Thus,
a0 (s ) =
0
qt (t )d(t ).
s
s
t= st : =s
s
So we have the date zero price of an asset that starts payo at date given history
s .
Consider the tail asset. How could we take this price and renormalize it into a date
price? We just have to divide by
The agents DPP:
V (x, X, Z ) = M axu cfw_R(x, X, Z, u) + V (x , X , Z ),
subject to:
x = g (x, X, Z, u) agents constraints.
X = G(X, Z ) conjectured agg. laws of motion.
Z = J (Z ) exogeneous states laws of motion.
Solution to this problem is of the for
This matrix has 1 unit eigenvalue:
= (0, 0.64, 0.36).
This is intuitive since we cannot end up in state 1 because once we are in state 2 or 3,
we cant get back to state 1.
Fact: If P has all strictly positive elements, then it has a single unique invari
5
Lecture 5: February 9, 2005
5.1
Dynamic Programming
Manipulate FOCs
Recall the set of FOCs from last time for our time separable problem:
rt
gt
L
=
+
t = 0 for t = 0, . . . , T .
ut
ut ut
rt
gt
L
=
+
t t1 = 0 for t = 1, . . . , T .
[1.2]
xt
xt xt
L
[
Economics 602: Macroeconomics
Enrique Mendoza & John Haltiwanger
Matthew Chesnes
Updated: May 11, 2005
1
Lecture 1: January 26, 2005
1.1
Bob Lucas Models of Business Cycles
What are the role of recursive tools in economics?
What are the models that are