PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

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Paper No and Title 5- Advance Microeconomics Module No and Title 22 Externalities

Module Tag ECO_P5_M22

TABLE OF CONTENTS

1. Learning Outcomes 2. Introduction

3. Externality

4. Consumption Externality

5. Quasilinear Preference and the Coase Theorem 6. Production Externality

7. Solution to externality Problem 8. Pigouvian Solution

9. Arrowian Solution 10. Tragedy of Commons 11. Summary

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

1. Learning Outcomes

· Understand the concept of externality

· Know about different types of externality

· Evaluate the problem caused by externalities

· Learn the solution to externalities problem

· Understand different solutions given by Pigou and Arrow

2. Introduction

In this module we will discuss another major problem of market failure that is externality.

Externality exists when action of any economic agent (consumers or firms) creates impact on the decision making of other economic agent or agents.

3. Externalities

Externality implies that the economic activity of one consumer or one firm affects the economic activity or activities of other consumers or firms. An externality arises when the production or consumption possibilities of a firm or consumer are influenced by another agent’s production or consumption. A consumption externality arises when one consumer cares directly about another agents of production or consumption. By external benefits in consumption we mean the consumption activities of an individual which increase the welfare of other consumers. For instance, when you consume more education (you are becoming literate) your neighbours become happy as the number of literate people with whom they can interact increases. Likewise, your well maintained lawn makes the neighbourhood look better. External costs in consumption (or negative consummation externality) occur when an individual’s consumption activities will reduce the welfare of other individuals. For instance, when your neighbour’s son plays loud music, your happiness is reduced because of the noise effect.

Whenever there exists negative or positive externality, the resource allocation provided by the market will not be efficient. In that case market fails to reach the optimum. When externalities are present in consumption, by fulfilling Paretian optimality conditions welfare of the

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

community will not be optimised. Welfare can

be increased by deviating from the Paretion conditions. Hence competitive equilibrium by fulfilling pareto optimal conditions will not optimise welfare. Welfare can be increased by encouraging the consumption of commodities generating external economies in

consumption; while discouraging the

consumption of commodities generating external diseconomies.

Next we approach the problem from the production side. A production externality arises when the production possibilities of one firm are influenced by the choices of another firm or consumer. As in consumption there are two types of externalities in production – external economies and diseconomies. Both consumption and production externalities can be positive or negative. The reason why a good or activity becomes an externality is because they do not have a market and no price is associated with them.

External economies results when the productive activities of firms and industries confer benefits to other activities for which they receive no payments. There are many examples of positive externalities.

Suppose a large housing project has developed parks and playing fields in a locality. It also helps other (neighbours of the housing project) to get fresh air, therefore, the housing project creates positive externality for other Another example of positive externality is that of opening of a national highway reduces traffic congestion and allows smooth flow of traffic thereby reducing transportation costs to the users.

External economies cause private and social benefits and cost to diverge. In particular private cost becomes more than social cost. Or social benefit exceeds private benefit. The pricing system takes into account only private cos- benefit calculations. While if social cost-benefit calculation is taken into account a different outcome would result. The price of the commodity whose production generates external economies does not provide the correct signal as to the social desirability of the commodity. Since the benefits conferred to others cannot be identified, measured and appropriated, hence cannot be included in the price of the commodity. Therefore if social cost (in case of negative externality) or social benefit (in case of positive externality) are not considered in the calculation, efficiency will not hold in decision making and market will fail to provide an efficient solution. Let us briefly introduce external

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

diseconomies in production which implies that the productive activity of a producing firm

imposes costs on other productive firms for which the concerned firm pays no compensation. Most common example of externalities are air and water pollutions. For example a chemical plant discharges polluted gas in the air. This creates lot of problems for the nearby farmers. Air pollution increase as the firm produces more and more and consequently agricultural production reduces more. The production of the chemical plant imposes cost to farmers. The costs imposed on others are not taken into account in determining the price of the commodity based on private cost- benefit calculations only. These is no automatic mechanism in the market, which can consider the external impacts in the calculations. For this reason, without government intervention the level of pollution is impossible to control. Generally proper designing of taxes and subsides or proper identification of property rights can help the society to internalise the external effects.

4. Consumption Externality

Let us start with an example of smokers and non-smokers

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

Suppose there are two room mates A and B. A likes money and smoke, i.e, both money and smoke are economic goods for A. B likes money but hates Smoke, i.e, money is economic good but smoke is economic bad for B.

Their preferences are represented by an Edge worth box diagram (figure 22.1). O_Aand O_Bare origins of person A and B. the amount of money with A and B is measured form their origins at O_Aand O_Brespectively or the horizontal axis

The amount of smoke for both A and B is measured vertically form O_A. This is because smoke unlike money cannot be divided between A and B.

both have to consume smoke in same quantity.

Therefor vertical measurement from origin O_Bgives the amount of clean air available to both. (Note that further away form O_B, we are vertically, closer are we to O_A, therefore less is the smoke and more is the clean air in room)

Hence interpretation of indifference cenres

( )

For A, IC^'sare downward sloping and convex to his origin O_A because, both money and smoke are economic goods for him,

For B; IC^'s are downward sloping and convex to his origin O_B because, both money and clean air are economic goods for him, (Remember clean air increases when smoke decreases)

The final outcome and initial endowment here depends on who has the property rights.

