Econ. 700
Tauchen/Frazier
Summer 2013
Answer: s to Final Examination
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to spend some time on
each question. 2. Write your name on only the backs of your answer sheets. At
L ECTURE N OTE 2: N UMBERS
F EI L I
August 2, 2016
1
NATURAL N UMBERS
Again, we adopt the naive approach to define natural numbers. Instead of construct it by using
Peano Axioms (See Tao, 2006), we assume the set of natural numbers exist and write it as
N
L ECTURE N OTE 0. L OGIC AND P ROOF
F EI L I
August 1, 2016
1
I NTRODUCTION
To be able to understand mathematics and mathematical arguments, it is necessary to have a solid
understanding of logic and the way in which known facts can be combined to prove n
L ECTURE N OTE 4: S EQUENCES AND L IMITS
F EI L I
August 8, 2016
1
M ETRIC S PACE
Since many of the central ideas in analysis depend on the concept of distance and closeness between two points, we have to start by introducing a definition of distance in g
L ECTURE N OTE 7: D IFFERENTIATION
F EI L I
August 11, 2016
1
S INGLE -VARIABLE F UNCTIONS
D EFINITION 1. Let f : E R where E R. For any x E, if for any sequence cfw_xn x s.t.
xn 6= x, n, and
f (xn ) f (x)
lim
xn x
xn x
exists, then f is called different
L ECTURE N OTE 10: C ONSTRAINED O PTIMIZATION
F EI L I
August 17, 2016
We are going to consider the following problem
v() = max f (x, )
x()
where Rn () is called constraint correspondence, f is called objective function, v is called
value function, x is c
L ECTURE N OTE 8: C ONVEX A NALYSIS
F EI L I
August 16, 2016
1
C ONVEX S ETS
We only consider convex sets in Rn .
D EFINITION 1. The set A Rn is convex if for any x, y A and [0, 1], x + (1 )y A
and it is strictly convex if x + (1 )y int(A)
T HEOREM 1. The
L ECTURE N OTE 3: F UNCTIONS
F EI L I
August 3, 2016
D EFINITION 1. Let A and B be sets. A function between A and B is a nonempty relation f AB
such that if (a, b) f and (a, b0 ) f , then b = b0 . The domain of f , denoted by domf , is the set
of all firs
L ECTURE N OTE 6: C ONTINUITY
F EI L I
August 10, 2016
Let (X, dx ) and (Y, dy ) be metric spaces. A function f : X Y builds a connection between
two spaces. For each sequence cfw_xn X, one have a corresponding sequence cfw_yn f (X)
where yn = f (xn ),
L ECTURE N OTE 9: C ONCAVE AND Q UASI - CONCAVE
F UNCTIONS
F EI L I
August 17, 2016
1
C ONCAVE F UNCTIONS
In the rest of this lecture, we focus on real-valued function f : E R where E Rn is convex.
D EFINITION 1. A function f : E R is concave if
f [x0 + (
L ECTURE N OTE 5: T OPOLOGY
F EI L I
August 9, 2016
In this lecture, unless otherwise told, we consider Euclidian space.
1
O PEN AND C LOSE SETS
D EFINITION 1. Let S R. A point s S is called a limit point of S if there exists a sequence
cfw_sn S and sn s
Econ. 700
Tauchen/Moore
Summer 2010
Final Exam
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to spend
some time on each question. 2. Write your name on only the backs of your answer sheets. At the
end of the exam, s
Econ. 700
Tauchen/Petranka
Fall 2008
Final Examination
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to spend
some time on each question. 2. Write your name on only the backs of your answer sheets. At the
end of the
Econ. 700
Tauchen/Petranka
Fall 2008
Answers to Midterm
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to spend some time on each
question. 2. Write your name on only the backs of your answer sheets. At the end of th
Econ. 700
Tauchen/Petranka
Fall 2008
Midterm
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to spend some time on each
question. 2. Write your name on only the backs of your answer sheets. At the end of the exam, sig
Econ. 700
Tauchen/Moore
Summer 2010
Answers to Midterm
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to spend
some time on each question. 2. Write your name on only the backs of your answer sheets. At the
end of the
Econ. 700
Tauchen/Frazier
Summer 2013
Answers to Midterm
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to spend some time
on each question. 2. Write your name on only the backs of your answer sheets. At the end of t
Econ. 700
Tauchen/Hinds/Petranka
Fall 2007
Answers to Exam #1
1. Answer: The leading pm of order 1 must be positive or a > 0. The leading pm of order 2
must be positive or a > a2 . Since a is positive, the previous inequality implies a < 1. The
determinan
Econ. 700
Tauchen/Hinds/Petranka
Fall 2007
Exam #1
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to
spend some time on each question. 2. Write your name on only the backs of your answer
sheets. At the end of the exa
Econ. 700
Tauchen/Hinds
Fall 2007
Exam #2
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to
spend some time on each question. 2. Write your name on only the backs of your answer
sheets. At the end of the exam, sign y
Econ. 700
Tauchen/Hinds
Fall 2007
Exam #3
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to spend
some time on each question. 2. Write your name on only the backs of your answer sheets. At the
end of the exam, sign y
Econ. 700
Tauchen/Moore
Summer 2010
Answers to Final Exam
Instructions: 1. Answer all questions. Partial credit is assigned and you are advised to spend
some time on each question. 2. Write your name on only the backs of your answer sheets. At the
end of