ECO 475, Fall 2009, Midterm Exam
Jay H. Hong
Oct 21, 2009
This exam has 3 questions, for a total of 100 points.
You have 3 hours. Manage your time wisely.
Feel free to make an appropriate assumption if needed. Good luck!
1. Computing the equilibrium (32 p
ECO 475 Homework 3
Jay H. Hong
Due: Sep 27, 2010
1 Properties of Value Function
Lets dene the following operator T : C C
(T v )(x) = max cfw_u(x, a) + v [f (x, a)],
a(x)
where C is the set of continuous and bounded real-valued functions on X . Show that
ECO 475 Homework 9
Jay H. Hong
Due: Nov 18, 2009
1 Computing the equilibrium
Consider the simple two agent pure exchange economy. There are two individuals (i = 1, 2) who live
forever and each individual enjoys utility from a sequence of consumption given
ECO 475 HW5 Solution
Joon Song
Oct 14, 2009
1. Small Open Economy
Let bt+1 be an amount of bond purchased at time t that delivers Rbt+1 unit of consumption good at time
t + 1. Then, the sequential problem is the following.
1
Pt
log (ct )
max
t=0
p
kt + (1
ECO 475 Homework 2
Jay H. Hong
Due: Monday, Sep 20, 2010
1 Value Function Iteration & Guess and Verify
Consider the following problem.
t u(ct )
max
cfw_ct ,kt+1 t=0
t=0
subject to an initial k0 and a law of motion for capital
kt+1 = F (kt ) + (1 )kt ct
ECO 475 Homework 5
Jay H. Hong
Due: Oct 13, 2010
WEDNESDAY Review Session
1 Computing the equilibrium
Consider an island where two individuals (i = 1, 2) live forever who maximize their lifetime utility given
by
t ln(ci ).
t
t=0
Let
ei
t
denote the time
ECO 475 HW3 Solution
Yu LIU
September 22, 2010
1
Properties of Value Function
T
(T v )(x)
: CC
= max cfw_u(x, a) + v [f (x, a)]
a(x)
C is the set of continuous and bounded real-valued functions on X .
First of all, let us think about a set of sucient cond
ECO 475 HW2 Solution
Yu LIU
September 16, 2010
1 Value Function Iteration & Guess and Verify
t u(ct )
max
cfw_ct ,kt+1 t=0
s.t.
t=0
kt+1 = F (kt ) + (1 )kt ct , t
kt+1 0, t
ct 0, t
k0 is given
(1) Bellman equation:
V (k ) = max cfw_u(c) + V (k )
c,k
s.t
Jay H. Hong
Oct 27, 2008
ECO 475, Fall 2008, Midterm Exam
This exam has 3 questions, for a total of 100 points.
You have 3 hours. Manage your time wisely.
Feel free to make an appropriate assumption if needed. Good luck!
1. Small Open Economy (30 points)
ECO 475 Homework 4
Jay H. Hong
Due: Oct 4, 2010
1 Neoclassical Growth Model
Consider the following problem.
t u(ct )
max
cfw_ct ,kt+1 t=0
(1)
t=0
subject to an initial k0 and a law of motion
kt+1 + ct = F (kt ) + (1 )kt .
Assume that kt 0, ct 0 for all
ECO 475, Fall 2007, Midterm Exam
Jay H. Hong
Oct 24, 2007
This exam has 3 questions, for a total of 100 points.
You have 2 hours. Manage your time wisely.
Feel free to make an appropriate assumption if needed. Good luck!
1. Two Production Possibilities (3
ECO 475 Homework 1
Jay H. Hong
Due: Review Session, Monday Sep 13, 2010
1 Golden Rule
Consider the Solow model with a production function, yt = F (kt ) and a law of motion for the capital
stock, kt+1 = (1 )kt + yt , where (0, 1) is the depreciation rate a
ECO 475 PS5 Solution
Yu LIU
November 30, 2010
Question 1
Assume 0 y1 < y2 1.
P rob (y2 ) = 1 .
Considering that the endowment process is i.i.d., let
Since rst best allocation is not sustainable, then
where
then
c1 < c2 .
From (20.6.4) in LS, the ergodic c
Economics 475 Part II
Problem Set 3
1. Consider a 2 period economy. Income in period 1 is y1 and income in period 2 is a
random variable y2 . Utility is u(c1 ) + Eu(c2 ). Assume u > 0, u < 0, and u > 0.
