ECONOMICS 602: GRADUATE MACROECONOMICS
HOMEWORK ASSIGNMENT 1
SPRING 2012
CHAPTER 3: CAPITAL ACCUMULATION AND GROWTH
Exercise 1: The Elasticity of Substitution between Capital and Labor
and the Income Distribution
PART 1. The Cobb-Douglas production functi
ECONOMICS 602: GRADUATE MACROECONOMICS
HOMEWORK ASSIGNMENT 5
Date: April 24, 2012
Due Date: May 8, 2012
CHAPTER 20: STABILIZATION POLICY
Exercise 1: Optimal Monetary Policy in Stochastic World
Consider an economy with stochastic demand and supply shocks w
Econ 601
Graduate Microeconomics
Problem Set I
Lau
Fall 2011
Indifference Curve Analysis
1.
Ms Pretty considers apples and oranges as equally good. She is willing to give up 1 apple
for 1 orange and vice versa.
a)
Draw Ms Pretty's indifference map for app
ECONOMICS 602: GRADUATE MACROECONOMICS
HOMEWORK ASSIGNMENT 2
SPRING 2012
CHAPTER 5: TECHNOLOGICAL PROGRESS AND GROWTH
Exercise 1: The General Solow Model in Continuous Time
In continuous time the general Solow model consists of the seven equations:
1
Y =
ECONOMICS 602: GRADUATE MACROECONOMICS
HOMEWORK ASSIGNMENT 5
Date: April 24, 2012
Due Date: May 8, 2012
CHAPTER 19: Explaining Business Cycles
Exercise 3: Interest Rate Smoothing in the AD-AS Model
We have so far assumed that the interest rate adjusts imm
ECONOMICS 602: GRADUATE MACROECONOMICS
HOMEWORK ASSIGNMENT 3
Date: March 27, 2012
Due Date: April 10, 2012
The Fed Tour:
Wednesday, April 18, 2012 at 1:30-3:00PM
Please email me by April 2 (Monday) if you would like to participate. Thanks!
CHAPTER 16: C
ECONOMICS 602: GRADUATE MACROECONOMICS
HOMEWORK ASSIGNMENT 4
Date: April 10, 2012
Due Date: April 24, 2012
Reminder: The Fed Tour, April 18, 1:30-3:00pm, 101 Market Street, San Francisco.
CHAPTER 17: Monetary Policy and Aggregate Demand
Exercise 1: Nomina
COMPREHENSIVE MACROECONOMICS EXAMINATION
SPRING 2008
Instructions. You have 4 hours to nish the exam. Please answer 4 out of 7 questions AND YOU MUST
ANSWER QUESTIONS 1 AND 2. If you answer all questions, I will grade the Questions 1 4 only.
Good Luck!
Qu
Econ 601 Graduate Microeconomics
Problem Set IV
Lau
Fall 2011
Hicksian Demand, Expenditure Function and Duality
For each of the following utility functions,
1.
2.
3.
4.
5.
U ( X , Y ) min(2 X , Y )
U ( X , Y ) 3X Y ,
U ( X , Y ) X ln Y
U ( X , Y , Z ) min
Econ 601
Graduate Microeconomics
Problem Set VIII
Lau
Fall 2011
Decision Under Uncertainty III
1.
a)
b)
c)
Derive the mean-variance frontier of 2 risky assets.
Derive the mean-variance frontier of 2 risky assets and 1 risk-free asset.
Explain how an inves
Econ 601
Graduate Microeconomics
Lau
Fall 2011
Problem Set VII
Decision Under Uncertainty II
1.
Suppose a person has $M of money. If she puts the money in the bank, she can get a return of
10% over a period. If she buys an asset X, she has 50% of chance t
Econ 601
Graduate Microeconomics
Problem Set VI
Lau
Fall 2011
Decision Under Uncertainty
1.
Consider a person with an initial wealth level of 100 who faces a chance to win 20 with
probability 1/2 and lose 20 with probability 1/2. If this person's utility
Econ 601
Graduate Microeconomics
Lau
Fall 2011
Problem Set V
Elasticity
1.
Let U ( X , Y ) X a Y b , a b 1
a)
find the Marshallian demand functions,
b)
find the indirect utility function,
c)
using the duality identities, find the expenditure function,
d)
Econ 601 Graduate Microeconomics
Problem Set III
Marshallian Demand and Indirect Utility Function
For each of the utility function,
1.
