Transcript Chapter Fourteen

Consumer’s Surplus
Molly W. Dahl
Georgetown University
Econ 101 – Spring 2009
1
Inverse Demand Functions

Taking quantity demanded as given and then
asking what the price must be describes the
inverse demand function of a commodity.
 Usually
we ask “Given p1 what is the quantity
demanded of x1?”
 But we could also ask the inverse question “Given
that the quantity demanded is x1, what must p1 be?”
2
Inverse Demand Functions
p1
Given p1’, what quantity is
demanded of commodity 1?
Answer: x1’ units.
p1’
x1’
x 1*
3
Inverse Demand Functions
p1
p1’
Given p1’, what quantity is
demanded of commodity 1?
Answer: x1’ units.
The inverse question is:
Given x1’ units are
demanded, what is the
price of
commodity 1?
x
*
1
x1’
Answer: p1’
4
Consumer’s Surplus
p1
Consumer’s surplus is the
consumer’s utility gain from
consuming x1’ units of
commodity 1.
CS
p'1
x'1
x*1
5
Change in Consumer’s Surplus

The change to a consumer’s total utility
due to a change to p1 is approximately the
change in her Consumer’s Surplus.
6
Change in Consumer’s Surplus
p1
p1(x1), the inverse ordinary demand
curve for commodity 1
p'1
x'1
x*1
7
Change in Consumer’s Surplus
p1
p1(x1)
p'1
CS before
x'1
x*1
8
Change in Consumer’s Surplus
p1
p1(x1)
p"1 CS after
p'1
x"1
x'1
x*1
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Change in Consumer’s Surplus
p1
p1(x1)
p"1
p'1
Lost CS
x"1
x'1
x*1
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In Class:
Calculating Consumer Surplus
11
Producer’s Surplus

Changes in a firm’s welfare can be
measured in dollars much as for a
consumer.
12
Producer’s Surplus
Output price (p)
S = Marginal Cost
y (output units)
13
Producer’s Surplus
Output price (p)
S = Marginal Cost
p'
'
y
y (output units)
14
Producer’s Surplus
Output price (p)
S = Marginal Cost
p'
Revenue
' '
p
= y
'
y
y (output units)
15
Producer’s Surplus
Output price (p)
S = Marginal Cost
p'
Variable Cost of producing
y’ units is the sum of the
marginal costs
'
y
y (output units)
16
Producer’s Surplus
Output price (p)
Revenue less VC
is the Producer’s
Surplus.
p'
S = Marginal Cost
Variable Cost of producing
y’ units is the sum of the
marginal costs
'
y
y (output units)
17
Cost-Benefit Analysis
Can we measure in money units the net
gain, or loss, caused by a market
intervention; e.g., the imposition or the
removal of a market regulation?
 Yes, by using measures such as the
Consumer’s Surplus and the Producer’s
Surplus.

18
Cost-Benefit Analysis
Price
The free-market equilibrium
Supply
p0
Demand
q0
QD , Q S
19
Cost-Benefit Analysis
Price
The free-market equilibrium
and the gains from trade
generated by it.
Supply
CS
p0
PS
Demand
q0
QD , Q S
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Cost-Benefit Analysis
Price
The gain from freely
trading the q1th unit.
Supply
Consumer’s
gain
CS
p0
PS
Producer’s
gain
q1
q0
Demand
QD , Q S
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Cost-Benefit Analysis
Price
The gains from freely
trading the units from
q1 to q0.
Consumer’s
gains
CS
Supply
p0
PS
Producer’s
gains
q1
q0
Demand
QD , Q S
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Cost-Benefit Analysis
Price
The gains from freely
trading the units from
q1 to q0.
Consumer’s
gains
CS
Supply
p0
PS
Producer’s
gains
q1
q0
Demand
QD , Q S
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Cost-Benefit Analysis
Price
Consumer’s
gains
CS
p0
PS
Producer’s
gains
q1
q0
Any regulation that
causes the units
from q1 to q0 to be
not traded destroys
these gains. This
loss is the net cost
of the regulation.
QD , Q S
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Cost-Benefit Analysis
Price
pb
An excise tax imposed at a rate of $t
per traded unit destroys these gains.
Deadweight
Loss
CS
Tax
Revenue
t
ps
PS
q1
q0
QD , Q S
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Cost-Benefit Analysis
Price
pf
CS
An excise tax imposed at a rate of $t
per traded unit destroys these gains.
Deadweight
Loss
So does a floor
price set at pf
PS
q1
q0
QD , Q S
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Cost-Benefit Analysis
Price
An excise tax imposed at a rate of $t
per traded unit destroys these gains.
Deadweight
Loss
CS
pc
So does a floor
price set at pf,
a ceiling price set
at pc
PS
q1
q0
QD , Q S
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Cost-Benefit Analysis
Price
pe
pc
CS
PS
An excise tax imposed at a rate of $t
per traded unit destroys these gains.
Deadweight
Loss
So does a floor
price set at pf,
a ceiling price set
at pc, and a ration
scheme that
allows only q1
units to be traded.
q1
q0
QD , Q S
Revenue received by holders of ration coupons. 28
Compensating Variation and Equivalent
Variation

