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C ’ S lConsumer’s Surplus
© 2010 W. W. Norton & Company, Inc.
Monetary Measures of Gains-to-T dTrade
You can buy as much gasoline as you wish at $1 per gallon once youyou wish at $1 per gallon once you enter the gasoline market. Q Wh i h ld Q: What is the most you would pay to enter the market?
© 2010 W. W. Norton & Company, Inc. 2
Monetary Measures of Gains-to-T dTrade
A: You would pay up to the dollar value of the gains-to-trade you wouldvalue of the gains to trade you would enjoy once in the market.H h i d b How can such gains-to-trade be measured?
© 2010 W. W. Norton & Company, Inc. 3
Monetary Measures of Gains-to-T dTrade
Three such measures are:Consumer’s Surplus– Consumer s Surplus
– Equivalent Variation, and– Compensating Variation.
Only in one special circumstance do Only in one special circumstance do these three measures coincide.
© 2010 W. W. Norton & Company, Inc. 4
$ Equivalent Utility Gainsq y Suppose gasoline can be bought
l i l f llonly in lumps of one gallon. Use r1 to denote the most a single 1 g
consumer would pay for a 1st gallon -- call this her reservation price for-- call this her reservation price for the 1st gallon.
r1 is the dollar equivalent of the marginal utility of the 1st gallon.g y g
© 2010 W. W. Norton & Company, Inc. 5
$ Equivalent Utility Gainsq y
Now that she has one gallon, use r2to denote the most she would pay forto denote the most she would pay for a 2nd gallon -- this is her reservation price for the 2nd gallonprice for the 2nd gallon.
r2 is the dollar equivalent of the 2marginal utility of the 2nd gallon.
© 2010 W. W. Norton & Company, Inc. 6
$ Equivalent Utility Gainsq y
Generally, if she already has n-1 gallons of gasoline then r denotesgallons of gasoline then rn denotes the most she will pay for an nth gallongallon.
rn is the dollar equivalent of the nmarginal utility of the nth gallon.
© 2010 W. W. Norton & Company, Inc. 7
$ Equivalent Utility Gainsq y
r1 + … + rn will therefore be the dollar equivalent of the total change toequivalent of the total change to utility from acquiring n gallons of gasoline at a price of $0gasoline at a price of $0.
So r1 + … + rn - pGn will be the 1 n Gdollar equivalent of the total change to utility from acquiring n gallons ofto utility from acquiring n gallons of gasoline at a price of $pG each.
© 2010 W. W. Norton & Company, Inc. 8
$ Equivalent Utility Gainsq y
A plot of r1, r2, … , rn, … against n is a reservation-price curve This is notreservation price curve. This is not quite the same as the consumer’s demand curve for gasolinedemand curve for gasoline.
© 2010 W. W. Norton & Company, Inc. 9
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline($) Res.
10Values
r1
68r2
r3
24r4
r50
1 2 3 4 5 6r6
Gasoline (gallons)
© 2010 W. W. Norton & Company, Inc. 10
$ Equivalent Utility Gainsq y
What is the monetary value of our consumer’s gain-to-trading in theconsumer s gain to trading in the gasoline market at a price of $pG?
© 2010 W. W. Norton & Company, Inc. 11
$ Equivalent Utility Gainsq y
The dollar equivalent net utility gain for the 1st gallon is $(r1 - pG)the 1st gallon is $(r1 pG)
and is $(r2 - pG) for the 2nd gallon, and so on, so the dollar value of the
gain-to-trade isgain to trade is$(r1 - pG) + $(r2 - pG) + …
for as long as r p > 0for as long as rn - pG > 0.
© 2010 W. W. Norton & Company, Inc. 12
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline($) Res.
10Values
r1
68r2
r3
24r4
r5pG
01 2 3 4 5 6
r6
Gasoline (gallons)
© 2010 W. W. Norton & Company, Inc. 13
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline($) Res.
10Values
r1
68r2
r3
24r4
r5pG
01 2 3 4 5 6
r6
Gasoline (gallons)
© 2010 W. W. Norton & Company, Inc. 14
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline($) Res.
10Values
r1$ value of net utility gains-to-trade
68r2
r3
24r4
r5pG
01 2 3 4 5 6
r6
Gasoline (gallons)
© 2010 W. W. Norton & Company, Inc. 15
$ Equivalent Utility Gainsq y
Now suppose that gasoline is sold in half-gallon unitshalf gallon units.
r1, r2, … , rn, … denote the ’ i i fconsumer’s reservation prices for
successive half-gallons of gasoline.g g Our consumer’s new reservation
price curve isprice curve is
© 2010 W. W. Norton & Company, Inc. 16
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline($) Res.
