Transcript Private Provision of Public Goods

Chapter 7
Public Goods
Public Finance and Public Policy
Author: Jonathan Gruber
Instructor: Yigang Zhang
Introduction
 Some markets do not work very well because the
good in question has public good characteristics to it.
 For example, in Dhaka, Bangladesh, public trash
collection is fairly inefficient, but attempts at
privatization have not fared any better.
 The key problem with private collection of garbage
is the free rider problem–with a private, voluntary
system, each resident could simply sneak his garbage
into his neighbor’s garbage and avoid making
payments.
Introduction
 Eventually, everyone would figure this out, and no
one would be willing to pay trash collection
voluntarily.
 In fact, most residents have figured out the
incentive to “free ride.” Only 50 of 1,100
neighborhoods have private garbage collection,
however.
Introduction
 This lesson explores the role of government in
providing goods like this, and shows that the private
sector tends to underprovide them.
 It also explores the notion of “crowd-out” where
public provision simply substitutes for already
existing private provision of a good.
 Reminder of the village commune system in China
prior to economic reform in 1978
Introduction
 The role of public goods is important in economics.
The subsequent lessons explore issues related to:




Cost-benefit analysis (opportunity cost, PDV)
Political economy (government failure)
State and local government (small states advantage)
Case Study: Education
OPTIMAL PROVISION OF PUBLIC
GOODS
 Pure public goods have two traits:


They are non-rival in consumption: My consuming
or making use of the good does not in any way affect
your opportunity to consume the good.
They are non-excludable: Even if I want to deny
you the opportunity to consume or access the public
good, there is no way I can do so.
 Table 1 gives some examples.
If a Ice
good
Icecream
cream
is both
isisrival,
rival
also and
because
excludable,
excludable,
This
my
Cable
Some
It is
table
excludable,
TV
goods
shows
is non-rival,
are
examples
since
“impure”
because
theof
public
cable
pure
my
consumption
because
aofprivate
simply
it precludes
good.
not share
you
public
company
goods
from
myconsumption
goods,
because
canimpure
simply
they
of itpublic
refuse
are
in no
non-rival,
way
goods,
to hook
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goods
asame
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non-excludable,
defense
public
goods
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ice cream.
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the
good
rival
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use the same sidewalk. protection does not diminish your
Yesconsumption of it.
No
Yes
Is the good
excludable? No
Ice cream, Cookies
Cable TV, Wifi
Crowded city sidewalk
National defense,
Light houses,
Firework
OPTIMAL PROVISION OF PUBLIC
GOODS
 It is helpful to think of public goods as goods with a
large, positive externality.
Optimal Provision of Private Goods
 Consider a private good, like ice cream.
 Figure 1 shows the market for ice cream cones,
assuming that the alternative use of the money is
buying cookies at $1 each.
 This makes cookies the numeraire good.
Adding
up
Ben’s
and
Jerry’s
At a price
Ben
ofhas
$3,
an
neither
individual,
person
Adding
up
Ben’s
and
Jerry’s
S=SMC
individual
demands
at
each
demands
downward-sloping
ice
cream.
demand
individual
demands
give
Jerry
alsomuch
has an
individual,
price
givesforsociety’s
demand.
curve
ice
cream.
society’s
demand
at $3.
downward-sloping
demand
curve
for ice
cream.
At a price
of Adding
$2,
Leading
bothup
people
to
Ben’s
a competitive
and Jerry’s
demand more
equilibrium
individual
ice cream.
atdemands
$2. Ben give
& Jerry
consume
society’s
different
demand
quantities.
at $2.
There
is a market supply curve
Price
of ice
cream
$3
associated with producing ice
cream.
$2
DJERRY
0
Figure 1
QJERRY QBEN QTOTAL
Demand for a private good
DBEN
SMB =DBEN+JERRY
Quantity
of ice
cream
Optimal Provision of Private Goods
 In this figure, as price adjusted, each person
changed his quantity consumed.
 For a private good, consumers demand different quantities
at the same market price.
Optimal Provision of Private Goods
 We can also represent this relationship
mathematically. Ben has preferences over cookies
(C) and ice cream (IC):
U B C, IC
 As does Jerry:
U J C, IC
Optimal Provision of Private Goods
 Utility maximization requires that each of their
indifference curves is tangent to the budget
constraint. For Ben, we have:
B
MU IC
PIC
B

