Microeconomics II MWG, Ch. 11 Externalities and Public Goods

Microeconomics II

MWG, Ch. 11 Externalities and Public Goods

Alzahra University Department of Economics

Hamid Kordbacheh

[email protected]

2

Externalities

• FFWT any competitive equilibrium is Pareto optimal. i.e. markets allocate resources efficiently.

• SFWT (given suitable convexity assumptions) any Pareto optimal allocation can be supported as a competitive equil.

• What happens if the behavior of some agent affects the welfare of others?

• When external effects are present, CE is still PO, as long as the effects are transmitted via prices, markets are efficient.

• market failures: violation of welfare theorems assumptions in which markets fail to deliver optimal results.

3 Chapter 11 MWG: Externalities and Public Goods,

Hamid Kordbacheh, Alzahra university, Iran

11.B: A simple Bilateral Externalities

• Bilateral Externality vs Multilateral Externality

• Externalities can be produced by consumers as well as firms.

o Consumption side: noise pollution

o Production side: Chemical plant’s discharges reducing fishery’s catch

• Externalities can be positive or negative

• Public Good -special kind of externality

o Non-rivalry in consumption: National defense & flood control

o Non-excludable: lighthouse

Basic Problem – Market failure or lack of market (no price)



Definition 11.B.1: An Externality is present whenever the wellbeing of a

consumer or the production possibilities of a firm are directly affected by the

actions of another agent in the economy.

• Directly Affected - not through prices

Viner (1931)

• Pecuniary externalities: actions affecting prices;

• Non-pecuniary (true) externalities actions not affecting prices (that's

what we're studying)

Fishery’s productivity affected by emissions from oil refinery.

Fishery’s profitability affected by price of oil.

Neighbor's flower garden



Simple Bilateral Externality

A two-agent partial equilibrium model

• 2 consumers (can think of 2 producers or 1 of each)

• L traded goods

• 𝒘𝐢 consumers I’s wealth

• Consumer i’s utility function

𝑢𝑖 𝒙𝐢, ℎ

𝒙𝐢= (𝑥𝑖1, 𝑥𝑖2,…𝑥𝑖𝐿)

h: amount of externality

Chapter 11 MWG: Externalities and Public Goods, Hamid Kordbacheh, Alzahra university, Iran

6

Simple Bilateral Externality

• Consumer 1 chooses externality h, assume h 0, h

• Consumer 2 takes the externality so 𝜕𝑢−𝑖

𝜕ℎ≠ 0

The Consumer derived their utility function on the level of h

𝑣𝑖 𝑤𝑖 , 𝑝, ℎ = max𝑥𝑖>0

𝑢 𝒙𝒊, ℎ

s.t. 𝑝𝑥𝑖 ≤ 𝑤𝑖


7

Equilibrium Choices are Not Efficient

• Given the quasi-linear preferences the consumer’s indirect utility function

takes the form

𝑣𝑖 𝑤𝑖 , 𝑝, ℎ = 𝑥1𝑖 + 𝑔(𝑥−1𝑖 , ℎ)

We know that 𝑥𝑖1= 𝑤𝑖 − 𝑝𝑥−1𝑖(𝑝, ℎ), then

𝑣𝑖 𝑤𝑖 , 𝑝, ℎ = 𝑤𝑖 − 𝑝𝑥−1𝑖 𝑝, ℎ + 𝑔 𝑥𝑖2, 𝑥𝑖3,…𝑥𝑖𝐿

or

𝑣𝑖 𝑤𝑖 , 𝑝, ℎ = 𝜙𝑖(𝑝, ℎ) + 𝑤𝑖

It can be written

𝜙𝑖(𝑝, ℎ)=𝜙𝑖(ℎ)

What is 𝜙𝑖(ℎ)?

Assume 𝜙′𝑖(ℎ) ≤ 0 and, 𝜙"𝑖 ℎ < 0




• How will consumer 1 choose h?

