Consider the following steps 1. Celia chooses how much care, z = [0, 1], to take in programming her robot. This effort costs her z²/2. 2. Nature chooses whether the robot steps on Peter's pet salamander, leading to emotional harm to Peter of H> 0 (with probability 1-2). 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 V - r²/2. Peter and Luke both get zero. • If there is an accident, but Celia is not identified as the culprit, then Celia gets V - 2²/2. 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-(3H-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 a in step 1. c) What will Celia's first-order condition be in step 1? Your answer should be an expression that involves D. d) What is Luke's first-order condition? What decision rule will Luke follow in step 3?
Consider the following steps 1. Celia chooses how much care, z = [0, 1], to take in programming her robot. This effort costs her z²/2. 2. Nature chooses whether the robot steps on Peter's pet salamander, leading to emotional harm to Peter of H> 0 (with probability 1-2). 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 V - r²/2. Peter and Luke both get zero. • If there is an accident, but Celia is not identified as the culprit, then Celia gets V - 2²/2. 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-(3H-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 a in step 1. c) What will Celia's first-order condition be in step 1? Your answer should be an expression that involves D. d) What is Luke's first-order condition? What decision rule will Luke follow in step 3?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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part a and b please
![Consider the following steps
1. Celia chooses how much care, z = [0, 1], to take in programming her robot.
This effort costs her z²/2.
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 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 - r²/2. Peter and Luke both get zero.
• If there is an accident, but Celia is not identified as the culprit, then
Celia gets V-²/2. 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 D € R+ for Celia to pay
Peter. Celia gets V-2²/2-D. Peter gets D-H. Luke gets - (3H-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 be
an expression that involves D.
d) What is Luke's first-order condition? What decision rule will Luke follow in
step 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 the
value judgement that the optimal level of care is the one that maximises the
expected sum of Celia's and Peter's payoffs. According to this approach, we
can ignore Luke's payoffs (as well as any payoff to the salamander or the
robot) when considering social optimality. Write down this expected sum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8eb668b1-db6e-470b-a40c-f668079bc7b7%2Fbcb26e2f-e3c8-40bf-b12a-e864d051201c%2Fqgopcx_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following steps
1. Celia chooses how much care, z = [0, 1], to take in programming her robot.
This effort costs her z²/2.
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 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 - r²/2. Peter and Luke both get zero.
• If there is an accident, but Celia is not identified as the culprit, then
Celia gets V-²/2. 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 D € R+ for Celia to pay
Peter. Celia gets V-2²/2-D. Peter gets D-H. Luke gets - (3H-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 be
an expression that involves D.
d) What is Luke's first-order condition? What decision rule will Luke follow in
step 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 the
value judgement that the optimal level of care is the one that maximises the
expected sum of Celia's and Peter's payoffs. According to this approach, we
can ignore Luke's payoffs (as well as any payoff to the salamander or the
robot) when considering social optimality. Write down this expected sum.
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Hi, just wanted to ask why the simplification changes x(V-x^2/2) to (1-x)*(V-x^2/2)
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