MRS

IC ,C
MU CB
PC
 For Jerry we have:
MU ICJ
PIC
J
 MRS IC ,C 
J
MU C
PC
Optimal Provision of Private Goods
 Recall that in equilibrium, the price of ice cream is
$2, and the price of cookies is $1 (because it is the
numeraire good).
 In equilibrium each person must be indifferent
between trading two cookies to get one ice cream.
Optimal Provision of Private Goods
 On the supply side, ice cream cones are produced
until the marginal cost equals the marginal benefit,
which equals the price in a competitive market.
MC IC  PIC
 Recall that PC=$1, meaning:
MRS
B
IC ,C
 MRS
J
IC ,C
 PIC  MCIC
Optimal Provision of Private Goods
 The private market equilibrium in this case is
socially efficient.
 The MRS for any quantity of ice cream equals the
SMB of that quantity–the marginal value to society
equals the marginal value to any individual in the
perfectly competitive market.
Optimal Provision of Public Goods
 Now consider the tradeoff between a public good,
like missiles, and a private good like cookies.
 Figure 2 shows the market for missiles, assuming
that the alternative use of the money is buying
cookies at $1 each.
Price of
missiles
$6
$4
$3
Adding
Adding
up Ben’s
up Ben’s
andand
Jerry’s
Jerry’s
willingness
willingnesstoto
pay
paygives
for each
society’s
quantitydemand
gives society’s
for 1 missile.
demand.
As does Jerry.
There is a market supply curve
Leading to a competitive
associated
with and
producing
Adding
up Ben’s
Jerry’s
equilibrium at 5 missiles.
Ben & tomissiles
willingness
pay gives society’s
Ben hasJerry
a downward
consumesloping
the same
Q.
demand
While
Ben’s
Jerry’s
willingness
willingness
to pay for
to
pay
the for the 5th missile.
S=SMC
demand
curve
for
missiles.
DJERRY
for the
firstfirst
missile
missile
is $2.
is $4.
While
Ben’s Jerry’s
willingness
willingness
to pay for
to pay
the
for the
fifthfifth
missile
missile
is $1.
is $2.
SMB=DBEN+JERRY
$2
$2
DBEN
$1
0
Figure 2
1
5
Demand for a public good
Quantity of
missiles
Optimal Provision of Public Goods
 Unlike the case of private goods, where aggregate
demand is found by summing the individual
demands horizontally, with public goods, aggregate
demand is found by summing vertically.
 That is, holding quantity fixed, what is each person’s
willingness to pay?
Optimal Provision of Public Goods
 We can also represent this relationship
mathematically. Ben has preferences over cookies
(C) and missiles (M):
U B C, M 
 As does Jerry:
U J C, M 
Optimal Provision of Public Goods
 To Ben, the marginal missile is worth:
MU MB
B

MRS
M ,C
MU CB
 For Jerry, the marginal missile is worth:
MU MJ
J

MRS
M ,C
MU CJ
Optimal Provision of Public Goods
 The social marginal benefit (SMB) of the next
missile is the sum of Ben and Jerry’s marginal rates
of substitution:
 MRS
i
M ,C
i
 Where “i” represents each person in society.
Optimal Provision of Public Goods
 The social marginal cost (SMC) is the same as
earlier: the marginal cost of producing a missile:
MC M
 Efficiency therefore requires:
 MRS
i
i
M ,C
 MC M
Optimal Provision of Public Goods
 That is, social efficiency is maximized when the
marginal costs are set equal to the sum of the
marginal rates of substitution (rather than each
individual’s MRS).
 This is because the good is non-rival. Since a unit can
be consumed by all consumers, society would like
the producer to take into account all consumers’
preferences.
PRIVATE PROVISION OF PUBLIC
GOODS:
Private-sector Underprovision
 In general, the private sector underprovides public goods
because of the free rider problem.
 Consider two people, Ben and Jerry, and two
consumption goods, ice cream and fireworks.
 Set the prices of each good at $1, but fireworks are a
public good. Assume that Ben and Jerry have
identical preferences.
Private-sector Underprovision
 Ben and Jerry benefit equally from a firework that is
provided by either of them.

