NAME
189
Her income is equal to $100 and the sexton allows her to ring the bell for
10 hours.
(a)
Due to complaints from the villagers, the sexton has decided to restrict
Ms. Moto to 5 hours of bell ringing per day. This is bad news for Ms.
Moto. In fact she regards it as just as bad as losing
$15
dollars of
income.
(b)
The sexton relents and offers to let her ring the bells as much as she
likes so long as she pays $2 per hour for the privilege. How much ringing
does she do now?
10 hours.
This tax on her activities is as bad
as a loss of how much income?
$20.
(c)
The villagers continue to complain.
The sexton raises the price of
bell ringing to $4 an hour.
How much ringing does she do now?
0
hours.
This tax, as compared to the situation in which she could
ring the bells for free, is as bad as a loss of how much income?
$30.
190
CONSUMER’S SURPLUS
(Ch.
14)
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 find a consumer’s reservation price for
a good.
Recall that the reservation price is the price that makes the
consumer indifferent between having the good at that price and not hav
ing the good at all.
Mathematically, the reservation price
p
∗
satisfies
u
(0
, m
) =
u
(1
, m
−
p
∗
), where
m
is income and the quantity of the other
good is measured in dollars.
Finally, 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.
For each demand function, find 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
. Then
dD
(
p
)
/dp
=
−
6 and
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)
.
192
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
≤
4 and
D
B
(
p
) = 0 if
p >
4.
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 Winter '08
 Staff
 Supply And Demand, red line, blue line, demanders

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