This preview shows page 1. Sign up to view the full content.
10
Economic Dynamics
Figure 1.1.
period
t
+
1. Thus
x
t
−
1
is the stock at the end of period
t
−
1 and
x
t
is the stock
at the end of period
t
. Now let
z
t
be a ﬂow variable
over
period
t
, and involving
dimension [
T
−
1
]. Of course, there is also
z
t
−
1
and
z
t
+
1
. Now return to variable
x
.
It is possible to consider the change in
x
over period
t
, which we write as
±
x
t
=
x
t
−
x
t
−
1
This immediately shows up a problem. Let
x
t
have dimension [
Q
], then by propo
sition (1) so would
±
x
t
. But this cannot be correct!
±
x
t
is the change
over
period
t
and must involve dimension [
T
−
1
]. So how can this be? The correct formulation
is, in fact,
±
x
t
±
t
=
x
t
−
x
t
−
1
t
−
(
t
−
1)
∈
[
QT
−
1
]
(1.3)
Implicit is that
±
t
=
1 and so
±
x
t
=
x
t
−
x
t
−
1
. But this ‘hides’ the dimension
[
T
−
1
]. This is because
±
t
∈
[
T
], even though it has a value of unity,
±
x
t
/±
t
∈
[
QT
−
1
].
Keeping with the convention
This is the end of the preview. Sign up
to
access the rest of the document.
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

Click to edit the document details