Chapter 4:

Public Goods

Econ 330: Public FinanceDr. Reyadh Faras

Definition of A Public Good Once it is provided, the additional resource cost

of another person consuming the good is zero, which means that consumption is nonrival.

To prevent anyone from consuming the good is either very expensive or impossible, which means that consumption is nonexcludable.

In contrast, consumption of a private good is rival and excludable.

Impure public good is a good that satisfies either condition.

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Even though everyone consumes the same quantity of the good, consumption is not valued equally by all.

Classification as a public good depends on market conditions and the state of technology.

Private goods are not necessarily provided exclusively by the private sector.

Public goods are not necessarily provided exclusively by the public sector.

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Types of Goods

EXCLUDABLE

RIVAL

YES NO

YES

NO

PRIVATEGOODS

PUBLICGOODS

COMMON RESOURCES

NATURALMONOPOLY

Efficient ProvisionPrivate Goods Market demand is a horizontal summation of quantities

consumed by all consumers. Equilibrium is reached where supply equals demand at

quantity ____ and price _____ . Adam consumes _____ units and Eve consumes ____

units. Note that there consumption does not have to be equal,

why? At equilibrium, resource allocation is pareto efficient:

A utility maximizing individual sets the marginal rateof substitution of the two goods equal to the price ratioof the two goods:  MRSfa = Pf / Pa

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Efficient Provision of Private GoodsPrice Adam

(DfA)

Eve (DfA) Market

(DfA+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

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 26

DfADf

E

DfA+E

Sf

$

Quantity of Pizza

 

Set Pa= $1, this reduces the condition to:

MRSfa = Pf

Adam and Eve both set MRS = ____

Producers set the marginal rate of transformation

MRTfa  = ____

At equilibrium, MRSAfa = MRSE

fa = MRTfa , which is

the condition for pareto efficiency.

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A. Deriving the Efficiency Contribution

Public Goods Assume Adam and Eve watch a firework show

consists of 19 rockets and each extra rocket costs $5.

Adam is willing to pay $6 for the extra rocket, while Eve is willing to pay $4.

Question, is it efficient to expand the size of the show by one extra rocket?

Answer, we need to compare the marginal ________ to the marginal ________.

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Efficient Provision of Public Goods

Units of Fireworks

1 2 3 4

Adam (DrA) $300 $250 $200 $150

Eve (DfE) 250 200 150 100

Market(Df

A+E)$550 $450 $350 $250

050100

150200250300350400

450500550600650

700750800

1 2 3 4

DrA

DrE

DrA+E

Sr

Quantity of Fireworks

$

Because consumption is nonrival, the 20th rocket isconsumed by both.

Hence, the marginal benefit of the 20th rocket is thesum of what they are willing to pay, which is $____.

Because the marginal cost is $5, it is worthy toconsume the 20th rocket.

Generally: if the sum of individuals' willingness topay for an additional unit of a public good exceeds itsmarginal cost, efficiency requires that the unit bepurchased; otherwise it should not.

Efficiency requires that provision of a public good beexpanded until reaching the level at which the sum of eachperson's marginal valuation on the last unit just equals themarginal cost.

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Efficiency is reached at the point where Adam's and

Eve's willingness to pay for an additional unit just

equals the marginal cost of producing a unit. Graphically, the marginal cost schedule, S, is

superimposed on the group willingness to pay

curve, DA+E. The intersection occurs at quantity 45 and marginal

cost $6. At equilibrium, MRSA

ra + MRSEra = MRTra , which is

the condition for pareto efficiency. For a public good, market demand is found by vertical

summation of individual demand curves.13

Note: For a private good, everyone has the same MRS, but

people can consume different quantities. Therefore, demands are summed horizontally over the

differing quantities.  Individuals see the same price and then decide what

quantity they want.  For a public good, everyone consumes the same

quantity, but people can have different MRS.  Therefore, vertical summation of quantities is

required to find the group willingness to pay.

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Everyone sees the same quantity and then decide what price they are willing to pay.

Problem: People have incentives to hide their true preferences for public good in order not to pay for it.

This is called the free rider problem, which results in a shortage in the supply of public goods (below the efficient amount).

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Solution: suppose 1) each person's demand curve is known, and 2) transferability of the good to another person is impossible, then each person is charged a price based on its willingness to pay, this is called perfect price discrimination.

Conclusion:

Since knowledge of individual preferences is impossible, private provision leads to inefficiency (even if a nonrival good is excludable).

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B. The Free Rider Problem

Some suggest as a solution to the free rider problem that the government provides the public good.

The government is able to find everyone's preference and then use its coercive power to force everyone to pay.

Free ridership is based on the hypothesis that people maximize a utility function that depends only on their own consumption.

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The Privatization Debate

Definition: Privatization means taking services that are supplied by the government and turning them over to the private sector for provision and/or production.

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A. Public Versus Private Provision

Some services provided by publicly provided goods can be obtained privately.

Examples: Protection (private policemen are 3 times public ones) and dispute settlement (40,000 cases are solved privately).

Historically, in the 17th century many services were provided privately, than now.

However, recent trends are towards private provisions in many communities.

What is the right mix of public and private provision? What criteria used to select inputs?

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There are several considerations:1. Relative wage and materials costs: the less

expensive sector is preferred on efficiency grounds.

2. Administrative costs: under public provision, fixed administrative costs are spread over a large group of people.

3. Diversity of Tastes: with diversity, private provision is more efficient because consumption can be fitted into tastes.

4. Distributional issues: community's notion of fairness requires the availability of some goods to everyone.

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B. Public Versus Private Production

Even with the agreement of providing goods publicly,disagreement may arise over whether they should beproduced publicly or privately.

This is due to differences regarding:1) the role of government in the economy.2) the relative costs of public and private production.

Little systematic evidence exists on the costdifferences between private and public productionbecause of differences in quality of services providedby each.

Opponents of privatization argue that privatecontractors produce inferior goods.

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Response:

1) The government writes a contract that specifies the level of desired quality,

2) Consumers switch to better quality producers,

3) Reputation makes private producers worry about quality in order to get future contracts.

4) Market environment matters. For example, a privately owned monopoly may produce inefficiently, while a public producer facing a lot of competition may produce efficiently.

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