lecture 2 public goods and externalities - altervista · 2016-06-13 · lecture 2 public goods and...

Lecture 2Public goods and externalities

Environmental Economics, Politecnico di Milano, Academic Year2015-2016

Giovanni Marin

IRCrES-CNR, Milanoe-mail: [email protected]

Giovanni Marin Environmental Economics - Lecture 2 1 / 43

Outline of the lecture

• Definition of market failure

• Public goods• Definition• Optimality• Free riding problem

• Partial equilibrium analysis

• Externalities• Definition• Market failure in presence of externalities• Optimality in presence of externalities• Coase theorem• Pigouvian tax


Assumption for markets leading to efficient allocations:

1. Markets exist for all goods and services produced and consumed

2. All markets are perfectly competitive ⇒ agents are price takers

3. All agents have perfect information

4. Private property rights are fully assigned on all resources andcommodities

5. All agents are maximizers

• In reality, markets often depart from one or more of theseassumptions ⇒ market failures

• Public goods and externalities arise because of the failure ofconditions 1 and 4


Public goods - Introduction

• Goods can be classified according to two different dimensions• Rivalry in consumption• Excludability

• Rivalry• One agent’s consumption does (not) prevent other agents to consume

the good ⇒ Ice cream vs view of a beautiful landscape

• Excludability• Agents can(not) be excluded from the consumption of the good ⇒

Clean air vs wilderness area


Some classical examples

• Defence

• Lighthouse

• Clean air


Taxonomy of goods

Excludable Non-excludable

Rivalrous Pure Private Good Open Access ResourceIce cream Ocean fishery

(non-territorial waters)

Non-rivalrous Congestible Resource Pure Public GoodWilderness area Defence


Private and public goods• Pure private goods exhibit both rivalry and excludability

• These are ’ordinary’ goods and services, such as ice cream• For a given amount of ice cream available, any increase in consumption

by A must be at the expense of consumption by others (rivalry)• Any individual can be excluded from ice cream consumption

• Pure public goods are nor rivalry or excludable• An example is the services of the national defence force

• Open access (or common) natural resources• There is rivalry in consumption• Excludability is impossible or characterized by prohibitive costs• Example: ocean fisheries outside territorial waters of any country

• Congestible resources exhibit excludability but not (up to the point ofcongestion) rivalry

• Example: wilderness area• The area is excludable (enforcing limit to access are feasible)• No rivalry exists up to the point of congestion (after which nobody can

‘consume’ the good)


Public goods in market economies

• Non-rivalry implies that all individuals consume the same amount ofthe public good

• The quantity that is consumed by any individuals is the same, butthey do not necessarily value the public good equally at the margin ⇒efficiency will not require that MRUS(A) = MRUS(B) as in the caseof private goods

• As the marginal cost of providing the public good to all individualsdoes not depend on the number of individuals that consume thegood, efficiency requires that in equilibrium marginal costs should beequal to the sum of marginal valuations (marginal willingness to pay)of all individuals ⇒ MC =

∑i MRUS(i) =

∑i MWTP(i)


Optimal provision of public good

X=public good

MC=MRT

Euro

MRUSA

MRUSB

MRUSA+MRUSB=MWTPA+MWTPB

X*


The problem with public goods...

• Choose four people

• Give everyone 1 euro

• Each person privately chooses how much to contribute ⇒ ci

• I take the ‘pot’ and double it ⇒ Ptot = 2∑4

i=1 ci

• I then distribute the pot equally to the four people ⇒ Ptot/4

• How much do you contribute?


The problem with public goods...

• Maximum net benefit attainable if ci = 1∀i ⇒ 4×24 − 1 = 1

• Net benefit for me if all except me contribute 1 ⇒ 3×24 − 0 = 1.5

while the others will get 3×24 − 1 = 0.5


Free rider problem

• People want to consume a public good, but they do not want tocontribute (as they cannot be excluded)

• Everyone hopes that someone else will contribute, and they the willconsume the public good thanks to other people’s contribution

• People do not want to contribute to avoid the upfront cost ofcontribution and because other people benefit from their contribution

• How do we solve the free rider problem? ⇒ public provision of thepublic good


Declared and actual WTP for public goods

X=public good

WTP

Declared WTP for public good

Actual WTP for public good


Public provision is not easy

• Taxation that finances the public provision of public goods is usuallydistortionary (e.g. income and consumption taxes)

• Optimal level of the public good is still unknown to the government⇒ not easy to quantify the aggregate sum MRUS


