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220
Economic Dynamics
When considering the phase space of this canonical form it is useful to consider
the following:
±
z
1
t
z
2
t
²
=
±
r
t
0
0
s
t
²±
z
10
z
20
²
Now take the ratio of
z
2
/
z
1
, then
z
2
t
z
1
t
=
s
t
z
20
r
t
z
10
=
³
s
r
´
t
µ
z
20
z
10
¶
and so the path of the system is dominated by the value/sign of
s
/
r
.
5.5 Graphing trajectories of discrete systems
The mathematics of solving simultaneous equation systems is not very straightfor
ward and it is necessary to obtain the eigenvalues and the eigenvectors. However,
it is possible to combine the qualitative nature of the phase plane discussed in
the previous section and obtain trajectories using a spreadsheet or the recursive
features of
Mathematica
and
Maple
.
5.5.1
Trajectories with
Excel
Example 5.8
Consider the following system of equations
x
t
=−
5
+
0
.
25
x
t
−
1
+
0
.
4
y
t
−
1
y
t
=
10
−
x
t
−
1
+
y
t
−
1
x
0
=
10
,
y
0
=
5
In cells B8 and C8 we place the initial values for
x
and
y
, namely
x
0
=
10 and
y
0
=
5. In cells B9 and C9 we place the formulas. These are
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.
 Fall '11
 Dr.Gwartney
 Economics

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