• Efficient outcome

𝜙′𝑖(ℎ) ≤ 0 with equality if ℎ > 0

Figure 11.B.1 shows this results

• Is there any problem with this result?

• What is the socially optimal level of h?



Pareto Optimal Allocation

The socially optimal level of h must maximize the JOIN surplus of the 2

consumers

maxℎ≥0

𝜙1(ℎ) + 𝜙2(ℎ)

FOC

𝜙′1(ℎ𝑜) + 𝜙′2(ℎ

𝑜) ≤ 0

For interior solution

𝜙′1(ℎ

𝑜) = − 𝜙′2(ℎ𝑜)

Result: ℎ∗ > ℎ𝑜

Figure 11.B.1 shows this results




• Three important points that come out of this results

• Externalities are not necessarily eliminated at the Pareto optimal solution

o When dose this happen?

• What would be the result if we have positive externalities

• What would happen if we relax the assumption of a quasilinear utility

functions?



Traditional Solutions to the Externality Problem



Quotas

• Suppose negative externality ℎ𝑜 < ℎ∗

• Social planer sets maximum of ℎ = ℎ𝑜

• Emitter solves

max0<ℎ<ℎ𝑜

𝜙1(ℎ)

We know ℎ𝑜 < ℎ∗, so polluter will do as much as he can

Perfect information Requirements:

• Policy maker needs to compute ℎ𝑜

• So he needs to compute 𝜙𝑖(ℎ)

• Taxes

• Pigouvian taxation: Imposing tax on the externality-generating activity

• Taxes consumer 1 for producing h ; sets per unit tax

𝑡ℎ = −𝜙′2 ℎ𝑜 > 0

• What does this mean?

• Emitter solves

maxℎ>0

𝜙1 ℎ − 𝑡ℎℎ

FOC 𝜙′1 ℎ𝑜 ≤ 𝑡ℎ with equality if ℎ𝑜 > 0

Figure 11.B.2


Two questions:

• How much tax must we impose in case that the negative externality is very

substantial (and ℎ𝑜=0)

• How can the previous discussion be extended to positive externality

Subsidies

• Policy maker sets the unit of subsidy 𝑠ℎ = −𝑡ℎ= 𝜙′2 ℎ𝑜 > 0

Where 𝑆 ≡ 𝑠(ℎ∗−h)

Emitter solve

maxℎ>0

𝜙1 ℎ +𝑠ℎ(ℎ∗−h)

FOC 𝜙′1 ℎ𝑜 + 𝑠ℎ ≤ 0 with equality if ℎ𝑜 > 0


Some important points about Pigouvian taxation:

• The Pigouvian view:

o Assumes ethical standpoints, and relies on social attitudes or norms to

determine the direction of an externality.

o Emphasizes an externality generator and a victim

• The Pigouvian tax charges a tax on the externality-generating activity but

not on the output that generated such pollution

o What would happen if the output was taxed?

o When does the tax on output lead to the same result?

• The quota and the Pigouvian tax are equally effective under complete

information


Fostering bargaining over externalities

Coase/Bargaining Solution

• Coase/Bargaining Solution: Coase’s famous paper (The Problem of

Social Cost ,Coase 1960), was a direct response to Pigou’s argument

• The key features of Coasean paradigm:

o Emphasizing reciprocity

o Relying on property right based on social attitudes and norms

o Free market alternative (possibility of private bargaining) to the

Pigouvian idea of explicit intervention in response to a “market failure”

o Bargaining between two parties results in Pareto efficient outcome

(irrespective of who has property rights).

o Irrelevance Theorem ( the neutrality proposition): the initial allocation of property rights does not affect the final allocation of resources


The key conditions

• Small numbers of agents involved

• Perfect information among the agents

• Assigned property right to externality otherwise No Big Deal



Example: two agents

• Still looking at negative externality

Case 1: 2 Has Property Right

• Assign right to externality-free environment to consumer 2.

