With the graph of the demand curve shown in Figure M.1 4(b), however, the story
is a bit different. Normally, economists say that the
quantity demanded
of a good is a
function of its
price
:
Q
D
= f
(
P
). In this way of expressing the relationship,
price
should
be the
independent
variable, and appear on the
horizontal
axis. Indeed, some economists
(notably Léon Walras and Frank Knight)
did
draw the graphs of demand functions in
this way. Who is to blame for the “backward” way that economists draw demand
curves? The culprit is Alfred Marshall, one of the great economists, who pioneered the
use of demand and supply curves in economics in Books 3 and 5 of his classic text,
Principles of Economics.
Why would Marshall, a solid mathematician, put
quantity
on the
horizontal axis? There are a number of reasons, but we will mention only one: in his ini
tial discussion of demand functions, Marshall dealt with the shortshort run (or “tem
porary”) equilibrium in a single market on a single marketday. Although he allowed
for some variation in the quantity supplied at different prices and also for some trading
at disequilibrium prices, if the supply brought to market that day were perfectly inelas
tic (a vertical line), so that the
same
quantity would be supplied
regardless
of the price,
then the quantity brought to market
would
determine the equilibrium market price.
Regardless of the reasons, however, it has become conventional to draw market
demand and supply curves with quantity on the horizontal axis and price on the verti
cal axis, even when implicitly or explicitly we are assuming that the
quantity demanded
of a good is a function of its
price
:
Q
D
= f
(
P
).
In Figure M.1 4(c) we have depicted the budget constraint for an individual who has
a budget of
M
dollars and spends it all on only two goods,
X
and
Y
, which have ±xed
prices
P
X
and
P
Y
, respectively. The equation for the budget line can be written in a
number of ways, including
M = P
X
X
+
P
Y
Y, or equivalently, Y = M/P
Y
–P
X
/P
Y
X,
(M.1.7)
where
M/P
Y
is the vertical intercept and
X
/P
Y
is the slope. The term
P
X
X
represents
the total amount spent on
X
, and similarly
P
Y
Y
represents the total amount spent on
Y
.
In this case, if we know the total budget
M
and how much has been spent on
X
, we can
then calculate how much has been spent on
Y
, and therefore (if we also know
P
Y
) how
many units of
Y
have been purchased. But we can also reverse the procedure: if we
know how much has been spent on
Y
, we can then calculate how much has been spent
on
X
, and therefore (if we know
P
X
) how many units of
X
have been purchased. Hence
in Figure M.1 4(c), the “causal” arrows can run in both directions.
The message of this section is
not
that “anything goes” in the placement of variables
on axes. In fact, economists
have
adopted certain conventions (and assume them) in the
graphical depiction of some of the basic economic relations. The message is rather that
it is important to learn these conventions,
and
what is being assumed about “causality”
in the standard diagrams.
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 Fall '12
 Danvo
 Supply And Demand, Monotonic function, Math Module, Julie y

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