Two additional dollar measures of the total
utility change caused by a price change
are Compensating Variation and
Equivalent Variation.
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Compensating Variation
p1 rises.
 Q: What is the extra income that, at the
new prices, just restores the consumer’s
original utility level?

 Or,
after the policy has been implemented,
how much must you be compensated to reach
the same utility as before the policy?

A: The Compensating Variation.
30
Compensating Variation
x2
p1=p1’
p2 is fixed.
' '
'
m1  p1x1  p2x 2
x'2
u1
x'1
x1
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Compensating Variation
p1=p1’
p1=p1”
x2
x"2
x'2
p2 is fixed.
' '
'
m1  p1x1  p2x 2
 p"1x"1  p2x"2
u1
u2
x"1
x'1
x1
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Compensating Variation
p1=p1’
p1=p1”
x2
x'"
2
x"2
x'2
p2 is fixed.
' '
'
m1  p1x1  p2x 2
 p"1x"1  p2x"2
" '"
m2  p1x1
'"
 p2 x 2
u1
u2
x"1 x'"
1
x'1
x1
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Compensating Variation
p1=p1’
p1=p1”
x2
x'"
2
x"2
x'2
p2 is fixed.
' '
'
m1  p1x1  p2x 2
 p"1x"1  p2x"2
" '"
m2  p1x1
'"
 p2 x 2
u1
u2
x"1 x'"
1
x'1
CV = m2 - m1.
x1
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Equivalent Variation
p1 rises.
 Q: What is the extra income that, at the
original prices, just restores the
consumer’s original utility level?

 Or,
how much would you pay to avoid moving
to the new policy?

A: The Equivalent Variation.
35
Equivalent Variation
x2
p1=p1’
p2 is fixed.
' '
'
m1  p1x1  p2x 2
x'2
u1
x'1
x1
36
Equivalent Variation
p1=p1’
p1=p1”
x2
x"2
x'2
p2 is fixed.
' '
'
m1  p1x1  p2x 2
 p"1x"1  p2x"2
u1
u2
x"1
x'1
x1
37
Equivalent Variation
p1=p1’
p1=p1”
x2
x"2
x'2
p2 is fixed.
' '
'
m1  p1x1  p2x 2
 p"1x"1  p2x"2
'"
m2  p'1x'"

p
x
1
2 2
u1
x'"
2
u2
x"1
'
x'"
x
1
1
x1
38
Equivalent Variation
p1=p1’
p1=p1”
x2
x"2
x'2
p2 is fixed.
' '
'
m1  p1x1  p2x 2
 p"1x"1  p2x"2
'"
m2  p'1x'"

p
x
1
2 2
u1
x'"
2
u2
x"1
'
x'"
x
1
1
EV = m1 - m2.
x1
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Consumer’s Surplus, Compensating
Variation and Equivalent Variation
When the consumer has quasilinear utility,
CV = EV = DCS.
Why? There are no income effects with
quasilinear utility.
Otherwise,
EV < DCS < CV.
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