Case I: Suppose B has the right to clean air and both individuals have the same amount point is therefore ‘E’ where E_A =( Rs 100, o smoke) and

EB= (Rs.100 all clean air).

(Remember o smoke means all clean air)

Since B has right to clean air, he can trade it for money, i. e, he can allow A to smoke if A pays him money for foregoing his right therefore, A and B will trade to the pareto efficient point ‘F’ where MRSA between

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

smoke and money = MRSB between smoke and money and their IC’^s are tangent to each other.

At point ‘F’ B has allowed some smoke in the room in lieu of money paid by A to him and both A and B are better off than they were at ‘E’ to show this we must draw ICs of A & B parsing through point E. These curves intersect each other at point E by trading both A&B move to higher indifference curves .

Case II: Suppose A has right to smoke and both have the same amount money : Rs: 100 the initial endowment point is E’ where E_A= (Rs 100, smoke filled room) and E_B= (Rs:100 clean air) .

Now A will trade his right to smoke for money paid to him by B. Now they will trade and reach final equilibrium at F’ which is again a pareto efficient point, and where both are better off than they were at E’.

It may be noted that even though F and F’ are both Pareto efficient , they are distributionally different because A is an a. higher indifference curve at F’ than he is at F while it is the reverse for B. Thus if A and B are free to trade and property rights are well defined then with any endowment they will end up somewhere on the contact curve of pareto efficient allocation of smoke and money.

Another way to solve their problem would be to create a market for smoke. Under a market mechanism the competitive equilibrium will be pareto efficient with externalities arising if property right are not well defined. Under such circumstance inefficient amount of externality gets generated and there is no scope of trade because of poorly defined property rights.

5. Quasilinear preference and the Coase Theorem

In the previous example, given well defined property rights two main points should be noted:

(1) The final outcome of trade will be Pareto efficient.

(2) The final amount of externality generated will depend on who has the property rights.

* There is more smoke at F ' when rights are with smoker at E ' than at F when rights are with non-smoker at E.

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

But if preferences of both A and B are quasi –

linear then the final amount of externality generated becomes independent of the assignment of property rights. Thus every Pareto efficient solution on the contract curve has the same amount of externality.

With quasilinear preferences IC '^S are just vertically shifted versions of same IC for both A and B. Thus the points of tangencies between the IC '^S of A and B will be on a horizontal line. Thus the contract curve will be a horizontal line and every Pareto efficient allocation will have the same amount of smoke but different amounts of money distribution between A and B.

Thus Coase theorem Says: “Under certain conditions the efficient amount of an externality is independent of the distribution of property rights.”

These certain conditions are : no income effects; i.e, for quasilinear preferences, income-effect is zero

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

i. *Remember even in this case even though the amount of externality

generated is independent of distribution of wealth and property rights, the individuals are not indifferent between them. Here again A would prefer a point like F ' to F because he has more money and hence is on a higher indifference curve (IC) at F ' than at F. By the same logic B would prefer F to F '

6. Production Externalities

Let us now consider a situation involving production externalitites. A steel firm produces steel S and also some pollution P along with it, which it dumps in the river. A fishery is located downstream and it gets adversely affected by this pollution

Cost function of steel firm =CS

(

)

Where dC S, PS

( )

( )

0 and 0

dS > dP <

Cost function of fishery =Cf

(

)

Where d Cf

(

)

(

)

0 and 0

dF > dP >

Thus pollution becomes a negative externality for the fishery because it affects the cost of fish production F adversely but the fishery has no control over it.

Thus when the steel mill and fishery operate independently the final outcome would be:

The steel mill’s Õ maximisation problem is

( )

S S S

S, P

Max Õ =P .S C S, P-

Õ maximisation conditions are

( )

(

)

S S

S S

dC S , P dC S, P

d 0 P 0 P

dS dS dS

Õ = Þ - = Þ =

(

)

S dC S , PS

d 0 0

dP dP

Õ = Þ =

The steel firms equilibrium is

(

)

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

The fishery takes P^*as given level of pollution and its Õ maximisation problem is

(

)

f f f

f

max Õ =P .F C- F, P

The Õ maximisation conditions are

(

)

f f

f

dC F , P

d 0 P

dF dF

Õ = Þ =

The externality here arises because of the fact that the pollution being generated by the steel firm affects the fishery, but the fishery has no control over it.

The steel firm while producing takes only its private cost into account and by definition the price of pollution it faces is zero. The steel firm ignores the social cost of pollution which in this case leads to increase in cost of fishery.

To get the socially optimal/ Pareto efficient level of pollution we consider the two firms as a single entity/ firm that produces both steel and fish.

By doing this we have internalized the externality. This is because by merging the firms, we have ensured that the steel firm will take into account the impact of its actions on the fishery since both are part of the same firm.

