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-r). 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 - 2²/2. 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 DE 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 z 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.
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-r). 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 - 2²/2. 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 DE 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 z 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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
part f and part g please
Transcribed Image Text:g) Take a first-order condition with respect to z. Find an expression for the
socially optimal level of z, 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 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)?
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.
![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%2F7652a6eb-d5f7-4c6b-98ed-2cb34055e823%2Fygmriu_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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 8 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education