Mathematics for Economists
Chapter 1:
Differential Equations
S. Aguey, PhD
African School Of Economics
Chapter 1 Systems of Two First
Order Equations
We introduce systems of two first order equations
In this chapter, we consider only systems of two
first

Mathematical Economics
Chap 4: Functional Equations (ctd3)
S. Aguey, Phd
African School Of Economics
6
Example: optimal growth model
6.1
Characterizing the policy
We introduce the neoclassical optimal growth model and see how to derive
properties of optim

Integrals and Primitives
S. Aguey, PhD
African School Of Economics
S. Aguey
1 / 34
Intuitive notion of the derivative
Suppose that a cyclist rolls from a position A to a position B
Starting from the point A, he looks at his watch and noted the time tA.
At

A Glimpse at Hyperbolic Discounting
An individual lives forever from t = 0,1,_.,oo. Think of the individual
as actually consisting of different personalities, one for each period. Each
personality is a distinct agent (timet agent] with a distinct utility

Mathematical Economics
Chap 4: Functional Equations
S. Aguey, PhD
African School Of Economics
1
Solving the FE
Now we make more assumptions on the primiti ves of the problem:
X is a convex subset of Rl ,
F (x; y) is continuous and bounded,
is continuous a

Mathematical Economics
Chap 4: Functional Equations (ctd1)
S. Aguey, Phd
African School Of Economics
2
Showing that T is a contraction
2.1
Blackwells sufficient conditions
One important step in applying our argument to the map T is to show that T
is a con

Chapitre 0: Do you remember these?
S. Aguey, PhD
African School Of Economics
S. Aguey (ASE)
1 / 37
Natural numbers
Natural numbers are used to count collections of objects indivisible
or designed as such.
"The set of natural numbers" is noted N
N = f0, 1,

Mathematical Economics
Chap 4: Functional Equations (ctd2)
S. Aguey, Phd
African School Of Economics
4
Continuity of the policy function
We are in the case of bounded returns and we are assuming strict concavity of
F and convexity of .
We proved that V is

Mathematical Economics
Chap 3: Optimal Control
S. Aguey, PhD
African School Of Economics
1
A portfolio problem
To set the stage, consider a simple nite horizon problem.
A risk averse agent can invest in two assets:
riskless asset (bond) pays gross return