10Values
r1
68r3
r5
24r7
r90
1 2 3 4 5 6r11 7 8 9 10 11
Gasoline (half gallons)
© 2010 W. W. Norton & Company, Inc. 17
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline($) Res.
10Values
r1
68r3
r5
24r7
r9pG
01 2 3 4 5 6
r11 7 8 9 10 11Gasoline (half gallons)
© 2010 W. W. Norton & Company, Inc. 18
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline($) Res.
10Values
r1$ value of net utility gains-to-trade
68r3
r5
24r7
r9pG
01 2 3 4 5 6
r11 7 8 9 10 11Gasoline (half gallons)
© 2010 W. W. Norton & Company, Inc. 19
$ Equivalent Utility Gainsq y
And if gasoline is available in one-quarter gallon unitsquarter gallon units ...
© 2010 W. W. Norton & Company, Inc. 20
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline
10
68($) Res.
Values
24
01 2 3 4 5 6 7 8 9 10 11
Gasoline (one-quarter gallons)
© 2010 W. W. Norton & Company, Inc. 21
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline
10
68($) Res.
Values
24
pG
01 2 3 4 5 6 7 8 9 10 11
Gasoline (one-quarter gallons)
© 2010 W. W. Norton & Company, Inc. 22
$ Equivalent Utility Gainsq yReservation Price Curve for Gasoline
10 $ value of net utility gains-to-trade
68($) Res.
Values
24
pG
0
Gasoline (one-quarter gallons)
© 2010 W. W. Norton & Company, Inc. 23
$ Equivalent Utility Gainsq y
Finally, if gasoline can be purchased in any quantity thenin any quantity then ...
© 2010 W. W. Norton & Company, Inc. 24
$ Equivalent Utility Gainsq y($) Res. Reservation Price Curve for GasolinePrices
Gasoline
© 2010 W. W. Norton & Company, Inc. 25
$ Equivalent Utility Gainsq y($) Res. Reservation Price Curve for GasolinePrices
pG
Gasoline
© 2010 W. W. Norton & Company, Inc. 26
$ Equivalent Utility Gainsq y($) Res. Reservation Price Curve for GasolinePrices $ value of net utility gains-to-trade
pG
Gasoline
© 2010 W. W. Norton & Company, Inc. 27
$ Equivalent Utility Gainsq y
Unfortunately, estimating a consumer’s reservation-price curveconsumer s reservation price curve is difficult,
i i h so, as an approximation, the reservation-price curve is replaced with the consumer’s ordinary demand curve.demand curve.
© 2010 W. W. Norton & Company, Inc. 28
Consumer’s Surplusp A consumer’s reservation-price p
curve is not quite the same as her ordinary demand curve Why not?ordinary demand curve. Why not?
A reservation-price curve describes ti ll th l f isequentially the values of successive
single units of a commodity. An ordinary demand curve describes
the most that would be paid for qthe most that would be paid for q units of a commodity purchased i lt l
© 2010 W. W. Norton & Company, Inc. 29
simultaneously.
Consumer’s Surplusp
Approximating the net utility gain area under the reservation-pricearea under the reservation price curve by the corresponding area under the ordinary demand curveunder the ordinary demand curve gives the Consumer’s Surplus measure of net utility gain.
© 2010 W. W. Norton & Company, Inc. 30
Consumer’s Surplusp($) Reservation price curve for gasoline
Ordinary demand curve for gasoline
Gasoline
© 2010 W. W. Norton & Company, Inc. 31
Consumer’s SurpluspReservation price curve for gasoline($)Ordinary demand curve for gasoline
pG
Gasoline
© 2010 W. W. Norton & Company, Inc. 32
Consumer’s SurpluspReservation price curve for gasoline($)Ordinary demand curve for gasoline
$ value of net utility gains-to-trade
pG
Gasoline
© 2010 W. W. Norton & Company, Inc. 33
Consumer’s SurpluspReservation price curve for gasoline($)Ordinary demand curve for gasoline
$ value of net utility gains-to-tradeConsumer’s Surplus
pG
Gasoline
© 2010 W. W. Norton & Company, Inc. 34
Consumer’s SurpluspReservation price curve for gasoline($)Ordinary demand curve for gasoline
$ value of net utility gains-to-tradeConsumer’s Surplus
pG
Gasoline
© 2010 W. W. Norton & Company, Inc. 35
Consumer’s Surplusp
The difference between the The difference between the consumer’s reservation-price and ordinary demand curves is due toordinary demand curves is due to income effects.
