Consider the following steps Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2. Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero. If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero. If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2. h) What would β have to equal, in order for Celia to choose the socially optimal level of x in a Subgame Perfect Equilibrium ? We are looking for a mathematical expression, rather than a specific number. i) What is the intuition for the result you got in (h) ?

h) β would have to equal π/(1-π) in order for Celia to choose the socially optimal level of x in a…

Answered: [0,1], to take in programming her…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the following steps

Celia chooses how much care, x ∈ [0,1], to take in programming her robot. This effort costs her x^2/2.

Nature chooses whether the robot steps on Peter’s pet salamander, leading to emotional harm to Peter of H > 0 (with probability 1 - x). If the robot does step on the salamander then there is a chance of π that Celia will be identified as the culprit.

If there is no accident (the salamander is not stepped on), then Celia’s payoff is V - x^2/2. Peter and Luke both get zero.

If there is an accident, but Celia is identified as the culprit, then Celia gets V - x^2/2. Peter gets -H. Luke gets zero.

If there is an accident, and Celia is identified as the culprit, then Like (the judge) decides a level of compensation D ∈ R+ for Celia to pay Peter. Celia gets V - x^2/2 - D. Peter gets D - H. Luke gets −(βH - D)^2.

h) What would β have to equal, in order for Celia to choose the socially optimal level of x in a Subgame Perfect Equilibrium ? We are looking for a mathematical expression, rather than a specific number.

i) What is the intuition for the result you got in (h) ?

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