Public Economics - Lecture 4: Public goods and - Marc Sangnier
4 Public Goods
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Transcript of 4 Public Goods
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Public FinancePublic Goods
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After This Session You Would After This Session You Would
KnowKnowFea tures o f Public GoodsDetermining the Op timal Amoun t of Public GoodsPigou-Dal ton Approach to the Op timal Amoun t of Public GoodsFree Rider ProblemThe Priva tiza tion Deba te
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SOME USEFUL DEFINITIONSEXTERNALITIES exis t when consump tion or produc tiondecisions made by one agen t a ff ec t the u tility or produc tion a ttainable by ano ther agen t or agen ts throughsome channel o ther the marke t price. Ex ternali ties arealso re f erred to as third par ty e ff ec ts and spillover e ff ec ts.PUBLIC GOODS are goods tha t can be join tlyconsumed by a number o f consumers wi thou t reducingany one consumers abili ty to enjoy tha t consump tion.We already know tha t compe titive marke ts do no t alloca te true ex ternali ties and public goods e ff ec tively.In general, too li ttle o f public goods will be supplied bythe priva te marke t and too many nega tive ex ternali ties
will be produced by the priva te marke t.
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C harac teris tics o f Goods
Excludable v Nonexcludable Excludable preven ting anyone f rom consuming the
good is rela tively easy
Nonexcludable preven ting anyone f rom consumingthe good is ei ther very expensive or impossible
Rival v Nonrival Rival once provided, the addi tional resource cos t of
ano ther person consuming the good is posi tive Nonrival once provided, the addi tional resource cos t
of ano ther person consuming the good is zero
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Types o f Goods
EXCLUDABLE
RIVAL
YES NO
YES
NO
PRIV ATEGOODS
PUBLI CGOODS
C OMMONRESOUR C ES
N ATUR ALMONOPOLY
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FE ATURES OF PUBLI C
GOODSC onsump tion o f public goods by one member o f the socie ty does no t e ff ec t the supply o f thesame public goods f or consump tion by o ther members o f the socie ty.The consump tion o f public goods is no t excludable. Tha t is, even i f the provider wan ts,any member o f the socie ty can no t be excludedf rom the consump tion o f public goods or suchexclusion is too expensive to implemen t.
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FE ATURES OF PUBLI C
GOODS (Cont)Even though everyone consumes the samequan tity o f the good, there is no requiremen t tha t this consump tion be valued equally by all.C an have M C=0 and o ften nega tive M C .C lassi f ica tion as a public good is no t anabsolu te; i t depends on marke t condi tions andtechnology (impure public goods).A commodi ty can mee t only par t of the de f inition
of a public good no t the o ther.
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FE ATURES OF PUBLI C
GOODS (Cont)A number o f things tha t are no t conven tionally though t of as commodi tieshave public goods charac teris tics.Thurows law.Priva te goods are no t necessarily providedexclusively by the priva te sec tor.Public provision o f a good does no t necessarily mean tha t it is also producedby the public sec tor
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Some O ther Public Goods
Basic researchPrograms to f igh t pover ty
Unconges ted non toll roadsFireworks display
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1 0
DETERMINING THE OPTIM AL AMOUNT OFPUBLI C GOODS
Let us f irs t review how individuals demand de terminesthe marke t demand and de termine the op timal quan tityf or priva te goods.
P 1
D1
P 2
D2
P m
Dm
Q 1 =5 Q2= 2 Q m= Q 1 + Q2=7
S m
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DETERMINING THE OPTIM AL AMOUNT OFPUBLI C GOODS (cont)
That is, the aggrega te marke t demand isthe sum o f individuals demand f or apar ticular commodi ty.The marke t produces where the aggrega tedemand curve in tersec ts the marke t supply curve.
Individual consump tion level variesaccording to their respec tive u tility curve.
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DETERMINING THE OPTIM AL AMOUNT OFPUBLI C GOODS (cont)
However, in case o f public goods, sincethe consump tion is non-excludable, thequan tity o f consump tion f or eachconsumer will be the same.The u tility derived f rom each individualf rom the same amoun t o f consump tionwould be di ff eren t.In other word, every one will be willing topay di ff eren t prices f or the same level o f
consump tion.
