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
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
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 p
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
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 R
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 applyi
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 s
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 stric
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