But, if the consumer’s utility function is quasilinear in income then thereis quasilinear in income then there are no income effects and Consumer’s Surplus is an exact $Consumer s Surplus is an exact $ measure of gains-to-trade.
© 2010 W. W. Norton & Company, Inc. 36
Consumer’s SurpluspThe consumer’s utility function is
ili i
Ux x v x x( ) ( )1 2 1 2 quasilinear in x2.
Ux x v x x( , ) ( )1 2 1 2 Take p2 = 1. Then the consumer’sp2choice problem is to maximize
Ux x v x x( ) ( ) Ux x v x x( , ) ( )1 2 1 2 subject toj
px x m1 1 2 .
© 2010 W. W. Norton & Company, Inc. 37
Consumer’s SurpluspThe consumer’s utility function is
ili i
Ux x v x x( ) ( )1 2 1 2 quasilinear in x2.
Ux x v x x( , ) ( )1 2 1 2 Take p2 = 1. Then the consumer’sp2choice problem is to maximize
Ux x v x x( ) ( ) Ux x v x x( , ) ( )1 2 1 2 subject toj
px x m1 1 2 .
© 2010 W. W. Norton & Company, Inc. 38
Consumer’s SurpluspThat is, choose x1 to maximize
v x m px( ) .1 1 1 The first-order condition is
v x p'( )1 1 0 v x p( )1 1 0
That is, p v x1 1 '( ).That is, p v x1 1( ).
This is the equation of the consumer’sqordinary demand for commodity 1.
© 2010 W. W. Norton & Company, Inc. 39
Consumer’s SurpluspOrdinary demand curve,p1
p v x1 1 '( )p1
CS'p1
x1*x1
'
© 2010 W. W. Norton & Company, Inc. 40
Consumer’s SurpluspOrdinary demand curve,p1
p v x1 1 '( )p1CS v x dx pxx '( ) ' ''
1 1 1 101
CS'p1
x1*x1
'
© 2010 W. W. Norton & Company, Inc. 41
Consumer’s SurpluspOrdinary demand curve,p1
p v x1 1 '( )p1CS v x dx pxx '( ) ' ''
1 1 1 101
v x v px( ) ( )' ' '1 1 10
CS'p1
x1*x1
'
© 2010 W. W. Norton & Company, Inc. 42
Consumer’s SurpluspOrdinary demand curve,p1
p v x1 1 '( )p1CS v x dx pxx '( ) ' ''
1 1 1 101
is exactly the consumer’s utility v x v px( ) ( )' ' '
1 1 10
'CS
is exactly the consumer s utilitygain from consuming x1’
units of commodity 1p1units of commodity 1.
x1*x1
'
© 2010 W. W. Norton & Company, Inc. 43
Consumer’s Surplusp
Consumer’s Surplus is an exact dollar measure of utility gained fromdollar measure of utility gained from consuming commodity 1 when the consumer’s utility function isconsumer’s utility function is quasilinear in commodity 2.
Otherwise Consumer’s Surplus is an approximation.approximation.
© 2010 W. W. Norton & Company, Inc. 44
Consumer’s Surplusp
The change to a consumer’s total utility due to a change to p1 isutility due to a change to p1 is approximately the change in her Consumer’s SurplusConsumer’s Surplus.
© 2010 W. W. Norton & Company, Inc. 45
Consumer’s Surpluspp1p1
p1(x1), the inverse ordinary demandf dit 1curve for commodity 1
'p1
x1*x1
'
© 2010 W. W. Norton & Company, Inc. 46
Consumer’s Surpluspp1p1
p1(x1)
CS before' CS beforep1
x1*x1
'
© 2010 W. W. Norton & Company, Inc. 47
Consumer’s Surpluspp1p1
p1(x1)
CS afterp" CS afterp1
'p1
x1*x1
'x1"
© 2010 W. W. Norton & Company, Inc. 48
Consumer’s Surpluspp1p1
p1(x1), inverse ordinary demandf dit 1curve for commodity 1.
p"
Lost CSp1
'p1
x1*x1
'x1"
© 2010 W. W. Norton & Company, Inc. 49
Consumer’s Surplusx1* px1
x1*(p1), the consumer’s ordinaryx1'
"p *
1 1demand curve for commodity 1.
