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Chapter 7: Public Goods

Outline

Optimal provision of public goods.




Under-provision generally characterizes markets with
public goods, absent government intervention.
Private sector provision.
Crowd out
Problems
OPTIMAL PROVISION OF
PUBLIC GOODS

Pure public goods have two traits:



They are non-rival in consumption: The marginal
cost of another person consuming the good is zero,
and does not affect your opportunity to consume
the good.
They are non-excludable: There is no way to deny
someone the opportunity to consume the good.
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
Table
1 it Iiscan
Yet
For
Other
itexample,
is non-excludable
goods
asame
are
crowded
“impure”
because
sidewalk
public
Finally,
It The
itis
National
is
isalso
pure
non-excludable,
defense
public
goods
is a classic
because
are both
consuming
icethe
cream
with
iceyou.
cream.
diminishes
but
they
and
upare
private
the
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(to
system.
some
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extent)
goods
rival
clearly
because
because
very
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your
are
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but
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not
an area
It is
and
isnon-rival
protected,
non-excludable.
because
everyone
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Defining
and
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goods
only
way
for
you
topure
consume
itexample.
isisnon-rival
toimpure
excludable.
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reduced
asfrom
excludable.
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pedestrians
the sidewalk.
also
consumption
“consumes”ofthat
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protection.
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make
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doesgood
not diminish
yourin
Is the
rival
consumption of it.
consumption?
Yes
Is the
No
good
excludable
?
Yes
No
Ice cream
Cable tv
Crowded city
sidewalk
National defense
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.
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. Moreover, suppliers set
P=MC. For Ben, we have:
B
MU IC
MU CB

B
 MRS IC
,C 
PIC MCIC

PC
MCC
For Jerry we have:
J
MU IC
MU CJ

J
MRS IC
,C
PIC MCIC


PC
MCC
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
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
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

To Ben, the marginal missile is worth
MU MB
B

MRS
M ,C
MU CB

Jerry’s preferences are


U J C, M 
To Jerry, the marginal missile is worth
MU MJ
J

MRS
M ,C
MU CJ

Optimal Provision of Public Goods
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The social marginal benefit (SMB) of the
next missile is the sum of Ben and Jerry’s
i
MRS
marginal rates of substitution:

M ,C


i
where “i” represents each person in society.
Efficiency requires

i
i
MRSM
,C
MCM

MCC
Optimal Provision of Public Goods
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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
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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
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Ben and Jerry benefit equally from a firework that is
provided by either of them.
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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.
For both Ben and Jerry, they set:
MRS F , IC  1, MU IC  MU F

Whereas optimal provision requires:  MRS Fi , IC  1
i
Private-sector Underprovision

With identical preferences, the optimal condition is:
 MU F
2
 MU IC




MU IC

1,
which
implies
MU


F
2

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
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There are some interesting examples of the freerider problem in practice.
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Only 7.5% of public radio listeners in New York
contribute to the stations–that is, there is a lot of freeriding. 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?
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Under what circumstances are private market
forces likely to solve the free rider problem?
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Intense preferences.
Altruism.
Utility from one’s own contribution to the public
good.
Some individuals care more than others
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When some individuals have especially high demand
for a public good, private provision may emerge
(but not necessarily provide efficiently – in
particular, the public good is still likely to be
underprovided).
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.
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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.
Altruism and Warm Glow
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A second reason is that there is evidence that many
individuals are altruistic, caring about the outcomes of
others as well as themselves.
A third reason is that that individuals may provide for a
public good is due to warm glow.
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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 also does not fully solve the underprovision problems.
PUBLIC PROVISION OF PUBLIC
GOODS
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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:
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Crowd-out.
Measuring costs and benefits.
Determining the public’s preferences.
Private Responses to Public Provision:
The Problem of Crowd-Out
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
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:
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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:
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
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
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
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
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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
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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?
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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.