Agents can save at an interest rate r.
(a) Derive th
ECO 475 PS2 Solution
Yu LIU
November 6, 2010
1
(a)
Ricardian Equivalence
Approach 1:
Government levies a one time lumpsum tax
=G
at time
T.
Consumer's Problem (SME):
Given
r,
t u (ct )
max
cfw_ct ,bt+1
t=0
subject to
ct + bt+1 = yt + (1 + r) bt , t = T
ECO 475 PS1 Solution
Yu LIU
October 30, 2010
1
Complete Market and Representative Consumer
(a) Arrow-Debrew equilirium:
0
An ADE is a set of price qt (st ) and allocation cfw_ci,t (st ) (i = 1, , I ) sequences such that
1. Consumer's Problem
0
Given qt (s
ECO 475 Homework 8
Jay H. Hong
Due: Nov 11, 2009
1 Firms own capital and the consumers own the rms
Consider the standard (deterministic) neoclassical growth model we studied. We have assumed that the
consumers own capital and the rms are renting capital f
ECO 475 Homework 10
Jay H. Hong
Due: Dec 2, 2009
1 More on Lucas Tree
Now consider the Lucas tree model with some modications. News arrives at time-zero unexpectedly that
a fraction of existing trees will die at the beginning of date T (before dividends a
ECO 475 Homework 6
Jay H. Hong
Due: Nov 18, 2010
1 Firms own capital and the consumers own the rms
Consider the standard (deterministic) neoclassical growth model we studied. We have assumed that the
consumers own capital and the rms are renting capital f
ECO 475 HW6 Solution
Joon Song
Oct 21, 2009
1. Simple Job Search
Model A
Let V (w) be a value of an unemployed worker with an oer of w at hand, and W = [w; w] be a support of
F . Then
V (w) = max V E (w) ; V U ,
(1)
where
V E (w)
VU
= w+
= b+
Z
) V E (w)
ECO 475 HW8 Solution
Joon Song
Nov 11, 2009
Assume the followings.
u ( ) is strictly increasing and strictly concave.
u is continuously dierentiable and limc&0 u0 (c) = 1
F ( ; ) is strictly increasing, strictly concave and F (k; 0) = F (0; n) = 0 for any
ECO 475 HW9 Solution
Joon Song
Nov 18, 2009
1. Computing the Equilibrium
To solve the problem, we need to specify a within-period timing assumption. There are two cases.
Case1 ADE: Decision is made before realization of time 0 state.
SME: Decision at time
ECO 475 PS3 Solution
Yu LIU
November 11, 2010
Question 1
(a) Consumer's Problem:
Given r,
max
cfw_c1 ,c2 (2 ),a
y
u (c1 ) + Eu (c2 (2 )
y
subject to
c1 + a = y1 ,
c2 (2 ) = y2 + (1 + r) a, y2
y
From FOCs and budget constraints, we can get the Euler equati
Economics 475 Part II
Problem Set 4
1. (OLG with money) Consider the overlapping-generations model discussed in class.
Specically, agents live two periods and supply labor only when young. Suppose utility is
log (cy ) + log (co ). There is no productivity
ECO 475 PS4 Solution
Yu LIU
November 18, 2010
Question 1
Dene aggregate capital:
savings:
sy,t
and
so,t ,
Kt ,
aggregate money holding:
individual money holding:
my,t
and
M;
mo,t .
for agents born at period
t,
individual
Since agents live two periods and
Economics 475 Part II
Problem Set 5
1. Consider the model of two-sided lack of commitment with no aggregate risk discussed
in class. Suppose that there are two possible realizations of person ones endowment (y1 , y2 )
and the endowment process is iid over
ECO 475 HW1 Solution
Yu LIU
September 11, 2010
1
Golden Rule
yt
kt+1
=
F (kt )
= (1 )kt + yt
(1)
(a) The law of motion of capital in steady state:
k
k
= (1 )k + F (k )
= F (k )
(2)
Since consumption is the amount of output not saved:
c
= (1 )F (k )
= F (
ECO 475 HW4 Solution
Yu LIU
September 29, 2010
1
Neoclassical Growth Model
t u(ct )
max
cfw_ct ,kt+1 t=0
t=0
s.t. ct + kt+1 = F (kt ) + (1 )kt
kt+1 0, ct 0 t
k0 > 0
(1) Control variable:
State variable:
is given
c
k
Bellman equation
v (k ) = max cfw_u(c