A small business owner can invest any amount of effort e ≥ 0 to produce output valued at 2e. The cost to the owner of effort level e is e². The government, which seeks to maximize its own revenue, may expropriate some fraction 7 € [0, 1] of the owner's output. The owner's payoff to choosing e if the government expropriates fraction 7 is 2e(1-7) - ².
A small business owner can invest any amount of effort e ≥ 0 to produce output valued at 2e. The cost to the owner of effort level e is e². The government, which seeks to maximize its own revenue, may expropriate some fraction 7 € [0, 1] of the owner's output. The owner's payoff to choosing e if the government expropriates fraction 7 is 2e(1-7) - ².
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![A small business owner can invest any amount of effort e > 0 to produce output valued at
2e. The cost to the owner of effort level e is e². The government, which seeks to maximize
its own revenue, may expropriate some fraction 7 € [0, 1] of the owner's output. The owner's
payoff to choosing e if the government expropriates fraction 7 is 2e(1-7) - e².
(a) Consider a sequential game in which the owner first chooses e and the government chooses
7 after observing the owner's choice. Find all subgame perfect equilibria of this game.
(b) Now consider a sequential game in which the government first chooses 7 and the owner
chooses e after observing the government's choice. Find all subgame perfect equilibria
of this game.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2Ffefd1def-ac74-4501-8214-68a29a87e03b%2Fy8vz8p_processed.png&w=3840&q=75)
Transcribed Image Text:A small business owner can invest any amount of effort e > 0 to produce output valued at
2e. The cost to the owner of effort level e is e². The government, which seeks to maximize
its own revenue, may expropriate some fraction 7 € [0, 1] of the owner's output. The owner's
payoff to choosing e if the government expropriates fraction 7 is 2e(1-7) - e².
(a) Consider a sequential game in which the owner first chooses e and the government chooses
7 after observing the owner's choice. Find all subgame perfect equilibria of this game.
(b) Now consider a sequential game in which the government first chooses 7 and the owner
chooses e after observing the government's choice. Find all subgame perfect equilibria
of this game.
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