i and j please 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, leadingto emotional harm to Peter of H> 0 (with probability 1-2). If the robotdoes step on the salamander then there is a chance of that Celia will beidentified as the culprit.• If there is no accident (the salamander is not stepped on), then Celia'spayoff is Vr²/2. Peter and Luke both get zero.If there is an accident, but Celia is not identified as the culprit, thenCelia 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 payPeter. 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 thesocially optimal level of r, according to the value judgement we made inquestion (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 amathematical 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 sociallyoptimal outcome would maximize the sum of all three human expected pay-offs (ie. including Luke's). Write down the optimisation problem that woulddefine this optimal outcome. You don't actually have to solve it, just writedown the problem.

When Celia chooses X level of effortIf no accidentPay off of Celia=V-(X2/2)Pay off of Peter=0Pay off…

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

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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