MATH MODULE 4: USING ECONOMIC UNITS
M4-3
Of course you probably did all of
these
calculations in your head, because the exam-
ples are fairly straightforward. With more complicated transformations, however, it
pays to keep track of the units systematically. Moreover, keeping the units in mind can
help resolve some of the more important
basic
difficulties that students encounter in the
early stages of mastering economics. Finally, and perhaps most important, keeping a
firm grasp on the units is one of the best ways of increasing your theoretical capacity
and your economic intuition. If you know the units in which your variables are mea-
sured, it is much easier to translate from economics into mathematics and back. Hence
the number-crunching is not just an abstract operation but becomes a representation of
the actual economic processes you are analyzing.
The next set of examples provides you with some practical tips for utilizing eco-
nomic units effectively.
Example 5: Stock and Flow Variables and the Time Dimension:
Both stock and ﬂow
variables are important in economics. Population censuses, inventories and balance
sheets pertain to a
moment in time
. They involve “taking stock” of the population, the
physical assets of a firm, and the assets and liabilities of a firm, respectively, at that
moment. They are
stock
variables, and their time dimension is zero. In contrast, the com-
ponents of Gross Domestic Product (private consumption and investment, government
consumption and investment, and net exports), or births, deaths, immigration and emi-
gration, or the volume of sales of a particular good, are
ﬂow
variables. They are mea-
sured with reference to a particular
period or duration of time.
You will notice that in the early chapters of the text, supply and demand are
explicit-
ly
specified with reference to a particular period, say a day or a week or a month. Even
when the time period is
not
explicitly mentioned, however, supply and demand curves
implicitly involve a
ﬂow
of goods within a specific period of given duration. If you con-
sume 1 pizza per week, you consume almost exactly 52 pizzas per year (52.143, or
52.286 in leap years).
Consider the following linear demand curve, which represents the demand for a
good over the period of a year, in which the
ceteris paribus
assumption holds, price
P
is
measured in $/kg, and quantity demanded is measured in kg/year:
Annual demand
:
P
= 78 – 1/24
Q
D
. If
P
= 0, then
Q
D
= 1872 kg/year.
If there are 12 months in a year (abstracting from the fact that some months are
longer than others), then on average we have:
Monthly demand
:
P
= 78 – 1/2
Q
D
. If
P
= 0, then
Q
D
= 156 kg/month. Note
that 156 kg is 1/12 of 1872 kg/year, and the slope of the demand curve
expressed on a monthly basis is hence 12 times as steep as the “annual”
curve.