" 1
'1
pp 11
*1 dp)p(xCS
x1Lost
measures the loss inConsumer’s Surplus.
CSp
p1p1"p1
'
© 2010 W. W. Norton & Company, Inc. 50
Compensating Variation and E i l t V i tiEquivalent Variation
Two additional dollar measures of the total utility change caused by athe total utility change caused by a price change are Compensating Variation and Equivalent VariationVariation and Equivalent Variation.
© 2010 W. W. Norton & Company, Inc. 51
Compensating Variationp g
p1 rises. Q: What is the least extra income Q: What is the least extra income
that, at the new prices, just restores h ’ i i l ili l l?the consumer’s original utility level?
© 2010 W. W. Norton & Company, Inc. 52
Compensating Variationp g
p1 rises. Q: What is the least extra income Q: What is the least extra income
that, at the new prices, just restores h ’ i i l ili l l?the consumer’s original utility level?
A: The Compensating Variation. A: The Compensating Variation.
© 2010 W. W. Norton & Company, Inc. 53
Compensating Variationp gp1=p1’ p2 is fixed.
x2m px p x1 1 1 2 2 ' ' '
'
u1
x2'
1
x1x1'
© 2010 W. W. Norton & Company, Inc. 54
Compensating Variationp gp1=p1’ p2 is fixed.
x2 p1=p1” m px p x1 1 1 2 2 ' ' '
'x2" p x p x1 1 2 2
" " "
x2'
u11
u2
x1x1'x1
"
© 2010 W. W. Norton & Company, Inc. 55
Compensating Variationp gp1=p1’ p2 is fixed.
x2
x2'"
p1=p1” m px p x1 1 1 2 2 ' ' '
x2"
'
x2 p x p x1 1 2 2
" " "
'"'"" xpxpm
u1
x2' 22112 xpxpm
1
u2
x1x1'x1
" x1'"
© 2010 W. W. Norton & Company, Inc. 56
Compensating Variationp gp1=p1’ p2 is fixed.
x2
x2'"
p1=p1” m px p x1 1 1 2 2 ' ' '
x2"
'
x2 p x p x1 1 2 2
" " "
'"'"" xpxpm
u1
x2' 22112 xpxpm
1
u2 CV = m2 - m1.
x1x1'x1
" x1'"
© 2010 W. W. Norton & Company, Inc. 57
Equivalent Variationq
p1 rises. Q: What is the least extra income Q: What is the least extra income
that, at the original prices, just h ’ i i lrestores the consumer’s original
utility level?y A: The Equivalent Variation.
© 2010 W. W. Norton & Company, Inc. 58
Equivalent Variationqp1=p1’ p2 is fixed.
x2m px p x1 1 1 2 2 ' ' '
'
u1
x2'
1
x1x1'
© 2010 W. W. Norton & Company, Inc. 59
Equivalent Variationqp1=p1’ p2 is fixed.
x2 p1=p1” m px p x1 1 1 2 2 ' ' '
'x2" p x p x1 1 2 2
" " "
x2'
u11
u2
x1x1'x1
"
© 2010 W. W. Norton & Company, Inc. 60
Equivalent Variationqp1=p1’ p2 is fixed.
x2 p1=p1” m px p x1 1 1 2 2 ' ' '
x2"
'
p x p x1 1 2 2" " "
m px p x' '" '"
u1
x2'
x'"
m px p x2 1 1 2 2
1
u2
x2
x1x1'x1
" x1'"
© 2010 W. W. Norton & Company, Inc. 61
Equivalent Variationqp1=p1’ p2 is fixed.
x2 p1=p1” m px p x1 1 1 2 2 ' ' '
x2"
'
p x p x1 1 2 2" " "
m px p x' '" '"
u1
x2'
x'"
m px p x2 1 1 2 2
1
u2
x2EV = m1 - m2.
x1x1'x1
" x1'"
© 2010 W. W. Norton & Company, Inc. 62
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
Relationship 1: When the consumer’s preferences areconsumer s preferences are quasilinear, all three measures are the samethe same.
© 2010 W. W. Norton & Company, Inc. 63
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
Consider first the change in Consumer’s Surplus when p1 risesConsumer s Surplus when p1 rises from p1’ to p1”.
