Lecture 8
Mathematical Economics
1 2
2 1
Good 1
x1 2
M s. 2
2 1
=(1, 2)
Good 2
x2 1
M s. 1
1 1
x =(x1,x2)
x1 1
x2 2
1 2
2 1
Good 1
=(1, 2)
Good 2
C
M s. 1
a
1 1
M s. 2
C
2 1
We can use this information to help us understand the types of exchanges each o
NotesandtheLawofIteratedExpectationsandonsolvinglinearstochasticdifferenceequations
We have been talking about the law of iterated expectations the last few lectures, and it seems clear thatthe
concept isnt quite sinking in. So I have prepared this little
Lecture 4
Econ 348 Mathematical
1. Review. In Week 1 we spent conomics time going through some
considerable amount of
Ein mathematical economics. Today we will focus
basic mathematical tools used
more on the math side, but before we do I want to do a quic
Lecture 3
Mathematical Economics
Review
The basic points of our last few lectures are as follows:
.
We set out to examine our most basic choice problem by first,
postulating some properties wed like to have in the form of solution
to our problem. These in
Lecture6
MathematicalEconomics
1. Taking Stock. In previous lectures we made the case that wed like to have superior sets
that are convex: these ensure the indifference curves will bow the right way and the
consumers optimum (i.e., her demand) will be uni
ClassProblem
SupposeaconsumerhaspreferencesrepresentedbyaCobbDouglas
preferences:
,
.TheagentwantstoMaximize
,
subjectto
.
A. SetuptheLagrangian forthisproblem.
B. Examinethesecondorderconditionforthesepreferences.
C. Findtheoptimalconsumptionbundleasafun
Econ 348 Mathematical Economics
Homework Set 2
You may work in groups of 3 or less on this assignment. If you work in a
group, please hand in 1 assignment. This problem set is due at the beginning
of class, 8 Feb 2013. Assignments turned after this time b
Econ 348 Mathematical Economics
Homework Set 4
You may work in groups of 3 or less on this assignment. If you work in a group, please hand in 1
assignment. This problem set is due Monday March 18th at noon. Assignments turned after this time but
before 5:
Consumption Rivalry
Consider our two friends again, (Pascal and Milton Friedman) in a pure exchange economy with two
goods and no free disposal. Pascal has a preference relation given by the utility function: uP xP ; xP =
1
2
ln xP + (1
) ln xP
xF ; while
1 Functions
3. Axioms for Preference Relations
A) Continuity. A function is continuous at a point if, for all
0, there
. A function is
exists a
0 such that
,
implies
,
called a continuous function if it is continuous at every point
Econ 348 Mathematical Economics
ANSWERS Homework Set 2
You may work in groups of 3 or less on this assignment. If you work in a
group, please hand in 1 assignment. This problem set is due at the beginning
of class, 8 Feb 2013. Assignments turned after thi
1 Functions
3. Axioms for Preference Relations
A) Continuity. A function is continuous at a point if, for all
0, there
. A function is
exists a
0 such that
,
implies
,
called a continuous function if it is continuous at every point