Recitation 2: Demand and Elasticity
February 25, 2009
1
Supply Curves
The supply curve gives the relation between the quantity of the good sup
plied by the productive sector (
Q
S
) and its price (
P
). If we assume a linear
form
Q
S
=
f
+
hP
The slope of this curve is
h
.
However
, since it is custom in economics to
put
P
on the vertical axes and
Q
on the horizontal axes, we often want to
invert the function:
P
=
1
h
Q
S

f
h
The slope of the inverted supply curve is 1
/h
2
Demand Curves
The demand curve ﬁves the relation between the quantity of the good de
manded by the consumers (
Q
D
) and its price (
P
). If we assume linear form
Q
D
=
a

bP
The slope of the demand curve is Δ
Q
D
/
Δ
P
=

b <
0.
The slope of the Inverse Demand is Δ
P/
Δ
Q
D
=

1
/b <
0
Remember that the slope of a linear function doesn’t change over the do
main.
Law of Demand
: when holding every factor aﬀecting price ﬁxed, there
is a negative relationship between quantity demanded and price of the good.
That is, the higher the price of the good, the lower the quantity demanded.
It is possible to have nonlinear demands: an example is
Q
=
a
P
b
1
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View Full Documentthis curve resembles a classic hyperbole: it is easy to see that the slope
changes in every point of the curve, going from
∞
to 0.
Δ
Q
Δ
P
=

ab
P
b
+1
=

abP

b

1
<
0
2.1
Identifying the Demand and the Supply
An analyst who wants to estimate the demand curve for a speciﬁc good in
a market can do so by collecting data of diﬀerent
quantitysupply
bundles.
Then he can estimate the demand by ﬁtting a linear curve through these
points.
This method might give very misleading results: the analyst might ﬁnd a
POSITIVE relationship between quantity and price, thus contradicting the
Law of Demand. Does this make sense? probably not. So, what happened?
What the analyst was estimating was the Supply function and not the de
mand. Remember that the
quantityprice
points are EQUILIBRIUM points,
that is, points that lie at the intersection between a demand curve and a
supply curve.
If the demand curve shifts, then the equilibrium points that we are measuring
are tracking the supply function. In fact we are moving over DIFFERENT
demand functions, and not along one of them. The only way to identify a
curve is to move
along
it.
So, in order to estimate the demand consistently, we need two conditions
•
the demand doesn’t move
•
the supply shifts
We can estimate the demand only by shifting the supply: in this way the
equilibrium points would all be ALONG the demand.
3
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 Spring '08
 JunNie
 Supply And Demand

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