eep101/econ 125 lecture 9 public goods david zilberman
TRANSCRIPT
Eep101/econ 125 lecture 9Public Goods
David Zilberman
Overview• Heterogeneity, Non-rivalry, and Market
Failure
• Non-excludability and Market Failure
• Optimal Provision with Homogeneous
Individuals
• Private Market Outcome for a Non-
excludable Public Goods
• Mechanisms for Providing the Socially
Optimal Level of Public Goods
• The Specification of Congestion Costs in
Public Goods Models
Public goods are goods or services that
can be consumed by several individuals
simultaneously
Non-rivalry-Multiple individuals can
consume the same good without diminishing
its value.
Non-excludability, an individual cannot
be prevented from consuming the good .
Examples, fresh air, a public park, a
beautiful view, national defense .
Original demand-1P
Q
Demand of one individualAnd the supply
Q1
D=a-bQMC=c-dQ
Q1 =a−cb+d
D1
Horizontal demand -2P
Q
Demand of one individualAnd the supply
Q1
D2H=a-Qb/2MC=c-dQ
Q2H =a−c
.5b+d
D1
Q2
Horizontal demand -large NP
Q
Demand of one individualAnd the supply
Q1
DINH=a-Qb/NMC=c-dQ
QNH =a−c
1 / Nb+d
DH1
DHN
DH2
Q2 QN
Vertical aggregation-2P
Q
Demand of two individualsAnd the supply
Q1
D2=2a-2bQMC=c-dQ
Q1 =2a−c2b+d
D1
D2
Q2
Vertical aggregation-3P
Q
Demand of three individualsAnd the supply
Q1
D3=3a-3bQMC=c-dQ
Q1 =3a−c3b+d
D1
D2
Q2
D3
Q3
Vertical vs horizontal aggregation
Horizontal demand lead to infinitely elastic demand at P=a. Vertical leads to infinitely in-ealstic at Q=a/b
Vertical aggregation is used to find demand for public goods
As the population increases the demand becomes more inelastic.
The demand becomes Dn=na-nb The equilibrium quantity is When there are infinite individuals the quantity
demanded is equal to b/a and the demand is inelastic
Qn=na−cnb−d
Provision of public goods Free riding- most people will wait that others will
pay for the public and then they will free ride One justification for government intervention is
provision of public goods Bigger communities will have larger public good
provision
Dn
D2n
Qn Q2no
v1v2 s2s1
The cost to community with n peoplev1s1QnoThe cost to community with2n peoplev2s2Q2no
Provision mechanism Public provision by taxes Donations, fund raising( nature conservancy) Volunteer activity( duck unlimited,Siera club) Tax deduction-for contribution to public good
generating organizations Advertisement and naming (TV,concert hall) Special institutions-
The church Army Art patron (giving back to the community)
Non rivalry with excludability
If access to a good with non rivalry is possible it can be provided privately
First by a monopoly- the entry fee aoc will capture all the surplus but outcome is efficient
MC
Dn
D1
Qn
a
oc
Alternative mechanism -gov’t provision fee cover costs Fee in the area OMQn/N Consumer surplus SMO
MC
Dn
D1
Qn
a
Oc
M
S
A third mechanism-concessionaire earns competitive profit Fee in the area RMQnO/N Consumer surplus SMR Producers surplus RMO
MC
Dn
D1
Qn
a
Oc
M
S
R
Column3 Column4a=demand intercept
b=demadn slope
c =Mc intercewpt
D=mc slope Column1
10 1 4 2
Number
of quanitymonopoly price
cost covering price
concessionaire price
social surplus
1.00 2.00 18.00 12.00 16.00 6.00
2.00 4.00 32.00 16.00 24.00 32.00
3.00 5.20 38.48 15.95 24.96 67.60
4.00 6.00 42.00 15.00 24.00 108.00
5.00 6.57 44.12 13.89 22.53 151.14
6.00 7.00 45.50 12.83 21.00 196.00
7.00 7.33 46.44 11.87 19.56 242.00
8 7.60 47.12 11.02 18.24 288.80
Simulation a good with non rivalry and excludability
Heterogeneity of preferences
Dless
Dmore
MC1
MC2
G
A and C optimal outcomes when only buyers that like the product more intensively are purchasing tickets. The price of ticket under monopoly are AOQcC and AOQGGC
A
QcOQG
Heterogeneity of preferences
Dless
Dmore
DtotalMC1
MC2
G
B
G and B optimal outcomes
In case of public good if marginal cost are high the benefits of the less interested group are important for determining the optimal outcome (Point G)
C
A
QcO Qb
Heterogeneity of preferences
Dless
Dmore
DtotalMC1
MC2
G
B
In case of excludabilityMonopoly will provide optimal outcome at G but will charge AGLO as entry fee so that half the population will be excluded
IN case of MC1 the monopoly will offer Qc
C
A
QcO Qb L
Example Two equal sized groups
Dmore =20-X Dless -10-X Joint demand
P =30-2X for X<10 =20-X for 20>X>10
Case 1:MC=.5X
• What is Optimal X* • Try 30-2X=.5X (point A)• X=12 is not feasible• Try 20-X (point B)• =.5X socially• optimal X=20/1.5=13.33• Fee by monopoly• 26.66*13.33/2=311 A B
Case 2 :MC=2X To find optimal X solve 30-2X=2X Optimal X=7.5 Benfits for people who like the product (20+20-7.5)*7.5/2=121.75 People who like less 12.5*7.5/2=46.675 Monopoly ignores second group. solves 20-X=X Optimal policy monopoly for the rich X=6.666 Fee $111 Alternative 1 regulated concessionaire providing
7.5 units for 46.675-income 93.35 Cost 56.25 Alternative 2 pay equals to cost divided by buyers
Excludability with heterogeneity
Differentiated provision- people pay different fees for different products
Exclusive vs public beach Hunting licenses Different housing accommodations in
national parks Allow to raise fund and pay and address
equity considerations
public good when part of the public does not care
2 groups-one does not care for D1=10-X D2=0 MC=X Should government provide public good? In this case the groups that like the product
may provide it through collective action-clubs Optimal X=5 Costs 25/2= 12.5/N will be paid by users
Clubs:Optimal size Benefits depend on amenity size X and
number of users N B(N,X) Cost increases with X Optimality problem Optimal decision rules
MAX
X,NNB(N .X) −c(X)
N∂B(N.X)∂X
−∂c(X)∂X
=0
B(N.X) +N∂B(N.X)
∂N=0
NMB=MCMarginal benefits of size=Marginal cost of congestion
Case 2 MC=2X30-2X=2XOptimal X=7.5Benfits for people who like the product(20+20-7.5)*7.5/2=178.125Peole who like less12.5*7.5/2=46.675Optimal policy monopoly for the rich X=6.666
Case 3Dmore 30-XMC=4XOptimal policy in X=8Monopoly price to more52*8/2=208Monopoly price to less12*8/2=48In this case the monopolywill solve30-X=4XX=6 and charge 54*6/2=162Which means under provisionOf public good