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144
Economic Dynamics
Figure 4.1.
with solutions
x
(
t
)
=
9
e
2
t
−
1
4
−
t
2
y
(
t
)
=
3
e
t
which clearly satisfy the initial conditions. Eliminating
e
t
, we can express the
relationship between
x
and
y
as
y
=
√
1
+
4
x
+
2
tx
≥
2
,
y
≥
3
which clearly depends on
t
. This means that where a system is at any point in
time in the (
x
,
y
)plane depends on precisely the moment the system arrives at
that point. For instance, in ±gure 4.1(b) we draw the system for three points of
time,
t
=
0
,
5
,
10
.
There is no longer a single trajectory in the (
x
,
y
)plane, but
a whole series of trajectories, one for each point in time. The system is clearly
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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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