14.462 Advanced Macroeconomics
Spring 2004
Problem Set
Solution
1. First lets ignore that some goods are non-traded. The rst order condition of the
consumer problem is
Z N
1
cl dl
c k 1 = pk
0
where is the multiplier on the budget constraint. Solving for
There are two countries, denoted by i = 1, 2. Each country produces a
mass (continuum) of traded goods Ni and of non-traded goods Pi . Each good
is produced by an individual monopolist. There is no overlap between the
goods produced by one country and tho
14.462
Problem set 4
Consider the following model
pt = p e
t
1
+ "t
Where pt is the endogenous variable (say an asset price), pe 1 its expected value,
t
and "t an iid shock with zero mean and variance 2 , which is not known a period
ahead.
1. What is the
14.462 Advanced Maroeconomics
Spring 2004
Problem Set 5
(due April 12)
Problem
There is a measure-one continuum of agents, indexed by i 2 [0, 1]. Each agent can choose
between two actions. The action of agent i is denoted as ki 2 cfw_0, 1, where ki = 0 re
14.454 - Macroeconomics IV
Problem Set 3 Solutions
Juan Pablo Xandri
05/09/2011
1
Question 1 - Jacklins Critique to DiamondDygvig
Take the Diamond-Dygvig model in the recitation notes, and consider Jacklins
implementation of the social optimum via a rm th
14.462 Advanced Macroeconomics
Spring 2004
Problem Set
Solution
1. It is easy to check that pt = "t is the (bubbleless) REE equilibrium. Next consider the
learning process. Substituting the model equation into the learning equation yields
e
pe = pt +
t+1
14.462
Midterm exam
March 17, 2004
Gilles Saint-Paul
Consider the following economy. There is continuum of workers with mass
1, each endowed with L units of labor, and a continuum of goods of mass N .
They have the same utility given by
U=
Z
1
e
b
0
bc
di
14.462 Advanced Macroeconomics
Spring 2004
Problem Set
Solution
1. The dierential equation in the case of one good is Q1 =
1 (Q1 )
=
1
[1
F (a0 + A(Q1 )
Here we are given a specic distribution:
F (x) = min max
x
1 (Q1 )
Q1 ] .
( )
y
,0 ,1
2
and so the c
14.462 Advanced Macroeconomics
Spring 2004
Problem Set 6 Solution
Problem
1. The guess
ki = xi + (1
)y.
K = + (1
)y.
implies
Combining this with the relationship y = K + y u yields
y=+
1
u u
Thus as a signal of the precision is 2 y . Dene
x
x + 2 y
=
Then
14.462 Advanced Maroeconomics
Spring 2004
Problem Set
Solution
The case
= is not interesting, so assume > . Let r and w be the (shadow)
prices of capital and labor. The cost functions corresponding to the two technologies are
1
r
w 1
r
w
and
, respect
14.462 Advanced Macroeconomics
Spring 2004
Midterm
xam Solution
1. The rst order condition for consumption is
bci
e
= pi
and solving for consumption yields
1
[log(pi ) + log()] .
b
ci =
Substituting into the budget constraint yields
1
log() = c
b
where c
14.462 Advanced Macroeconomics
Spring 2004
Problem Set 5 Solution
Problem 1
1. The best response function is
g(K, ) =
log(1 + K )
log(1 + K )
1 log(c)
0 < log(c)
c
We have = log 2 and = log(c). If < , then it is best not to invest even if
everybody else d
14.462 Advanced Macroeconomics
Spring 2004
Problem Set 6
(due May 7)
Problem
The economy is populated by a continuum of measure one of agents, indexed by i and
uniformly distributed over the [0, 1] interval. Agents are risk neutral with utility
1 2
k
2 i