively, invest. This will result in a disutility
of x²/2 for Player 1 and a disutility of y2/2 for player 2. However, it will result in a joint return of
(x+y) which the players split evenly.
a) Left to their own devices, what effort levels will the players' choose? Show calculations.
b) What is the efficient effort levels? Show calculations.
c) Why isn't the efficient effort levels achieved when the player's are left to their own devices?
How could the partnership attempt to address this issue?
d) Relating it to a law firm, what would you expect to happen to effort levels as the number of
partners at a law firm increases? What are possible explanations as to why the average size
of a law firm has increased significantly in recent years?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F144161ac-559f-4b1a-80a0-0fffa7827db1%2F1f8765a7-08f3-4f45-b3f5-77c028b0696e%2Fjb86kwm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Player 1 and Player 2 have formed a partnership (e.g., a law firm). Suppose both players
simultaneously invest some effort and split the joint return equally. Let x and y denote the
amounts of effort that Player 1 and Player 2, respectively, invest. This will result in a disutility
of x²/2 for Player 1 and a disutility of y2/2 for player 2. However, it will result in a joint return of
(x+y) which the players split evenly.
a) Left to their own devices, what effort levels will the players' choose? Show calculations.
b) What is the efficient effort levels? Show calculations.
c) Why isn't the efficient effort levels achieved when the player's are left to their own devices?
How could the partnership attempt to address this issue?
d) Relating it to a law firm, what would you expect to happen to effort levels as the number of
partners at a law firm increases? What are possible explanations as to why the average size
of a law firm has increased significantly in recent years?
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