12
Economic Dynamics
form
q
d
=
a
−
p
. On the face of it this is dimensionally inconsistent.
a
∈
[
QT
−
1
]
and
p
∈
[
MQ
−
1
] and so cannot be subtracted! The point is that the coefficient of
p
is unity with dimension [
Q
2
T
−
1
M
−
1
], and this dimension gets ‘hidden’.
Example 1.4
A typically dynamic version of example 1.3 is the cobweb model
q
d
t
=
a
−
bp
t
a
,
b
>
0
q
s
t
=
c
+
dp
t
−
1
d
>
0
q
d
t
=
q
s
t
=
q
t
(1.5)
Here we do subscript the variables since now two time periods are involved. Al
though
q
d
t
and
q
s
t
are quantities per period to time with dimension [
QT
−
1
], they
both refer to period
t
. However,
p
∈
[
MQ
−
1
] is for period
t
in demand but period
t
−
1 for supply. A model that is specified over more than one time period is a
dynamic model.
We have laboured dimensionality because it is still a muchneglected topic in
economics. Yet much confusion can be avoided with a proper understanding of
this topic. Furthermore, it lies at the foundations of economic dynamics.
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 Fall '11
 Dr.Gwartney
 Economics, 1 m, Nonlinear system, Multiple Equilibria, Nonlinearities

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