4 Public Goods

8/8/2019 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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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

Documents

4 Public Goods