© 2010 W. W. Norton & Company, Inc. 64
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
Ux x v x x( ) ( )If thUx x v x x( , ) ( )1 2 1 2 If then
CSp v x v px( ) ( ) ( )' ' ' '0CSp v x v px( ) ( ) ( )1 1 1 10
© 2010 W. W. Norton & Company, Inc. 65
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
Ux x v x x( ) ( )If thUx x v x x( , ) ( )1 2 1 2 If then
CSp v x v px( ) ( ) ( )' ' ' '0CSp v x v px( ) ( ) ( )1 1 1 10
and so the change in CS when p1 risesand so the change in CS when p1 risesfrom p1’ to p1” is
' "CS CSp CSp ( ) ( )' "1 1
© 2010 W. W. Norton & Company, Inc. 66
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
Ux x v x x( ) ( )If thUx x v x x( , ) ( )1 2 1 2 If then
CSp v x v px( ) ( ) ( )' ' ' '0CSp v x v px( ) ( ) ( )1 1 1 10
and so the change in CS when p1 risesand so the change in CS when p1 risesfrom p1’ to p1” is
' "CS CSp CSp ( ) ( )' "1 1
( ) ( ) ( ) ( )' ' ' " " "0 0 v x v px v x v p x( ) ( ) ( ) ( )1 1 1 1 1 10 0
© 2010 W. W. Norton & Company, Inc. 67
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
Ux x v x x( ) ( )If thUx x v x x( , ) ( )1 2 1 2 If then
CSp v x v px( ) ( ) ( )' ' ' '0CSp v x v px( ) ( ) ( )1 1 1 10
and so the change in CS when p1 risesand so the change in CS when p1 risesfrom p1’ to p1” is
' "CS CSp CSp ( ) ( )' "1 1
( ) ( ) ( ) ( )' ' ' " " "0 0 v x v px v x v p x( ) ( ) ( ) ( )1 1 1 1 1 10 0
v x v x px p x( ) ( ) ( )' " ' ' " "
© 2010 W. W. Norton & Company, Inc. 68
v x v x px p x( ) ( ) ( ).1 1 1 1 1 1
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation Now consider the change in CV when Now consider the change in CV when
p1 rises from p1’ to p1”. The consumer’s utility for given p1 is
v x p m px p( ( )) ( )* *1 1 1 1 1
and CV is the extra income which, at
v x p m px p( ( )) ( )1 1 1 1 1
and CV is the extra income which, at the new prices, makes the consumer’s utility the same as at theconsumer s utility the same as at the old prices. That is, ...
© 2010 W. W. Norton & Company, Inc. 69
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
' ' 'v x m px( )' ' '1 1 1
CV" " " v x m CV p x( ) .1 1 1
© 2010 W. W. Norton & Company, Inc. 70
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
' ' 'v x m px( )' ' '1 1 1
CV" " " v x m CV p x( ) .1 1 1SoSoCV v x v x px p x ( ) ( ) ( )' " ' ' " "
1 1 1 1 1 1p p( ) ( ) ( )1 1 1 1 1 1CS.
© 2010 W. W. Norton & Company, Inc. 71
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation Now consider the change in EV when Now consider the change in EV when
p1 rises from p1’ to p1”. The consumer’s utility for given p1 is
v x p m px p( ( )) ( )* *
and EV is the extra income which at
v x p m px p( ( )) ( )1 1 1 1 1
and EV is the extra income which, at the old prices, makes the consumer’s
tilit th t th iutility the same as at the new prices. That is, ...
© 2010 W. W. Norton & Company, Inc. 72
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
' ' 'v x m px( )1 1 1
EV( )" " " v x m EV p x( ) .1 1 1
© 2010 W. W. Norton & Company, Inc. 73
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent Variation
' ' 'v x m px( )1 1 1
EV( )" " "
That is, v x m EV p x( ) .1 1 1
,EV v x v x px p x ( ) ( ) ( )' " ' ' " "
1 1 1 1 1 1
CS.
© 2010 W. W. Norton & Company, Inc. 74
Consumer’s Surplus, Compensating V i ti d E i l t V i tiVariation and Equivalent VariationS h th h iliSo when the consumer has quasilinearutility,
CV = EV = CS.
But, otherwise, we have:
Relationship 2: In size, EV < CS < CV.
© 2010 W. W. Norton & Company, Inc. 75
Producer’s Surplusp
Changes in a firm’s welfare can be measured in dollars much as for ameasured in dollars much as for a consumer.
