d e and f please 1. Celia chooses how much care, z = [0, 1], to take in programming her robot.This effort costs her x²/2.2. 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 V2²/2. Peter and Luke both get zero.If there is an accident, but Celia is not identified as the culprit, thenCelia gets Vr²/2. 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.Now answer the following questions.a) Draw a game tree to represent this model.b) Write down Celia's expected payoff when she chooses x in step 1.c) What will Celia's first-order condition be in step 1? Your answer should bean expression that involves D.d) What is Luke's first-order condition? What decision rule will Luke follow instep 3?e) Now substitute the equilibrium expression for D that you obtained in ques-tion (d), into Celia's condition that you obtained in (c).f) Now we turn to social optimality rather than equilibrium. Consider thevalue judgement that the optimal level of care is the one that maximises theexpected sum of Celia's and Peter's payoffs. According to this approach, wecan ignore Luke's payoffs (as well as any payoff to the salamander or therobot) when considering social optimality. Write down this expected sum.

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

1. Celia chooses how much care, z € [0, 1], to take in programming her robot. This effort costs her r²/2. 2. Nature chooses whether the robot steps on Peter's pet salamander, leading to emotional harm to Peter of H> 0 (with probability 1-r). 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 V22/2. Peter and Luke both get zero.

1. Celia chooses how much care, z € [0, 1], to take in programming her robot. This effort costs her r²/2. 2. Nature chooses whether the robot steps on Peter's pet salamander, leading to emotional harm to Peter of H> 0 (with probability 1-r). 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 V22/2. Peter and Luke both get zero.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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