ECON 3123: PROBLEM SET 2
PROFESSOR RICHARD HOLDEN
This is due at the start of lecture in Week 6. Late problem sets receive zero credit.
(1) Find all Pure Strategy Nash Equilibria of the following game. Explain why
they are Nash Equilibria. (HINT: Use the
ECON3123: Economics of Corporations
Semester 2, 2012
Ashley Cheng
Midterm Examination
Solutions
15 September 2012
Question 1: Problem
(1) Write down the Agents Optimization Problem
This ought to be pretty simple. The Agent is going to maximise, with respe
ECON3123 Midterm Exercises
Adam Solomon
Question 1
In this question, well work through the standard model with noisy output, with the following twist: the
principal is risk-averse, while the agent is risk-loving.
The principals payoff function is Up = E[x
Solutions to ECON3123 Midterm Exercises
Adam Solomon
Question 1
a) For step 3, given the principals offer (w = + x), write down the agents maximization problem, and
calculate his payoff-maximizing effort choice e as a function of and .
Noting that
E(w) =
ECON3123: Economics of Corporations
Semester 2, 2012
Ashley Cheng
Solutions to Problem Set 2
21 August 2012
Question 1
We start by examining the denition of a Nash Equilibrium. As strategy prole = i , i is a
Nash Equilibrium if:
Ui i , i Ui
i , i
i Si and
ECON3123: Economics of Corporations
Semester 2, 2012
Ashley Cheng
Hints for Problem Set 3
13 September 2012
Question 1(a):
Remember what First Best is (if in doubt, see my Feedback form from Problem Set 1). Remember that
you need to add accross both perio
ECON 3123: PROBLEM SET 4
PROFESSOR RICHARD HOLDEN
This is due at the start of lecture in week 11. Late problem sets receive zero credit.
We ackowledge this Problem Set as based on the work of Dr. Jonathan Lim.
(1) Suppose that Denso is making air-conditio
ECON3123: Economics of Corporations
Semester 2, 2012
Ashley Cheng
Solutions to Problem Set 4
Based on Solutions to Problem Set 4 by Dr. J. Lim
08 October 2012
In preparing these solutions, I am indebted to Dr. Jonathan Lim who provided me with a comprehen
ECON 3123: PROBLEM SET 1
PROFESSOR RICHARD HOLDEN
This is due at the start of lecture in Week 4. Late problem sets receive zero credit.
(1) Consider a setting with a risk-averse worker and a risk-neutral rm. The
worker puts in some eort level a which the
ECON3123: Economics of Corporations
Semester 2, 2012
Ashley Cheng
Midterm Examination
Feedback
07 October 2012
General Feedback
This exam was not an particularly easy exam. Nor, however, was it a particularly dicult exam. The
exam was algebraically tediou
ECON 3123: Economics of Corporations
Semester 2, 2012
Solutions to Problem Set 1
Ashley Cheng
Question 1
Part (a):
This is a simple application of your rules concerning variances and expected values.
()
(
)
()
()
(
)
()
()
(
)
()
(
()
)
Part (b):
All you
ECON3202
S2/2016
Mathematical Economics
Lecture 7
1
Review: Optimization
1.1
Second-Derivative Test
Given the function y = f (x), if for x = x0 , f 0 (x0 ) = 0 then f (x0 ) will be
1) relative max if f 00 (x0 ) < 0, or
2) relative min if f 00 (x0 ) > 0.
C
ECON3202
S2/2016
Mathematical Economics
Lecture 5
1
Comparative Statics of General-Function Models
Given
F1 (x, y, w; z) = 0
F2 (x, y, w; z) = 0
F (x, y, w; z) = 0
3
y
w
we want to solve x
z , z and z
Step 1: Start by determining whether the Jacobian |J
ECON3123
Problem Set 2 Solution
Question 1 Solution
Remember that a strategy profile (in this case, a pair of choices, one for each player) is an equilibrium if no player can do strictly better by deviating from his strategy, holding fixed the other
playe
ECON 3123
Problem Set 4 Solution
Question 1
a) The principals expected payo is
1
E [1p + 2p ] (E1 + E2 )2 .
