Chapter 7: Public Goods PUBLIC GOODS

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.

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use the same sidewalk. proItesctiotnhdeoesgnootoddiminrisihvyaolurin ccoonsnusmuptimon poftiti. on?

Yes

No

Yes

Ice cream

Cable tv

Is the good No

excludable

?

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.

1

Price of ice cream

$3

$2

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S=SMC

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demand meoqrueinilidcbierviiudcmrueaalmtd$e.2m. aBnedns g&ivJeerry

conssoucmietey'dsifdfeermenaTtnhqdeuaraetn$tisi2ti.easm. arket supply curve

associated with producing ice

cream.

DJERRY 0 QJERRY QBEN QTOTAL

DBEN

Figure 1 Demand for a private good

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:

MU

B IC

MUCB

= MRSIBC,C

=

PIC PC

=

MCIC MCC

For Jerry we have:

MU

J IC

MU

J C

= MRSIJC,C

=

PIC PC

=

MCIC 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.

2

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 $$22 $1

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There is a market supply curve

Leading to a competiAtivadesdsinogciautpedBewni'tsh apnroddJuecrirnyg's

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for tfhifethfimfthismsiliessisile$1is. $2.

DBEN

SMB=DBEN+JERRY

0

1

5

Figure 2 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

To Ben, the marginal missile is worth

( ) MU

B M

MU

B C

=

MRS

B M

,C

Jerry's preferences are U J C, M

To Jerry, the marginal missile is worth

MU

J M

MU

J C

=

MRS

J M

,C

3

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

where "i" represents eaich person in society.

Efficiency requires

i

M

RS

i M

,C

=

MCM MCC

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.

For both Ben and Jerry, they set:

MRS F,IC = 1, MU IC = MU F

Whereas optimal provision requires:

MRS

i F

,

IC

=1

i

4

Private-sector Underprovision

With identical preferences, the optimal condition is:

2

MU F MU IC

= 1,

which

implies

MU F

=

MU IC 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

There are some interesting examples of the freerider problem in practice.

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?

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 ? 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.

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.

5

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