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Celia chooses how much care, z € [0, 1], to take in programming her robot. This effort costs her x²/2. Nature chooses whether the robot steps on Peter's pet salamander, leading to emotional harm to Peter of H> 0 (with probability 1-2). If the robot does step on the salamander then there is a chance of 7 that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia's payoff is Vr2/2. Peter and Luke both get zero. If there is an accident, but Celia is not identified as the culprit, then

Celia chooses how much care, z € [0, 1], to take in programming her robot. This effort costs her x²/2. Nature chooses whether the robot steps on Peter's pet salamander, leading to emotional harm to Peter of H> 0 (with probability 1-2). If the robot does step on the salamander then there is a chance of 7 that Celia will be identified as the culprit. If there is no accident (the salamander is not stepped on), then Celia's payoff is Vr2/2. Peter and Luke both get zero. If there is an accident, but Celia is not identified as the culprit, then

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Celia chooses how much care, z = [0, 1], to take in programming her robot. This effort costs her x²/2. Nature chooses whether the robot steps on Peter's pet salamander, leading to emotional harm to Peter of H> 0 (with probability 1-2). If the robot does step on the salamander then there is a chance of that Celia will be identified as the culprit. • If there is no accident (the salamander is not stepped on), then Celia's payoff is Vr²/2. Peter and Luke both get zero. If there is an accident, but Celia is not identified as the culprit, then Celia gets V x²/2. Peter gets -H. Luke gets zero. • If there is an accident, and Celia is identified as the culprit, then Luke (the judge) decides a level of compensation DER for Celia to pay Peter. Celia gets V-2²/2-D. Peter gets D-H. Luke gets - (BH-D)².
Transcribed Image Text:Celia chooses how much care, z = [0, 1], to take in programming her robot. This effort costs her x²/2. Nature chooses whether the robot steps on Peter's pet salamander, leading to emotional harm to Peter of H> 0 (with probability 1-2). If the robot does step on the salamander then there is a chance of that Celia will be identified as the culprit. • If there is no accident (the salamander is not stepped on), then Celia's payoff is Vr²/2. Peter and Luke both get zero. If there is an accident, but Celia is not identified as the culprit, then Celia gets V x²/2. Peter gets -H. Luke gets zero. • If there is an accident, and Celia is identified as the culprit, then Luke (the judge) decides a level of compensation DER for Celia to pay Peter. Celia gets V-2²/2-D. Peter gets D-H. Luke gets - (BH-D)².
g) Take a first-order condition with respect to z. Find an expression for the socially optimal level of r, according to the value judgement we made in question (f). h) What would have to equal, in order for Celia to choose the socially op- timal level of 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)? j) Finally, imagine a different value judgement, according to which the socially optimal outcome would maximize the sum of all three human expected pay- offs (ie. including Luke's). Write down the optimisation problem that would define this optimal outcome. You don't actually have to solve it, just write down the problem.
Transcribed Image Text:g) Take a first-order condition with respect to z. Find an expression for the socially optimal level of r, according to the value judgement we made in question (f). h) What would have to equal, in order for Celia to choose the socially op- timal level of 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)? j) Finally, imagine a different value judgement, according to which the socially optimal outcome would maximize the sum of all three human expected pay- offs (ie. including Luke's). Write down the optimisation problem that would define this optimal outcome. You don't actually have to solve it, just write down the problem.
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