
Solutions
14.06 2004  Midterm
Prof: Marios Angeletos
Question 1 (Continuous Time): (a) The household takes , wt , rt and Tt as given and selects a
consumption path to solve
Z
max
et u (ct ) dt
0
su
14.30 PROBLEM SET 7
TA: Tonja Bowen Bishop
Due: Tuesday, April 25, 2006
Note: The rst three problems are required, and the remaining three are
practice problems. If you choose to do the practice probl
14.30 PROBLEM SET 3
TA: Tonja Bowen Bishop
Due: Tuesday, March 8, 2006 , by 4:30 p.m.
Note: The rst four problems are required, and the remaining two are
practice problems. If you choose to do the pra
14.30 PROBLEM SET 5
TA: Tonja Bowen Bishop
Due: Tuesday, April 4, by 4:30 p.m.
Note: The rst three problems are required, and the remaining two are
practice problems. If you choose to do the practice
14.30 PROBLEM SET 1  SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
a.
For any A and B , we can create two sets that are disjoint and
exhaustive on B : A \ B and AC \ B . Thus
Pr (B ) = Pr (A \ B
14.30 PROBLEM SET 4
TA: Tonja Bowen Bishop
Due: Tuesday, March 21, by 4:30 p.m.
Note: The rst three problems are required, and the remaining two are
practice problems. If you choose to do the practice
14.30 PROBLEM SET 8
TA: Tonja Bowen Bishop
Due: Tuesday, May 2, by 4:30 p.m.
Note: The rst three problems are required, and the remaining two are
practice problems. If you choose to do the practice pr
14.30 PROBLEM SET 3  SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
a.
E (ag1 (X) + bg2 (X) + c) =
Z
1
(ag1 (x) + bg2 (x) + c) fX (x) dx
Z
Z 1
Z 1
=
ag1 (x) fX (x) dx +
bg2 (x) fX (x) dx +
cfX (x
14.30 PROBLEM SET 2
TA: Tonja Bowen Bishop
Due: Tuesday, February 28, 2006 , by 4:30 p.m.
Note: The rst four problems are required, and the remaining two are
practice problems. If you choose to do the
14.30 PROBLEM SET 9
TA: Tonja Bowen Bishop
Due: Never! These are all practice problems. Please note that these
problems are mostly theoretical and NOT necessarily representative of what
will be on the
14.30 PROBLEM SET 8 SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
Suppose that the sample statistics for a random sample of 10 observations
from a N ; 2 population are the following:
X = 5
S2 = 4
14.06 Final
Spring 2004
You have 1h30min. Please answer each question in separate booklets. Each question counts for
a total of 60 points. Allocate your time eciently. If you can not answer some part
14.06 Midterm
Spring 2004
You have 1.5 hours.
Total points: 100.
luck!
You must answer all questions. No books or notes are allowed.
Answer question 1 in either continuous or discrete time. Good
Quest
14.30 PROBLEM SET 6 SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
e
e
a.
Let X denote the sum of the weight of the 100 sampled coins: X =
100
P
e
Xi . Now, X must be distributed normally, because
Final Exam Answers
Course 14.06 Intermediate Applied Macroeconomics
1. Question #1
(a) The firms problem is as follows:
max = At Kt L1 rt K t wt Lt
t
K ,L
The FOCS can be written as:
rt = At kt 1
wt =
14.06 Macroeconomics Spring 2003
Final Exam Solutions Part A (True, false or uncertain) 1. Because more capital allows more output to be produced, it is always better for a country to have more capita
14.30 PROBLEM SET 1
TA: Tonja Bowen Bishop
Due: Tuesday, February 21, 2006 , by 4:30 p.m.
Note: The rst four problems are required, and the remaining two are practice problems. If you choose to do the
14.30 PROBLEM SET 5  SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
The joint pdf of X and Y will be equal to the product of the marginal
pdfs, since X and Y are independent.
fX,Y (x, y) = fX (x)
14.30 PROBLEM SET 6
TA: Tonja Bowen Bishop
Due: Thursday, April 13, by 4:30 p.m.
Note: The rst three problems are required, and the fourth is a practice
problem. If you choose to do the practice probl
14.30 PROBLEM SET 9 SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
For parts (a)(g), please refer to the relevant sections in the handouts/textbooks.
(h) False. With the knowledge of the distribu
14.30 PROBLEM SET 4  SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
a.
The distribution of Y jX is the distribution of + X + ", where
" is the only random variable and + X is xed, call it C. Then
14.06 Macroeconomics
Spring 2003
Midterm Exam Solutions
Part A (True, false or uncertain)
1. An economy that increases its saving rate will experience faster growth.
Uncertain. In the Solow model an
14.12 Game Theory Final (Answers)
12/21/2007
Prof. Muhamet Yildiz
Instructions. This is an open book exam; you can use any written material. You have two
hour and 50 minutes. Each question is 25 point
14.30 PROBLEM SET 2  SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
a.
There are 12 5 dierent ways for the team to accumulate a 732
7
3
7
3
2
record, and the probability of each of these outcom
14.30 PROBLEM SET 7 SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Problem 1
a.
For the statistic to be unbiased we must have
!
n
X
ci Xi
= E
i=1
= E (Xi )
n
X
ci
i=1
n
X
=
ci
i=1
So the statistic will be u