lec04
TRANSCRIPT
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Public Economics
Chikako YamauchiGRIPS
Lecture 4
Public Goods
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Outline
1. Definition of Public Goods2. Efficient Provision of Private
Goods3. Efficient Provision of Public Goods4. Numerical Example5. Problems in Achieving Efficiency
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1. Definition of Public Goods
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Introduction What is the difference between pizza and
national defense? two people cant consume a pizza simultaneously a person can be excluded from eating pizza
but consumption of national defense by one person does not diminish the consumption by another person
its difficult to exclude someone from consuming national defense
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Definition of pure public good1. Consumption of a public good is nonrival
Once provided, the additional resource cost of another person consuming the good is zero.
2. Consumption of a public good is nonexcludable
preventing someone from consuming the good is either very expensive or impossible
Impure public goods: some characteristics of a public good
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Examples Pure public goods
National defense Clean air House cleaning in an apartment with many roommates
Private goods Pizza Medical and health service Public housing
Impure public goods Lighthouse A scenic view
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Pureness of public goods depend on state of technology
Lighthouse Nonrival: once the beacon is lit, one ship can take
advantage of it without impinging on another ships ability to do the same
Nonexcludable: no particular vessel can be excluded from taking advantage of the signal
Light house disturbed by new technology: a jamming device Excludable: unless you have obtain a special
receiver, you cannot receive the signal from lighthouse
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Pureness of public goods depend on market condition & legal setting
A scenic view Pure public good when there are few people
(number of consumers is small) But increased usage (number of consumers is
larger) leads to congestion and decreased quality, so it becomes a rival good
If new technology and law allow charging entry fee, it will become an excludable good
Other examples like this include major roads and firework watching
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People may value public goods differently
even though everyone consumes the same quantity of a public good, they do not necessarily value it equally Ex. Missile defense: some may have a
negative valuation if they think it makes the world more dangerous
Ex. Apartment cleaning: everyone benefits from a clean apartment, but some roommates may value a clean apartment more than others.
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Abstract things can have public good characteristics
Examples honesty in business fairness in the income distribution a legal framework, law and order
An application to analysis of terrorism Where governments and economies function poorly,
sects often become major suppliers of social services, political action, and coercive force [Eli Berman, NBER working paper 10004, 2003; The Economist, Jan 15, 04]
Implication: improving law and order, transparency, fairness and social services is one way to combat religious militancy [Berman, Shapiro & Felter, Quarterly Journal of Economics, 2011 August]
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Label of providers and nature of goods do not have to match
Private goods can be provided by the public sector Pizza: provided by private firms Medical care and housing: provided by either private
firms or the government
Public goods can be provided by the private sector garbage collection, fire protection, libraries, public
transportation government plans public good provision, but hires labor
and capital to actually produce the public good government can hire firms, which provide these public
goods
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2. Efficient Provision of Private Goods
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How do we derive aggregate demand for private goods? [Fig.4.1]
Each persons demand curve represents the willingness-to-pay for an additional unit of a good
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For private good, holding P constant, add together individual quantities (Horizontal summation)
How do we derive aggregate demand for private goods? [Fig.4.1]
Each persons demand curve represents the willingness-to-pay for an additional unit of a good
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Everyone pays the same price, 4, but individuals consume different quantities their taste, income, etc. are different. This is possible because fig leaves are private goods.
Equilibrium in private good marketEquilibrium where supply curve intersects aggregate demand curve
Sf
4
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Pareto efficiency in private good market
Utility-maximizing individuals set MRSfa = Pf/Pa Since only relative prices matter for rational
choice, the price of apples can be arbitrarily set at any value. For simplicity, consider Pa=$1
Then, MRSfa = Pf Because demand curve shows the maximum
price consumers would pay (Pf) at each level of fig leave output, it also shows MRSfa at each level of fig leave output
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Pareto efficiency in private good market
Profit-maximizing firms set MCk = Pk (k=f,a) And thus MRTfa = MCf / MCa = Pf / Pa Since Pa=$1, MCa=Pa=$1, and MRTfa = MCf = Pf Because supply curve shows the minimum price
(Pf) firms would sell at each level of fig leave output, it also shows MRTfa at each level of fig leave output
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Combining the conditions derived for consumers and firms, at the equilibrium (where demand and supply curves cross), MRTfa = MRSfaAdam = MRSfaEve
This is the necessary conditions for Pareto efficiency
Thus, the equilibrium price and output are PE
Pareto efficiency in private good market
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3. Efficient Provision of Public Goods
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Efficient provision of public goods: Intuition
Consider a fireworks display as a public good it is nonrival and nonexcludable.
Suppose the fireworks display already has 19 rockets. For the 20th rocket:
Should we add a 20th rocket? We know MC. What is MB from adding another
rocket? ?