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1 3
DETERMINING THE OPTIM AL AMOUNT OFPUBLI C GOODS (cont)
Ver tical summa tion f or publicgoods wi th f ixed level o f ou tpu t
P 1= 1 0
D1 D2
P m= P 1 + P 2= 1 5
Dm
Q 1 =5 Q2=5 Q m= Q 1 = Q2=5
S m
P 2=5
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E ff icien t Provision o f Priva te
GoodsPrice Adam
(Df
A)Eve
(Df
A)Ma rket (D
f
A+E)$11 5 1 6
$9 7 3 10
$7 9 5 14
$5 11 7 18
$3 13 9 22
$1 15 11 26
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0
1
2
3
4
5
6
7
8
9
10
11
12
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Df ADf E
Df A+E
S f
$
Quan tity o f Pizza
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Pare to E ff iciency Priva te
GoodsC
aseMRSf a = P f /P aSet P a = $ 1MRSf a = P f Df A shows MRS f a f or AdamDf E shows MRS f a f or EveSf shows MRT f aNecessary condi tion f or Pare to e ff iciency:MRS f a
Adam = MRS f a Eve = MRT f a
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E ff icien t Provision o f Public
Goods
Un its of F irew orks
1 2 3 4
Adam (D r A) $300 $250 $200 $150
Eve (D f E) 250 200 150 100
Ma rket(D f A+E)$550 $450 $350 $250
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0
50
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
1 2 3 4
Dr A
Dr E
Dr A+E
Sr
Quan tity o f Fireworks
$
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Pare to E ff iciency Public
GoodsC
aseMRSf a = P f /P aSet P a = $ 1MRSf a = P f Df
Ashows MRS f a f or AdamDf E shows MRS f a f or Eve
Sf shows MRT f aNecessary condi tion f or Pare to e ff iciency:MRS f a
Adam + MRS f a Eve = MRT f a
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2 0
PIGOU-D ALTON APPRO AC H TO THE OPTIM AL AMOUNT OF PUBLI C GOODS
Two Principles o f Alloca tive -Budge t Policy: Public expendi tures should be pushed to the
poin t where the sa tis f ac tion ob tained f rom thelas t taka expended is equal to the sa tis f ac tionlos t f rom the las t taka taken in taxes.
Resources should be dis tribu ted amongdiff eren t public uses so as to equalize themarginal re turn o f sa tis f ac tion f or each type o f ou tlay.
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2 1
PIGOU-D ALTON APPRO AC H TO THE OPTIM AL AMOUNT OF PUBLI C GOODS (cont.)
MU privateMU public
E
Z
MU tax
Q publicQ private
MU of a publicgood
MU of
a privategood
MU of taxpayment
Q
K J
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PIGOU-D ALTON APPRO AC H TO THE OPTIM AL AMOUNT OF PUBLI C GOODS (cont.)
MU privateMU public
E
Z
MU tax
Q publicQ private
MU of a publicgood
MU of
a privategood
MU of taxpayment
Q
K J
Equal Dis tance
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PIGOU-D ALTON APPRO AC H TO THE OPTIM AL AMOUNT OF PUBLI C GOODS (cont.)
At point Z: MU public > MU tax which would cause under alloca tion to public goods and over-alloca tion to priva tegoods.