• Initial state ℎ = 0

• Consumer 1 cannot produce externality without Consumer 2’s permission

• Bargain – agents will bargain to reach an agreement over (h,T) ; if no agreement is reached the default value is (0,0)

• Bargaining Power - this is independent of the property right and reliant on the ability of negotiation.



• Assume consumer 2 has all the bargaining power so he can make a take-

it-or-leave-it offer, (h, T ) to consumer 1 demanding a payment T

• Consumer 1 accepts iff 𝜙1 ℎ − 𝑇 ≥ 𝜙1(0)

• Consumer 2 will pick the offer (h,T) to solve

maxℎ≥0

𝜙2 h + T

𝑠. 𝑡 𝜙1 ℎ − 𝑇 ≥ 𝜙1 0

The constraint will be binding in

maxℎ≥0

𝜙2 h + 𝜙1 ℎ − 𝜙1 0



Efficient Choice

𝜙′2 ℎ + 𝜙′1(ℎ) ≤ 0 with equality if ℎ > 0

• This coincides with that solving the social planner’s problem

• i.e. ℎ = ℎ0 with 𝑇 = 𝜙1 ℎ0 − 𝜙1 0 > 0


20


• Assign right to the polluter (consumer 1) to generate as much as the

externality she wants

• In the absence of any agreement, consumer 1 will generate ℎ∗

• Assume consumer 2 has all the bargaining power so he can make a take-

it-or-leave-it offer, (h, T ) to consumer 1 for a payment T

• Indeed, consumer 2 can pay $T the consumer 1 in exchange of a lower

level of pollution

• Consumer 1 accepts iff 𝜙1 ℎ + 𝑇 ≥ 𝜙1(ℎ∗)


21

• Consumer 2 will choose the offer (h,T) to solve

maxℎ≥0

𝜙2 ℎ − T

𝑠. 𝑡 𝜙1 ℎ + 𝑇 ≥ 𝜙1 ℎ∗

The constraint will be binding in

maxℎ≥0

𝜙2 h + 𝜙1 ℎ −𝜙1 ℎ∗

Efficient Choice

𝜙′2 ℎ + 𝜙′1(ℎ) ≤ 0

• Again this coincides with that solving the social planner’s problem

• i.e. ℎ = ℎ0 with 𝑇 = 𝜙1 ℎ0 − 𝜙1 ℎ∗ > 0



Results


• Consumer 1 pays 𝑇 = 𝜙1 ℎ0 − 𝜙1 0 > 0 to be allowed to set ℎ0> 0


• Consumer 2 pays 𝑇 = 𝜙1 ℎ0 − 𝜙1 ℎ∗ > 0 for setting ℎ0 < ℎ∗

Coase paradigm : If trade of the externality can occur then

bargaining will lead to an efficient outcome no matter how PR are

allocated.



Although the initial allocation of PR does not affect the level of the ext., it

affects the wealth distribution of the two agents.


• 1 must pays 𝑇 = 𝜙1 ℎ0 − 𝜙1 0 to 2

Then consumer 2’s utility is 𝜙2 ℎ0 + T and then consumer 1’s utility is

𝜙1 ℎ0 − T= 𝜙1 0

Hence, consumer 2’s utility is higher than that of consumer 1 if

𝜙2 ℎ0 + 𝜙1 ℎ0 > 2𝜙1 0


24

Coase/Bargaining Solution


• 2 must pays 𝑇 = 𝜙1 ℎ∗ − 𝜙1 ℎ0 to 1

Then consumer 1’s utility is 𝜙1 ℎ0 + T = 𝜙1 ℎ∗ but consumer 2’s utility is

𝜙2 ℎ0 − T

Hence, 1’s utility is bigger than that of consumer 2 if

2𝜙1 ℎ∗ > 𝜙1 ℎ0 + 𝜙2 ℎ0

• Therefore, when the agent has bargaining power has a total utility higher

the average of welfare at the Pareto optimum, and vice versa.