Simple ‘partial equilibrium’ representation• In partial equilibrium, we just consider good X taking the level of Y

as fixed/given

Consumers• Utility (consumer benefits) is increasing in the consumption of goodX , but at a decreasing rate ⇒ B(X )

• dB/dX > 0; ddB/ddX < 0• dB/dX > 0 can be also seen as the (marginal) willingness to pay,MWTP(X ), for being able to consume an additional unit of X ⇒ itcorresponds to the marginal benefits arising from the consumption ofX ⇒ MB(X )

Producers• Total production costs, C (X ), are increasing more than proportionally

in the production of X• dC/dX > 0; ddC/ddX > 0• dC/dX > 0 can be also seen as the marginal costs, that is the cost of

producing an additional unit of XGiovanni Marin Environmental Economics - Lecture 2 15 / 43

Benefits and costs

X

B(X)

C(X)

Max B(X)-C(X)

X*


Simple ‘partial equilibrium’ representation

• Consumers will purchase X up to the point in which the price (PX )equals the marginal benefit from consumption ⇒ MB(X )

• Producer will produce X up to the point in which the price equals themarginal cost of producing X ⇒ MC (X )

• Welfare is maximized when marginal benefits equal marginal costs(and both equal prices) ⇒ MC (X ∗) = MB(X ∗) = PX


Maximization of welfare

X

MB(X)

Max B(X)-C(X)

X*

MC(X)


Consumers’ surplus and producers’ surplus

X

MB(X)

Max B(X)-C(X)

X*

MC(X)

Consumer’s surplus

P*

Producer’s surplus


Externalities

• An externality occurs when the production or consumption decisionsof one agent have an impact on the utility or profit of another agentin an unintended way, and when no compensation/payment is madeby the generator of the impact to the affected party

• Consumption and production behaviours often affect inuncompensated/unpaid ways the utility gained by other consumers orthe output produced, and profit earned, by other producers

• Externalities can be either positive or negative

• Externalities are a source of market failure


Externalities

• A decision that benefits someone else (with no market transactions)generates a positive externality

• Vaccines prevent an individual from getting a disease, but also has thepositive effect of the individual not being able to spread the disease toothers

• A decision that harms someone else (with no market transactions)generates a negative externality

• A steel producing factory releases pollution in the air. The factory paysfor labour and capital needed to produce steel, while the individualsliving near to the factory are harmed by the pollution (higher medicalexpenses, poorer quality of life, etc). The production of steel by thefactory generates a damage for individuals living near the factory and inabsence of specificic actions the factory will not compensate for thedamage it generates


Externalities

• Given that all of the other institutional conditions for a pure marketsystem to realize an efficient allocation hold, if there is:

• a positive externality, the market will produce too little of it in relationto the requirements of allocative efficiency

• a negative externality, the market will produce more of it than theamount required by allocative efficiency

• Why?


Negative externalities: private vs social costs

• Private costs for a producer of a good, service, or activity include thecosts the firm pays to purchase/rent capital equipment, compensatelabour, and buy materials and other intermediate inputs

• Social costs include both the private costs and any other externalcosts imposted on the society as a consequence of the production orconsumption of a good or service

• An external cost is the economic harm imposed on others due to thepresence of a negative externality

• The private costs of driving a car include fuel consumption,maintenance costs, depreciation, time spent by the driver while drivingthe car

• The social costs include all these private costs as well as the costsimposed on other people other than the driver in terms of congestionand air pollution induced by the use of the car



• The private costs of producing output include the cost of labour,capital and other inputs ⇒ ‘conventional’ upward-sloped marginalcost function (MC )

• The social costs of producing output include all these private costs(labour, capital and other inputs, MC ) and also the costs imposed onother people (external marginal cost, MEC , or marginal damage,MD) ⇒ marginal social cost MSC = MC + MEC = MC + MD



• In presence of negative externalities, competitive markets deliver‘poor’ performance (in terms of allocative efficiency) because:

1. Firms in competitive markets decide how many units of output toproduce by balancing private gains and costs (P ′ = MC ′)

2. As they do not bear the external costs of their activity, the will fullydisregard external effects

3. Welfare-maximizing output level would be such that social gains andcosts would be equal (P∗ = MSC ∗)

4. As MSC > MC , firms in competitive markets produce too muchoutput thus generating too much negative externality


Externality

X

MB(X)

MSC(X) =MC(X)+MEC(X) =MC(X)+MD(X)

X’

MC(X)

P’ MEC(X)=MD(X)

P*

X*

Efficient equilibrium

Competitive equilibrium


Externality: competitive equilibrium

X

MB(X)

MSC(X)

X’

MC(X)