What matters is the total amount of fireworks.
 Each person chooses combinations of ice cream and
fireworks in which his own MRS equals the ratio of
price.
Private-sector Underprovision
 For both Ben and Jerry, they set:
MRS F , IC  1, MU IC  MU F
 Whereas optimal provision requires:
 MRS
i
i
F , IC
1
Private-sector Underprovision
 With identical preferences:
 MU F 
MU IC
2
  1, MU F 
2
 MU IC 
 Recall that marginal utilities diminish with increasing
consumption of a good.
 In this example, optimal provision would require
that fireworks are consumed until their utility equals
half the marginal utility of ice cream.
 Thus, each individually buys too much ice cream
privately.
The Free Rider Problem in Practice
 There are some interesting examples of the free-
rider problem in practice.


Only 7.5% of public radio listeners in New York
contribute to the stations–that is, there is a lot of
free-riding. In the United Kingdom, the BBC
charges an annual licensing fee for all television
owners.
Many users of file sharing services never contribute
uploaded files; they only download files. Some of
these services, like Kazaa, give download priority to
those who contribute.
When Is Private Provision Likely to Overcome
the Free Rider Problem?
 While the free-rider problem clearly exists, there are
also examples where the private market is able to
overcome this problem to some extent.
 But the private market may still fall short of the
socially optimal amount.
Can Private Providers Overcome the Free Rider
Problem?
 Examples of private provision of a public good:


Privately financed fireworks displays.
Privately owned British lighthouses until 1842.
Business Improvement Districts
 A final example concerns business improvement districts (BID).
 The quality of city streets is a public good.
 During the 1980s, New York City’s Times Square had high
crime and many social problems. The city had given up on
cleaning up Times Square.
 In 1992, local businessmen started a BID–a legal entity to
provide security and sanitation, with fees collected from local
businesses.
 New York law makes participation of businesses compulsory
if BID organizers can get 60% of local businesses to join,
allowing the organizers to overcome the free-rider problem.
 The BID was a clear success in New York City.
Business Improvement Districts
 On the other hand, Massachusetts law allows
businesses to “opt-out” of a BID within 30 days of
the BID approval by the local government.
 This deters formation of BIDs in the first place,
because there are fixed costs of doing so.
 As a consequence, only 2 BIDs have been formed in
Massachusetts.
When Is Private Provision Likely to Overcome the
Free Rider Problem?
 Under what circumstances are private market forces
likely to solve the free rider problem?



Intense preferences.
Altruism.
Utility from one’s own contribution to the public
good.
Some individuals care more than others
 When some individuals have especially high demand
for a public good, private provision may emerge
(but not necessarily provide efficiently).
 The key intuition is that the decision to provide a
public good is a function of the enjoyment that the
individual gets from the total amount of the public
good, net of cost.

If a person gets a lot of enjoyment, or has a lot of
money, he will choose to purchase more of the
public good even though it benefits others.
Some individuals care more than others
 Olson and Zeckhauser (1966) studied the financing
of NATO, which was a voluntary organization at
the time.