2
Well start with the term 1p , which represents the payo to the principal from project 1.
Because the principal has decision making authority,
If
ECON3202
S2/2016
Mathematical Economics
Lecture 11
1
Exam Time
Exam timetable has been released:
Monday 7 November at 13:45, The Scientia - Gallery
10 minute reading time
2 hour exam
Please check myUNSW for your exam timetable and location
myUNSW: My
ECON3202
S2/2016
Mathematical Economics
Lecture 12
Consultation for the final exam:
NO consultation on next Monday, Oct 24, 2016.
Consultation time: 10:30-13:30, Thursday 3 Nov, 2016, in ASB 402.
1
Overview
Previous lectures:
Focus was on static models
Economics of Corporations (ECON 3123)
Problem Set 2
This is due on Tuesday August 23 by 12pm.
Question 1
Find all pure-strategy equilibria of the following simultaneous-move game.
Player 2
Left Right
Up (1,1)
(0,0)
Player 1
Down (-4,-4) (2,3)
Question 2
D
1
Non-Congruent Performance Measures
As we noted at the beginning of this chapter, it is hard to think of m(any) situation(s) where
everything that the principal cares about is contractiblein the sense that it will be enforced by
a court. So one motivatio
Organisational Economics
Introduction to Incentives
Hongyi Li
July 2016
1
Introduction: The Principal-Agent Framework
In this lecture, we will take a first look at what is called the Principal-Agent Problem. Basically, we will discuss how to motivate one
Organisational Economics (ECON 3123)
Problem Set 1
This is due on August 9 by 12pm.
Question 1
In this problem, we will consider a multitasking problem where the principal can only incentivize
the agent on one task.
There are two tasks (task 1 and task 2)
Organisational Economics (ECON 3123)
Game Theory Exercise
Adam Solomon
August 7, 2016
Question 1
Find all Nash equilibria of the following game.
Stag Hunt
Stag (3,3) (0,1)
Hunt (1,0) (1,1)
Question 2
Find all Nash equilibria of the following game.
L
R
U (
Organizational Economics
Multi-Tasking and Performance Measures
August 2016
1
The Basic Multi-Tasking Model
So far we have focused on situations where the agent performs a single task for the principal. In
reality, of course, there are many situations of
Organisational Economics
ECON 3123, Lecture 3
August 2016
1
Simultaneous-Move Games
How to define a game:
a set of players
for each player, a description of the possible actions (strategies) for that player
a description of the consequences of players
Organisational Economics
Introduction to Incentives
Hongyi Li
August 2016
1
Noisy Incentives and Risk-Aversion
So far, weve been writing down models where there is a precise link between effort and
output specifically, effort exactly equals output. Thus
ECON 3123
Exercise 3 Solution
Question 1
a)
i) Suppose B owns the machine. If bargaining fails, then S walks away with nothing (he
cannot produce the widget, and even if he could, it has no value to anyone other than the
buyer), so us0 = 0. B can produce
ECON3123 Exercise 2 Solutions
Adam Solomon
Question 1
Find all NE
Stag Hunt
Stag (3,3) (0,1)
Hunt (1,0) (1,1)
By checking if either player has an incentive to deviate we immediately see that (S, S) and (H, H) are
nash
equilibria.
Now we look for a mixed e
Organisational Economics (ECON 3123)
Exercise 1
Question 1
Consider the second model from Week 1, with a small modification. The principal benefits from
the agents output, but only up to a certain limit b > 0:
Up = min cfw_x, b w.
The rest of the model re
ECON3123: Economics of Corporations
Semester 2, 2012
Ashley Cheng
Solutions to Problem Set 3
22 October 2012
In writing these solutions, I am indebted to the guidance provided by Prof. Richard Holdens solutions.
Part (a) Solve for the First Best. What det
ECON3123: Economics of Corporations
Semester 2, 2012
Ashley Cheng
Solutions to Problem Set 5
Based on Solutions to Problem Set 5 by Dr. J. Lim
22 October 2012
Again, in preparing these solutions, I am indebted to Dr. Jonathan Lim who provided me with a
co