At point J: MU public < MU tax would cause over alloca tion to public goods and under alloca tion to priva tegoods.At point E: MU public = MU tax would cause op timal in ter-sec tor alloca tion o f public and priva te goods
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FREE RIDER PROBLEM
Lets go back to the op timum public goods produc tion curvesIt is assumed here tha t bo th consumer 1 and 2 will reveal their real pre f erences to the public goods
P 1= 1 0
D1 D2
P m= P 1 + P 2= 1 5
Dm
Q 1 =5 Q2=5 Q m= Q 1 = Q2=5
S m
P 2=5
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2 5
FREE RIDER PROBLEM (cont)
But if consumer 2 hides his pre f erence thenthe en tire equilibrium changesC onsumer 2 can s till consume 3 uni t of public goods f or no price
P 1= 1 3
D1 D2
P m= P 1 + P 2= 1 3
Dm
Q 1 =3 Q2=3 Q m= Q 1 = Q2=3
S m
P 2=0
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2 6
FREE RIDER PROBLEM (cont)
Suppose tha t each o f 1 00 rich people arewilling to con tribu te Tk. 1 000 to build apublic highway- AS LONG AS ALL MAKETHE CONTRIBUTION.Assume tha t each member o f the richer group gains a bene f it o f 1 .5 paisa per takaspen t on the highway.If one person con tribu tes a takaindividually, the person would gain 1 .5 paisa bu t expend a taka. ( O f course, this
mo tiva tes f ree-rider s ta tus)
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2 7
FREE RIDER PROBLEM (cont)
But if each person con tribu tes a $ 1 thecollec tive gain is Tk. 1 * .0 1 5 * 1 00 = Tk. 1 .5 .So Tk. 1 000 dona ted by each o f the 1 00 rich people would collec tively yield a gainof = >Tk. 1 000 * 1 00 * Tk.1 .5 = Tk. 1 50 ,000
However, suppose one o f the rich peoplehide his weal th and abs tain f romcon tribu ting to the f und.
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2 8
FREE RIDER PROBLEM (cont)
If so then the to tal collec tive gain f or thesocie ty (since highway is no t excludable)would be= >Tk. 1 000 * 99 * Tk. 1 .5 = Tk. 1 4 8 ,500
However, the person, who couldsuccess f ully conceal his weal th, end upwith Tk. 1 4 8 ,500 wor th o f collec tive gainplus Tk. 1 ,000 which he would have tocon tribu te to the common f und.
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2 9
FREE RIDER PROBLEM (cont)
That is the person who is concealing isge tting Tk. 1 49, 500 of gain ins tead o f Tk.1 50 ,000 of gain.This brings up a cen tral ques tion to theproblem. As we can see, even the personwho is wi thholding his con tribu tion mayultima tely lose.However, the person who did con tribu tedTk. 1 000 is deprived f rom ge tting Tk.1 ,500 wor th o f bene f it because o f the
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FREE RIDER PROBLEM (cont)
Indeed, two main reasons why f ree rider problem exis ts are It is always di ff icul t to convince people tha t
though con tribu ting to public f unds mayseems to produce less re turn in the f irs t sigh t (a person would gain 1 .5 paisa by spending ataka) bu
tif
everyone contribu
tes
then i
twouldbring higher re turn; and
Since, i f no t every one con tribu te, the ac tualgain reduces subs tan tially, i t is impera tive to
ensure f ull par ticipa tion. This is ano ther
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Pre f erence Revela tion
MechanismsT Eve = MRT ra (MRS ra To tal MRS ra Eve )Eves choice: T Eve = MRS ra Eve
By subs titu tion:MRT ra (MRS ra To
tal MRS ra Eve ) = MRS ra Eve
Add (MRS ra
To tal
MRS raEve
)to bo
th sides:MRT ra = MRS ra To tal
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3 2
PRIV ATIZ ATION DEB ATE
As men tioned earlier, there exis ts manyins tances where public goods are providedpublicly. Examples o f such provision canbe: Priva te garbage collec tion by the dwellers o f a
mohalla or para
Priva te arbi tra tion arrangemen t by con trac tingpar ties to avoid li tiga tion time lag
Priva te primary schools and housingsocie ties, e tc. are providing so called meri t goods.
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PRIV ATIZ ATION DEB ATE (cont)
The deba te as to how much o f the public goodsshould be provided by priva te sec tor is growing.Here are some cri terions tha t can be used to f ind
the answer Rela tive wage and ma terials cos ts Adminis tra tive C os ts Diversi ty o f tas tes Dis tribu tional issues
C ommodi ty egali tarianism no tion tha t some commodi ties ough t to be made
available to everyone