Although countries had an incentive to free-ride on
the contributions of others, the largest nations (such
as the United States) did contribute.
 Higher incomes or stronger tastes can mitigate the
free rider problem to some extent, but are unlikely
to solve it completely. Thus, underprovision is still
likely to occur.
Altruism
 Another reason is that there is evidence that many
individuals are altruistic, caring about the outcomes
of others as well as themselves.
Altruism
 Laboratory experiments are becoming more popular
in the economics profession.
 Some experiments examine the incentive for college
students to contribute to a pool of money, where
the dominant, self-interested strategy should be to
not contribute.
 The experiments suggest that between 30% and
70% of participants contribute to the public good.

As the experiment is repeated in multiple rounds,
contributions fall, but rarely reach zero
contributions.
Private Provision of Public Goods:
When is private provision likely to overcome the
free rider problem ?
 Of course, these experiments may be of limited
applicability to the real world:



Individuals may behave differently in a contrived
laboratory setting.
The stakes are often small, so the cost of being
altruistic is low.
College undergraduates may not be representative of
the population more generally.
Private Provision of Public Goods:
When is private provision likely to overcome the
free rider problem?
 On the other hand, some real-world evidence is
consistent with altruism in private support of public
goods.

Brunner (1998) found that the number of public
radio listeners who contribute decreases only
modestly as the total number of listeners increases.
Warm glow
 A final reason is that that individuals may provide
for a public good is due to warm glow.
 The warm glow model is a model of public good
provision in which individuals care about both the
total amount of the public good and their particular
contributions as well.
 For example, they may get some psychological
benefit from knowing they helped a worthy cause.
 In this case, the public good becomes more like a
private good, though it does not fully solve the
underprovision problems.
PUBLIC PROVISION OF PUBLIC
GOODS
 In principle, the government could solve the optimal
public goods provision problem and then either
provide the good directly or mandate individuals to
provide the amount.
 In practice, three problems emerge:



Crowd-out.
Measuring costs and benefits.
Determining the public’s preferences.
Private Responses to Public Provision:
The Problem of Crowd-Out
 In some cases, the private market may already be
providing a socially inefficient level of the private
good.
 In this case, public provision may crowd-out some
of the private provision–as the government provides
more of the public good, the private sector provides
less.
Private Responses to Public Provision:
The Problem of Crowd-Out
 For example, in the fireworks example with Ben and
Jerry, if one assumes:



Ben and Jerry care only about the total number of
fireworks provided.
Government provision will be financed by charging
equal amounts to each of them.
And the government provides no more fireworks
than were being provided privately beforehand.
 Then each dollar of public provision will crowd out
private provision one-for-one.
Private Responses to Public Provision:
The Problem of Crowd-Out
 The full crowd-out in the fireworks example is rare,
though partial crowd-out is much more common
and can occur when:


People who don’t contribute to the public good are
taxed to finance its provision.
Or when individuals derive utility from their
individual contributions as well as the total amount
of the public good provided.
Private Responses to Public Provision:
The Problem of Crowd-Out
 If noncontributors are forced to help pay for the
good (but it is still below the social optimum), then
the contributors’ effective income levels are higher
than before.
 As a result of this income effect, contributors buy
more if the public good is a normal good, offsetting
the crowd-out to some extent.
Private Responses to Public Provision:
The Problem of Crowd-Out
 Alternatively, as discussed previously, there may not
be full crowd-out if an individual cares about his
own contributions (the warm glow model).
 In this case, an increase in government
contributions will not fully crowd out giving.
Public Provision of Public Goods:
Measuring the costs and benefits of public goods
 Another problem for government provision is
measuring costs and benefits of the public good.
This entails the field of cost-benefit analysis, discussed
in the next lesson.
 For example, improving a highway involves
valuations of commuting time saved as well reduced
traffic fatalities.
How Can We Measure Preferences for the
Public Good?
 Finally, our model of optimal public good provision
assumes the government knows each person’s
preferences over public and private goods.
 In practice, this runs into problems with preference
revelation, preference knowledge, and preference
aggregation.
 These issues are addressed in the field of political
economy.
Recap of Public Goods
 Optimal provision of public goods
 Private provision
 Public provision
 Questions on page 200 and 201 (#3, #11, etc.)