P’ MEC(X)=MD(X)

P*

X*



External cost


Externality: social optimum

X

MB(X)

MSC(X)

X’

MC(X)

P’ MEC(X)=MD(X)

P*

X*


Positive externalities: private vs social benefits

• Private benefits for a producer (or a consumer) of a good or serviceinclude the gains (i.e. surplus) of the producer (or the consumer)obtains when she produces (or uses) the good or service

• Social benefits include the private benefits and any other externalbenefit to society that arises from the production (or consumption) ofa good or service


Positive externalities: private vs social benefits

• The private benefit for a bee-keeper is the money he earns fromselling honey

• For each unit of output, this corresponds to the conventional marketprice. More generally, we may refer to the private benefits of each unitof production (or consumption) as marginal benefits (MB)

• The social benefits include all the private benefits and also thebenefits by people other than the bee-keeper as a consequence ofhoney production, for example farmers whose fields are pollinated bythe bees

• For each unit of output this is the marginal social benefit (MSB)• The additional benefit due to pollination is the marginal external

benefit (MEB)• MSB = MB + MEB


Positive externality

X

MB(X)

X*

MC(X)

P*

P’

X’

Competitive equilibrium

Social optimum

MB(X)

ME(X)

MSB(X)=MB(X)+MEB(X)


Private remedies to externalities

• Although externalities generate inefficiencies in markets, directintervention by the government is not necessarily needed to solve theproblem

• In some specific circumstances people can develop private solutions

1. Moral codes and social sanctions

2. Mergers & Acquisitions

3. Enforcement of property rights coupled with negotiation/bargaining(Coase solution):

• Externalities emerge because property rights are not well defined• To obtain efficient allocations it is indifferent to attribute the property

right to one party or to the other• Public intervention should be limited, in this case, to the assignment

and enforcement of property rights


Example: noise pollution

• A lives in a flat next to B

• A plays the saxophone and enjoys it

• A gets tired while playing the saxophone ⇒ decreasing marginalbenefits

• B does not like listening to A playing the saxophone

• The irritation of B is small for the first hours, and gets larger for eachadditional hour of saxophone playing ⇒ increasing marginal externalcosts


Optimal level of saxophone playing

Hours of music

€ MEC MB

24 0 h*


Solution: assign property rights over ‘silence’

• The government may enforce property rights over silence

• Rights may be assigned to either A or B

• A and B can bargain over property rights


Property rights assigned to A (player)

Hours of music

€ MEC MB

24 0 h*


Property rights assigned to B (listener)

Hours of music

€ MEC MB

24 0 h*


Coase theroem: problems

• Problems with property rights and negotiation• Bargaining can be impractical: it can require substantial time and effort• Transaction costs and incentive to free ride (when the group of

damaged agents is large)• The assignment of property rights may be ambiguous• Parties involved in the negotiation may have limited information on

costs, benefits, and may not be able to monitor the compliance withthe terms of the agreement of the other party (asymmetric information)

• Possible income effects ⇒ if the compensation (given or received) is alarge share of income, bargaining is biased


Remedies to externality: public solutions

• Pigouvian taxes (negative externalities)• The idea is to increase the private marginal cost for the party that

generates the negative externality by imposing a tax such thatMC (X ∗) + Tax = MSC (X ∗)

• Pigouvian subsidies (positive externalities)• The idea is to compensate the party that generates the positive

externality with a subsidy on the top of private marginal benefit suchthat MB(X ∗) + Subsidy = MSB(X ∗)

• Regulation


Pigouvian tax

• Principle: the party that pollutes should pay for the external cost ofpollution (polluter-pays principle)

• Suppose A produces good X , obtaining a marginal benefit• MB(X ) = marginal benefit enjoyed by A

• The production of good X causes a damage do B• MD(X ) = MEC (X ) = marginal damage suffered by B

• The negative externality is proportional to X

• Suppose that the government levies a Pigouvian tax, t

• The cost incurred by the producer now shifts upward ⇒ MC (X ) + t


Pigouvian tax

X

MB(X)

MSC(X)

MC(X)

MEC(X)

P*

X*

MC(X)+t*

t*


Examples of Pigouvian taxes

• Gas taxes

• Landfill taxes

• Water pollution taxes

• Carbon tax

• Problem with Pigouvian taxes ⇒ setting the optimal Pigouvian tax(i.e. equal to marginal damage at the social optimum)

• The government should have information on marginal costs, marginalexternal costs and marginal benefits to set the optimal tax


lecture 2 public goods and externalities - altervista · 2016-06-13 · lecture 2 public goods and...

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