Introduction
9
To clarify these ideas, and other to follow, we list the following set of primary
dimensions used in economics:
(1)
Money [
M
]
(2)
Resources or quantity [
Q
]
(3)
Time [
T
]
(4)
Utility or satisfaction [
S
]
Apples has, say, dimension [
Q
1] and bananas [
Q
2]. We cannot add an apple to
a banana (we can of course add the number of objects, but that is not the same
thing). The
value
of an apple has dimension [
M
] and the value of a banana has
dimension [
M
], so we can add the value of an apple to the value of a banana. They
have the same dimension. Our reference to [
Q
1] and [
Q
2] immediately highlights a
problem, especially for macroeconomics. Since we cannot add apples and bananas,
it is sometimes assumed in macroeconomics that there is a
single
aggregate good,
which then involves dimension [
Q
].
For any set of primary dimensions, and we shall use money [
M
] and time [
T
]
to illustrate, we have the following three propositions:
(1)
If
a
∈
[
M
] and
b
∈
[
M
] then
a
±
b
∈
[
M
]
(2)
If
a
∈
[
M
] and
b
∈
[
T
] then
ab
∈
[
MT
] and
a
/
b
∈
[
MT
−
1
]
(3)
If
y
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 Fall '11
 Dr.Gwartney
 Economics, Algebra, Space, Supply And Demand, Utility, Spacetime

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