© 2010 W. W. Norton & Company, Inc. 76
Producer’s Surplusp
Output price (p)Output price (p)
Marginal Cost
y (output units)
© 2010 W. W. Norton & Company, Inc. 77
Producer’s Surplusp
Output price (p)Output price (p)
Marginal Cost
'p'
y (output units)y'
© 2010 W. W. Norton & Company, Inc. 78
Producer’s Surplusp
Output price (p)Output price (p)
Marginal Cost
'p'
Revenue' '= py
y (output units)y'
© 2010 W. W. Norton & Company, Inc. 79
Producer’s Surplusp
Output price (p)Output price (p)
Marginal Cost
'p'Variable Cost of producing
fy’ units is the sum of themarginal costs
y (output units)y'
© 2010 W. W. Norton & Company, Inc. 80
Producer’s Surplusp
Output price (p)Output price (p)Revenue less VCis the Producer’s
Marginal Cost
'
is the Producer sSurplus.
p'Variable Cost of producing
fy’ units is the sum of themarginal costs
y (output units)y'
© 2010 W. W. Norton & Company, Inc. 81
Benefit Cost AnalysisBenefit-Cost Analysis
Can we measure in money units the net gain or loss caused by a marketnet gain, or loss, caused by a market intervention; e.g., the imposition or the removal of a market regulation?the removal of a market regulation?
Yes, by using measures such as the y gConsumer’s Surplus and the Producer’s Surplus.Producer s Surplus.
© 2010 W. W. Norton & Company, Inc. 82
Benefit-Cost AnalysisyPrice The free-market equilibrium
Supply
p0
D d
QD QS
Demand
q© 2010 W. W. Norton & Company, Inc. 83
QD, QSq0
Benefit-Cost AnalysisyPrice The free-market equilibrium
and the gains from tradeSupply
and the gains from tradegenerated by it.
CSCSp0
PS
D d
PS
QD QS
Demand
q© 2010 W. W. Norton & Company, Inc. 84
QD, QSq0
Benefit-Cost AnalysisyPrice The gain from freely
trading the q th unitSupply
Consumer’s
trading the q1th unit.
CS
Consumer’sgain
CSp0
PS
D d
PS Producer’sgain
QD QS
Demand
g
© 2010 W. W. Norton & Company, Inc. 85
QD, QSq0q1
Benefit-Cost AnalysisyPrice The gains from freely
trading the units fromSupply
trading the units fromq1 to q0.
Consumer’s
CS
Consumer’sgains
CSp0
PS
D d
PS Producer’sgains
QD QS
Demand
g
© 2010 W. W. Norton & Company, Inc. 86
QD, QSq0q1
Benefit-Cost AnalysisyPrice The gains from freely
trading the units fromSupply
trading the units fromq1 to q0.
Consumer’s
CS
Consumer’sgains
CSp0
PS
D d
PS Producer’sgains
QD QS
Demand
g
© 2010 W. W. Norton & Company, Inc. 87
QD, QSq0q1
Benefit-Cost AnalysisyPrice
Consumer’sAny regulation that
CS
Consumer’sgains
causes the unitsfrom q1 to q0 to be
CSp0
PS
not traded destroysthese gains. This
PS Producer’sgains
loss is the net costof the regulation.
QD QSqq
g
© 2010 W. W. Norton & Company, Inc. 88
QD, QSq0q1
Benefit-Cost AnalysisyPrice An excise tax imposed at a rate of $t
t d d it d t th iper traded unit destroys these gains.
Deadweight
pbCS
gLoss
TaxRevenuet
PSps
QD QSqq© 2010 W. W. Norton & Company, Inc. 89
QD, QSq0q1
Benefit-Cost AnalysisyPrice An excise tax imposed at a rate of $t
t d d it d t th iper traded unit destroys these gains.
Deadweight So does a floor
pfCS
gLoss price set at pf
PS
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QD, QSq0q1
Benefit-Cost AnalysisyPrice An excise tax imposed at a rate of $t
t d d it d t th iper traded unit destroys these gains.
Deadweight So does a floorgLoss price set at pf,
a ceiling price setgat pcCS
pc PS
QD QSqq© 2010 W. W. Norton & Company, Inc. 91
QD, QSq0q1
Benefit-Cost AnalysisyPrice An excise tax imposed at a rate of $t
t d d it d t th iper traded unit destroys these gains.
Deadweight So does a floorgLoss price set at pf,
a ceiling price setpeCS
gat pc, and a rationscheme that
pc allows only q1units to be traded.PS
QD QSqq© 2010 W. W. Norton & Company, Inc. 92
QD, QSq0q1Revenue received by holders of ration coupons.