2𝜙1 ℎ∗ > 𝜙1 ℎ0 + 𝜙2 ℎ0 >2𝜙1 0


25

Figure 11.B.3: The final distribution of utilities under different PR and BP

• At point a consumer 2 has the property right ( h = 0)

• Therefore, the take-it-or-leave-it offer leads to point f in the first case and

point e in the second case

• At point b consumer 1 has the property right

• The , the take-it-or-leave-it offer leads to point d in the first case and point

c in the second case


26

Some important points

The Key assumptions of Coase theorem:

• Property rights must be perfectly defined.

• Property rights must be perfectly enforced,

• The polluter must know the cost of the externality for the affected agents

• The affected agents must know the polluter’s profit function

Questions on Coase theorem

• Are these assumptions practical?

• Isn’t Coase theory itself a blackboard economics?


27

Externalities as missing markets

Missing Market definition

• Lack of coordination

• Technology

• Transaction costs

• Trust or information

An alternative view to externalities:

• Externalities are a commodity which lacks a market.

• We can simply show that, if externalities were a traded commodity, the

produced level of that coincides with the Pareto optimal level ℎ = ℎ0.

• Suppose a well defined property rights, and a competitive market for the

right

• 𝑝ℎ: the price of one unit of externality-generating activity


28


• consumer 1 (the emitter) chooses how many polluting rights to buy

maxℎ1≥0

𝜙1 ℎ1 − 𝑝ℎℎ1

F.O.C: 𝜙′1 ℎ1 < 𝑝ℎ with equality if ℎ1 >0

• Similarly, the individual affected decides how many polluting rights to sell,

maxℎ2≥0

𝜙2 ℎ2 + 𝑝ℎℎ2

• F.O.C: 𝜙′2 ℎ2 + 𝑝ℎ < 0 with equality if ℎ2 >0


29


• the competitive market for polluting rights must clear

ℎ1 = ℎ2 = ℎ∗∗

𝜙′1 ℎ∗∗ ≤ 𝑝ℎ ≤ −𝜙′2 ℎ∗∗

Or simply

𝜙′1 ℎ∗∗ ≤ -𝜙′2 ℎ∗∗ with equality if ℎ∗∗ >0

• Interestingly, this condition coincides with the F.O.C under the Pareto

optimal level of the externality ℎ0. i.e.

𝑝∗ℎ = 𝜙′1 ℎ0 = − 𝜙′2 ℎ0


30

11.C. Public Goods

• DEFN 11.C.1: A public good is a commodity for which use of a unit of the

good by one agent does not preclude its use by other agents.

Distinction

• Non-Excludable: public goods usual known non-excludable, but in Mas-

Colell they can be either excludable or non-excludable;

• Non-Rivalrous: consumption of additional units of the good involves zero

social marginal costs of production


31

The taxonomy of four different types of goods


32

Rivalrous Non-rivalrous

Excludable Private Good Club Good

Non-excludable Common property

resource

Public Good

Conditions for Pareto Optimality

Model

• I consumers,

• One public good x

• L traded private goods

Assume:

• quasi-linear utility function over L private goods and the public good

• 𝑢 𝐱𝐢, 𝑥 = 𝑥𝑖1 + 𝑢 (𝑥𝑖2, 𝑥𝑖3,…𝑥𝑖𝐿) + 𝜙𝑖(𝑥)

• 𝐱𝐢 = (𝑥𝑖1, 𝑥𝑖2,…𝑥𝑖𝐿)


33

• 𝑥: amount of public good which is actually a good (𝜙′𝑖 𝑥 > 0)

• 𝜙𝑖(𝑥) is concave (𝜙′′𝑖 𝑥 < 0)

• level of consumption of x has no effect on prices of the private goods

• Cost to produce public good is C(𝑞)

• C(𝑞) are convex in q

• q : amount of public good produced


34

Pareto Optimal Solution

The partial equilibrium model

The social planner maximizes aggregate surplus,

max𝑞≥0

𝜙𝑖(𝑞)𝐼1 -C(q)

F.O.C: Samuelson rule

𝜙′𝑖(𝑞𝑜)𝐼

𝑖=1 > C′(𝑞𝑜) with equality if 𝑞 >0

• The social planner increases the provision of a public good until that the

sum of the consumers’ marginal benefit ( or marginal social benefit) is

equal to its marginal cost.