1
3
1
3
U ( X ,Y ) X Y ,
[Hint: No need to set up the Lagrangian function. Use the short-cut formula.]
2.
U ( L, R) min(
Econ 601
Graduate Microeconomics
Lau
Problem Set II
General Equilibrium I
1.
Suppose there are 2 price-taking consumers, consumer A and consumer B. Consumer A has an
initial endowment of ( X , Y ) (1,0.5) and an utility function of U ( X , Y ) XY . Consum
MACROECONOMICS
1880
1900
1920
1940
1960
1980
2000
Matthias Doepke
University of Chicago
Andreas Lehnert
Board of Governors of the Federal Reserve System
Andrew W. Sellgren
George Mason University
A This book was typeset in Palatino and Computer Modern usi
Fall Semester '05-'06 Akila Weerapana
Lecture 16: The IS-LM Model
I. OVERVIEW
In the last two lectures, we derived the IS-LM model, which is a short run model of the determination of output. The model has two main parts: an IS curve that summarizes all t
7 Stylized Facts
(1) Some countries are rich and some are
poor, the differences are enormous, and
Lecture One
it has pretty much stayed like that in relative
terms over the last 40 years.
Some Facts about Prosperity and Growth
However, there is some tende
Homework for Monday, February 6, 2012
1. Please compare the evolution of the bilateral nominal exchange rate between the Yuan
and the U.S. dollar, the nominal effective exchange rate of the Yuan and the real effective
exchange rate of the Yuan since the f
Econ 601
Graduate Microeconomics
Problem Set XI
Lau
Fall 2011
Cost Functions and Perfect Competitive Markets
1.
Show that profit maximization implies cost minimization.
2.
Without using the envelop theorem, prove the four properties of the profit function
Econ 415/615
Mathematical Economics I
Problem Set I
Lau
Fall 2011
One-variable calculus
c)
d)
y f ( x) 3x5 2 x0.2
ln( x 1)
y f ( x)
x
3
y f ( x) x ax 2 e2 x
y f ( x) 2 x2 ( x2 ax0.5 ) 2 2ax2.5
e)
y f ( x)
f)
g)
h)
i)
y
y
y
y
j)
y
k)
l)
1
y
y
a)
b)
2.
x2
Econ 415/615
Mathematical Economics I
Problem Set II
Lau
Fall 2011
Multi-variable calculus
1.
Find the partial derivatives of the following functions:
a)
y f ( x, z ) x 2 z 3 ln( x 1) e3 z
b)
y f ( x, z ) ( x 5)a ( z b)c
c)
y f ( x, z ) ln( x z ) ( xz )2
Eco 415/615 Mathematical Economics I
Problem Set IV
Lau
Fall 2011
Marshallian Demand Functions and Hicksian Demand Functions (2 choice variables)
1.
Let U ( X , Y ) XY 3
a)
Find the Marshallian demand functions and calculate
b)
Find the Hicksian demand fu
Eco 415/615 Mathematical Economics I
Problem Set V
Lau
Fall 2011
Concave/convex functions (1 variable), homogeneous and homothetic functions
1.
Which of the functions are i) homogeneous, ii) homothetic but not homogeneous, iii)
neither?
a)
f ( X , Y , Z )
Eco 415/615 Mathematical Economics I
Lau
Fall 2011
Problem Set VI
Integration
1.
Find the value of the followings:
10
a)
x dx
x
b)
c)
e 7 dx
x
5
4
dx
x
d w2 dw
d)
10
dx
6
d ( w2 ln w)dw
e)
x
dx
2.
Let D : P eQ , calculate the maximum amount of money con
Econ 615
Mathematical Economics I
Lau
Fall 2011
Problem Set X
1.
Comparative Statics
Consider the following macroeconomics model:
Goods market:
Consumption function:
C C (Y , r ) C0
CY 0, Cr 0
where C0 : autonomous consumption
(exogeneous variable)
Invest
Econ 615
Mathematical Economics
Problem Set XI
Lau
Fall 2011
Differential Equations and Phase Diagrams
1.
Solve the following differential equations.
a)
y '(t ) 10
y(2) 8
4
b)
y '(t ) t
y (0) 1
c)
y '(t ) y(t ) 2
y(0) 1
d)
y '(t ) 5 y(t ) 10
y(0) 1
e)
y '