20 20 20$5 $6 $4Adam EveMC MB MB
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Efficient provision of public goods: Intuition
MB is sum of willingness to pay because the additional rocket will be consumed by both (nonrival, nonexcludable)
MB from adding another rocket = $4+$6 = $10 This is higher than MC = $5
Yes, we should add another rocket More generally, public goods should be provided
until:iMB MC
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Adam
Eve
Market
Adam is willing to pay $6 for the 20th rocket
Eve is willing to pay $4 for the 20th rocket
Their group willingness to pay is $10, so the group willingness to pay schedule in C, DA+Er, must be 10 at r = 20
Other points on DA+Er are determined by repeating this procedure for each output level [Vertical Summation]
The efficient quantity of rockets is found where the sum of A & Es willingness to pay for an additional unit just equals the marginal cost of producing a unit. It occurs at r=45, p=$6
Efficient provision of public goods: graphical illustration
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Efficiency in public goods market
Again, Adam and Eves marginal willingness to pay can be interpreted as their MRS
Thus, the sum of the prices they are willing to pay is the sum of their MRS: MRSraAdam + MRSraEve
From the production standpoint, price still represents MRTra Thus, the equilibrium is characterized by:
MRSraAdam + MRSraEve = MRTra
the sum of individual marginal benefits equals the marginal cost
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4. Numerical Example
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Numerical example Consider 2 individuals, Adam and Eve who
have the following inverse demand curves, and face a marginal cost curve below.
How do we derive the equilibrium if the good is a private good?
How about if the good is a public good?
P QA A 100 12
P QE E 200MC Q 2
3
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Numerical Example: private good
If the good was a private good, then the aggregate demand curve is:
With a private good, everyone pays the same price.
200 2 200A E A EQ Q Q P P
200 2 200 400 3400 13 3
A E
A E
P P PQ P P P
P Q
Aggregate demand for the
private good
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Numerical Example: private good
In a competitive market, P=MC
Approximately 133 units of the private goodare provided at a price of $88. Adam consumes around 22 units and Eve consumes around 111 units.
400 23 3 3
400 800133 P 883 9
QP MC Q
Q
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Numerical Example: public good
If the good is a public good, the aggregate willingness to pay is:
With a public good, everyone consumes the same quantity.
1100 2002A E A E
P P P Q Q
33002
A EQ Q Q
P Q
Aggregate willingness to pay
for the public good
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Numerical Example, public good Efficient provision would require: P=MC
Efficient provision would imply that Adam & Eve consume 138.46 units of the public good.
Private market may not arrive at this allocation The equilibrium under the assumption that the good
is a private good: Q=133, P=88
3 23002 3
138.46 P 92.3
P MC Q Q
Q
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5. Problems in Achieving Efficiency
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Does the 1st theorem apply to public goods?
Competitive market will provide private goods efficiently
Does competition lead to efficient provision of public goods as well?
People may have incentives to hide their true preferences, or willingness to pay for a public good ..because if Adam can get Eve to pay for the
public good, he can use his income for other purposes and still enjoy the public good.
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Free Rider Problem This incentive to let others pay for the public
good while still enjoying the benefits is known as the free rider problem.
If everyone understates his/her willingness to pay, the private market will fall short of providing the efficient amount of the public good.
This incentive to free ride occurs because the public good is nonrival and nonexcludable: A person gets to consume the good even if he
does not pay for it.
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Free Rider Problem Return to the public goods numerical example.
Suppose Adam chooses to free ride, and Eve therefore provides her optimal amount.
Eve chooses:
After Eve contributes 120 units of the public good, Adam does not provide any additional contributions, because the marginal benefit to Adam of the 120th unit is less than the marginal cost.
120E EP MC Q Q
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Solutions to the free rider problem
Governmental intervention If government can
find everyones true preferences force people to pay for public goods using coercive power
(through taxation) Then government can prevent the free rider problem
Private collective action There are instances when free riding does not occur,
and individuals act collectively without coercion Volunteer fund raising for libraries, music halls, etc.
The importance of the free rider problem is an empirical question
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Experiment to test the importance of the free rider problem
Laboratory experiments on college students A class with 10 students Each student is given 10 tokens Each student can decide how many tokens to keep
and how many to contribute to the group exchange For any tokens the student keeps, that student
receives 500 yen per token. For any tokens the student contributes, every student
in the class receives 300 yen each.
Ones contribution is thus nonexcludable and nonrival a pure public good
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Public goods experiment: theory
If all ten students contribute all ten tokens, each receives 10 tokens * 10 students * 300 yen = 30,000 yen Total economic pie = 30,000 yen * 10 students = 300,000 yen
If students maximizes their personal utility You cannot control others behavior, so it is the best to keep all
of your tokens, regardless of what other people do. If no one contributes, then each student receives: 10 tokens * 500 yen = 5,000 yen Total economic pie = 10 students * 5,000 yen = 50,000 yen
Individual rational choice implies the free-rider problem and under-provision of public goods
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Public goods experiment: results
On average, people contribute 50% Some free riding exists, but it is not the case that free
riding leads to zero or trivial amounts of public goods Other findings
Contribution reduces when the game is repeated and larger reward from keeping tokens is used
Contribution increases with prior communication A caution
Results may not purely reflect preferences for contribution for public goods, but also from a warm glow feeling of satisfaction from giving