35

Inefficiency of private provision of public goods

• Show that market provision of PG (i.e. competitive, price taking

equilibrium) is inefficient

• Assume a market exists for the public good

• Market-Clearing - at p* public good produced (supplied) equals public

good consumed

• Total amount of PG purchased 𝑥 = 𝑥𝑖𝐼𝑖=1

• No Exclusion: 𝑥∗𝑘𝐼𝑘≠𝑖 optimal purchases of public good all other

consumers


36

At a competitive equilibrium:

1. Consumers maximize utility

each consumer i’s purchase of the public good 𝑥∗𝑖 must satisfy

max𝑥𝑖≥0

𝜙𝑖 𝑥𝑖 + 𝑥∗𝑘𝐼𝑘≠𝑖 −𝐼

1 𝑝∗𝑥𝑖

F.O.C

𝜙′𝑖 𝑥∗𝑖 + 𝑥∗𝑘

𝐼𝑘≠𝑖 ≤ 𝑝∗ with equality if 𝑥∗𝑖 >0

or

𝜙′𝑖 𝑥∗ ≤ 𝑝∗ with equality if 𝑥∗ >0


37

2. Firms maximize profit:

The firm producing the public good must solve the fallowing PMP

max𝑞≥0

(𝑝∗𝑞 − 𝐶(𝑞))

F.O.C

𝑝∗ − 𝐶′(𝑞∗) ≤ 0 with equality if 𝑞∗ >0

At a competitive equilibrium 𝑞∗ = 𝑥∗

𝜙′𝑖 𝑞∗ = 𝐶′(𝑞∗) if 𝑞∗ >0 and 𝜙′𝑖 𝑞

∗ < 𝐶′(𝑞∗) if 𝑞∗= 0


38

Compare:

Pareto Efficient Solution 𝜙′𝑖(𝑞𝑜)𝐼

𝑖=1 = C′(𝑞𝑜)

Market Provision 𝜙′𝑖 𝑞∗ = 𝐶′(𝑞∗)

Conclusion: when people make voluntary contributions, the market will

provide too little of the public good, 𝑞𝑜 > 𝑞∗

• This fact can be understood in terms of positive externalities

• Free rider problem.


39

Free rider problem.

• Suppose

𝜙′1 𝑥 < 𝜙′2 𝑥 < ⋯ < 𝜙′𝐼 𝑥

In this case, condition 𝜙′𝑖 𝑥∗ ≤ 𝑝∗ can hold for at most one consumer.

This consumer must be consumer I, who values it the most (on the margin).

(why?)

Remedies for the Free-Rider Problem

Government interventions

• Regulation

• Price-based interventions: compulsory participation (Taxation, Tying)


40

Suppose there are I consumers each with benefit function 𝜙𝑖 𝑥

Using the Pigouvian taxation we can implement the optimal consumption xO by setting the per unit subsidy to each consumer equal to

𝑠𝑖 = 𝜙′𝑘(𝑥𝑜)

𝑘≠𝑖

Because

max𝑥𝑖≥0

𝜙𝑖 𝑥𝑖 + 𝑥𝑘

𝐼

𝑘≠𝑖

+ 𝑠𝑖𝑥𝑖 − 𝑝∗𝑥𝑖


41

The necessary and sufficient first-order condition for this problem is

𝜙′𝑖 𝑥𝑖 + 𝑥𝑘

𝐼

𝑘≠𝑖

+ 𝑠𝑖 = 𝑝

Substituting in the above subsidy and combining with the market-clearing

condition

𝜙′𝑖 𝑥 𝑖 + 𝑥 𝑘

𝐼

𝑘≠𝑖

+ 𝜙′𝑘(𝑥𝑜)

