Chapter 15
NAME
Market Demand
Introduction.
Some problems in this chapter will ask you to construct
the market demand curve from individual demand curves. The market
demand at any given price is simply the sum of the individual demands at
that price. The key thing to remember in going from individual demands
to the market demand is to
add quantities
. Graphically, you sum the
individual demands horizontally to get the market demand. The market
demand curve will have a kink in it whenever the market price is high
enough that some individual demand becomes zero.
Sometimes you will need to Fnd a consumer’s reservation price for
a good.
Recall that the reservation price is the price that makes the
consumer indi±erent between having the good at that price and not hav
ing the good at all.
Mathematically, the reservation price
p
∗
satisFes
u
(0
,m
)=
u
(1
,m
−
p
∗
), where
m
is income and the quantity of the other
good is measured in dollars.
²inally, some of the problems ask you to calculate price and/or in
come elasticities of demand. These problems are especially easy if you
know a little calculus. If the demand function is
D
(
p
), and you want to
calculate the price elasticity of demand when the price is
p
, you only need
to calculate
dD
(
p
)
/dp
and multiply it by
p/q
.
15.0
Warm Up Exercise.
(Calculating elasticities.)
Here are
some drills on price elasticities. ²or each demand function, Fnd an ex
pression for the price elasticity of demand. The answer will typically be
a function of the price,
p
. As an example, consider the linear demand
curve,
D
(
p
)=30
−
6
p
.Th
en
dD
(
p
)
/dp
=
−
6and
p/q
=
p/
(30
−
6
p
), so
the price elasticity of demand is
−
6
p/
(30
−
6
p
).
(a)
D
(
p
)=60
−
p
.
−
p/
(60
−
p
)
.
(b)
D
(
p
)=
a
−
bp
.
−
bp/
(
a
−
bp
)
.
(c)
D
(
p
)=40
p
−
2
.
−
2
.
(d)
D
(
p
)=
Ap
−
b
.
−
b
.
(e)
D
(
p
)=(
p
+3)
−
2
.
−
2
p/
(
p
+3)
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MARKET DEMAND
(Ch. 15)
(f)
D
(
p
)=(
p
+
a
)
−
b
.
−
bp/
(
p
+
a
)
.
15.1 (0)
In Gas Pump, South Dakota, there are two kinds of consumers,
Buick owners and Dodge owners. Every Buick owner has a demand func
tion for gasoline
D
B
(
p
)=20
−
5
p
for
p
≤
4and
D
B
(
p
)=0i
f
p>
4.
Every Dodge owner has a demand function
D
D
(
p
)=15
−
3
p
for
p
≤
5
and
D
D
(
p
)=0for
p>
5. (Quantities are measured in gallons per week
and price is measured in dollars.) Suppose that Gas Pump has 150 con
sumers, 100 Buick owners, and 50 Dodge owners.
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 Summer '09
 JOHNG.SESSIONS
 Microeconomics, Supply And Demand, red line

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