𝑘≠𝑖

= 𝑝

𝜙′𝑖 𝑞 + 𝜙′−𝑖 𝑞

𝑂 ≤ 𝑐′ 𝑞


42

Lindahl Equilibrium

A market-based solution to public goods

Firm charges each consumer 𝑝∗∗

In the demand side

max𝑥𝑖≥0

𝜙𝑖 𝑥𝑖 − 𝑝𝑖∗∗𝑥𝑖

FOC 𝜙′𝑖 𝑥∗∗ ≤ 𝑝𝑖

∗∗with equality if 𝑥∗∗ > 0

In the supply side

max𝑞≥0

𝑝𝑖∗∗ 𝑞 − 𝐶(𝑞))

FOC 𝑝𝑖∗∗ − 𝐶′ 𝑞∗∗ ≤ 0 with equality if 𝑞∗∗ > 0


43

Lindahl Equilibrium

Market clearing condition

𝜙′𝑖 𝑞∗∗ = 𝐶′(𝑞∗∗) for an interior solution

Thus 𝑞∗∗ = 𝑞𝑜

• The right kind of market can result in the Pareto optimal allocation, even in

the public goods case

Problems -

• Need power to exclude

• Price taking consumer even they are the only buyers of a particular good

• Discriminating (needs perfect information)

• Consumer has to believe that to consume the good have to purchase it!


44

Example

For a public good Assume

𝜙𝑖 𝑞 = ln𝑞

𝐶 𝑞 =𝑞2

2

a. Derive the efficient levels of x, p q

b. Derive Lindahl price


45

11.D: Multilateral Externalities

• Agents who suffers externalities are different than those who generates

• Differentiate between depletable and non-Depletable externalities.

• Depletable externalities

• Partial equilibrium approach: Given price P of L tradable goods in a

competitive market

• Firms generating externality ℎ𝑗 ∈ ℝ+

• 𝜋 ℎ𝑗 : is a concave profit function over the level of the externality

• I consumers, who have quasi-linear utility function

• 𝜙𝑖 ℎ𝑖 : consumer I’s utility over the amount of depletable externalities

• Negative externality 𝜙′𝑖 ℎ𝑖 > 0, 𝜙′′𝑖 ℎ𝑖 < 0, 𝜋′′𝑗 ℎ𝑗 < 0


46

• At the CE firm j (polluter) chooses the level of ℎ𝑗 that solves its PMP

maxℎ𝑗≥0

𝜋𝑗 ℎ𝑗

FOC 𝜋′𝑗(. ) ≤ 0 with equality if ℎ𝑗∗ > 0

In contrast, PO allocation involves

maxℎ 1,….,ℎ 𝐼ℎ1,….,ℎ𝑗

𝜙𝑖 ℎ 𝑖𝐼𝑖=1 + 𝜋𝑗

𝐽𝑗−1 ℎ𝑗

s.t. ℎ 𝑖 = ℎ𝑗𝐽𝑗=1

𝐼𝑖=1


47

𝐹𝑂𝐶

𝜙𝑖′ ℎ 𝑖 ≤ 𝜇 with equality if ℎ 𝑖𝑜>0

𝜇 +𝜋′𝑗( ℎ𝑗𝑜) ≤ 0 with equality if ℎ𝑗

𝑜 > 0

ℎ 𝑖 = ℎ𝑗

𝐽

𝑗=1

𝐼

𝑖=1

then

𝜙𝑖 ℎ 𝑖 ≤ −𝜋′𝑗( ℎ𝑗𝑜)

• Importantly, these conditions match the same conditions at competitive

markets in Ch. 10.

• Result


48

Non−Depletable externalities

• market is normally unable to result in an efficient allocation.

• Assume externality is completely non-rival in consumption:

o If all J firms generate an aggregate amount of externality ℎ𝑗𝐽𝑗=1

o Every consumer suffers an externality ℎ𝑗𝐽𝑗=1

• CE: each firm increases its level of ℎ𝑗∗ until 𝜋𝑗 ℎ𝑗

∗ = 0


49

Non−Depletable externalities

In contrast, PO allocation involves

maxℎ1,….,ℎ𝑗

𝜙𝑖 ℎ𝑖𝐼𝑖=1 + 𝜋𝑗

𝐽𝑗−1 ℎ𝑗

FOC 𝜙′𝑖 ℎ𝑖𝑜𝐼

𝑖=1 + 𝜋𝑗′(ℎ𝑗𝑜) ≤ 0 with equality if ℎ𝑗

𝑜>0

• This exactly coincides with the optimality conditions for a public good

(11.C.1)

• Therefore, unlike in the case of depletable externalities ℎ𝑗∗ (in CE) does not

necessarily coincide with ℎ𝑗𝑜 (PO)

• The free-rider problem arises in non-depletable ext. so, the equi. level of

the negative externality exceeds its optimal level


50

Non−Depletable externalities: Methods to achieve the optimality

• If the regulator has adequate information over firms’ profit functions and

consumers’ harm, it can guarantee optimality using quotas or taxes.

1. Setting quotas : ℎ1𝑜, ℎ2

𝑜, . ℎ𝐽

𝑜

2. Taxes. 𝑡ℎ = − 𝜙′𝑖 ℎ𝒊𝑜𝐼

𝑖=1

• firm j’s PMP after the tax

maxℎ𝑗

𝜋𝑗 ℎ𝑗 − 𝑡ℎℎ𝑗


51

F.O.C

𝜋𝑗′ ℎ𝑗𝑜 − 𝑡ℎ ≤ 0 with equality if ℎ𝑗

𝑜>0

then

𝜋𝑗′ ℎ𝑗𝑜 + 𝜙′𝑖 ℎ𝑖

𝑜𝐼𝑖=1 ≤ 0 with equality if ℎ𝑗

𝑜>0

• Which exactly coincides with the FOC that solves the social planner problem

3. Tradable Externality Permits.

• Using externality permits to solve the externality problem.

Assume:

• ℎ𝑜 = ℎ𝑗𝑜

• every firm receives ℎ 𝑗

• Price taking firms

• 𝑝ℎ∗: the permits equilibrium price


52

firm j’s PMP

maxℎ𝑗

𝜋𝑗 ℎ𝑗 + 𝑝ℎ∗(ℎ 𝐽 − ℎ𝑗)

F.O.C 𝜋′𝑗 ℎ𝑗 + 𝑝ℎ∗ ≤ 0 with equality if ℎ𝑗

𝑜>0

• If all J firms are carrying out this PMP, we need the market clearing

condition ℎ𝑜 = ℎ𝑗𝑜

𝑝ℎ∗ = − 𝜙′𝑖 ℎ𝑖

𝑜

𝐼

𝑖=1

So

𝜋′𝑗 ℎ𝑗 − 𝜙′𝑖 ℎ𝑖𝑜

𝐼

𝑖=1

≤ 0

Chapter 11 MWG: Externalities and Public Goods,

Hamid Kordbacheh, Alzahra university, Iran 53

Multilateral Externalities

• This exactly coincides with the F.O.C that solves the social planner

problem

• ℎ𝑗=ℎ𝑗𝑜

• Advantage of tradable externality Permits

o Requirement of minor information is the advantage of tradable

externality permits, relative to other policy instruments, Data about the

optimal level of pollution, ℎ𝑜. (industry profits,consumers’ damage)


54

Documents

Microeconomics II MWG, Ch. 11 Externalities and Public Goods