The merged firms Õ maximisation problem is

( ) ( )

S f S f

S, f , P

max Õ =P .S+ P .F C S, P- -C F, P The Õ maximisation conditions are:

( )

( )

S

S S

dC S, Pˆ ˆ dC S, P

d 0 P 0 P

dS dS dS

Õ = Þ - = Þ = …(1)

( )

( )

f

f f

dC F, Pˆ ˆ dC F, P

d 0 P 0 P

dF dF dF

Õ = Þ - = Þ = …(2)

…(3) and the equilibrium is

(

)

Equation (3) shows that the merged firm does not take the price of pollution as zero, instead the price of pollution is taken as the cost this

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

pollution imposes on the fishery. Therefor steel firms takes social cost of its action into account.

When the steel firm acts independently it takes price of pollution as zero and accordingly produces P^* where

(

)

MCS S , P =0 or ^dCS

(

)

dP =0

The merged firm on the other hand produces pollution till the point where marginal cost to steel mill is equal to marginal cost to fishery, i.e, at

( )

( ) ( )

S ˆ ˆ f ˆ ˆ

MC S, P MC f , P

- =

Since MC_f of pollution is positive, therefore the steel firm will produce pollution till the point where

S S

MC MB

- = (marginal benefit to steel firm) is > 0

Given a downward sloping -MCS

(

)

( )

S ˆ

ˆ ˆ

P, -MC S, P >0

While at P^*, ^MCS

(

)

This can be seen from the Figure 26.3 below:

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

Here the profit (Õ) maximizing independent steel firm produces pollution till the point where marginal benefit from an extra unit ^{=Zero at P}

{

}

the other hand the pareto efficient level pollution is produced till the point where marginal benefit to steel firm is equal to marginal cost to fishery

{ }

Thus due to divergence between provate and social cost the good generating externality gets over produced under a free market.

7. Solution to externality problem

Three solutions have been given for externality problem. Those are;

(1) Coasian solution: Well defined property rights and costless bargaining.

(2) Pigouvian solution: Put a tax on the production of good generating externality

(3) Arrowian solution: Create a market for the externality through well defined property rights and prices will automatically ensure optimal generation of externality.

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

Coasian Solution: According to coase if property rights are well defined and there is

costless bargaining then the two agents involved would bargain and reach the pareto optimal level of pollution.

CASE I: Property rights with steel mill

When the steel mill has the property right to generate as much pollution as it wants it will produce P* units of pollution

At P*, MBS = O while MCF =CP*

Since steel firm has property rights the fishery will bargain with the steel firm to reduce the P* unit of pollution. The fishery will make a payments to the steel mill such that

MBs < payment made < MCf

Therefore for the pollution unit, some payment like C₁¢will be made by fishery to steel mill and the P* unit of pollution will not be produced.

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

As long as MC_f >MB_s, the fishery will make a

payment to the steel mill to reduce that pollution unit. Therefore, through bargaining the final pollution production will be reduced from P*

to ˆP .

CASE 2: Property rights with fishery

In this case initial pollution production world be at zero and the steel mill will pay the fishery to produce pollution. Here again through bargaining the final pollution production would be increased From O to ˆP .

The final payment made for each additional unit of pollution world be such that:

MCF <Payment made to fishery <MB_S

Thus irrespective of who has the property rights, as long as property rights are well defined and bargaining is costless the final production of pollution world be at the pareto optimal level ˆP .

8.Pigouvian Solution

According to Pigou one way to bring pollution to the efficient level ˆP is to place a tax an pollution generated by the steel mill. This will make sure that the polluter faces the correct social cost of its actions.

Suppose we put a tax of t per unit of pollution generated by steel mill. Thus the profit maximization problem of steel mill becomes;

MaxII P S C S P= _s. - _s( , )-t P. The II maximization conditions become;

0 ( , ) 0 ( , )

( , ) ( , )

s s

s

s s

dc s p dc s p

dII o P Ps

dp ds ds

dc s p dc s p

dII o t o t

dp dp dp

= Þ - = Þ

= Þ - - = Þ - =

If we want P P= ˆthen form socially Optimal condition;

ˆ ˆ ( , ) dc s ps

t dp

= ¢

This particular level of tax is known as a Pigovian tax.

Diagrammatically, it can be represented as;

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

MCs

- and MC_f represent the marginal benefit and Marginal cost of pollution to steel mill and fishery respectively. If a pigon tax of

ˆ ˆ ( , ) dc s ps

t = dp

is imposed the marginal benefit to steel mill of every unit of pollution reduces by t. Therefore the -MC_scurve shifts parallel inwards by t to

s. MC¢ -

It can be seen from figure 22.7 above that the post tax marginal benefit of pollution becomes zero at the level ˆp instead of the original P*. Thus the steel mill which produces pollution till the level where -MC_s =0,will post tax generate ˆp level of pollution which is social optimal.

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

The problem with pigouvian tax is that we need to know the optimal level of pollution and

the marginal cost and Marginal Benefit associated with that to impose the tax.

But if we know the optimal level pollution then we do not need the tax at all, we can just tell the steel mill to directly produce that much pollution.

9. Arrowian Solution

According to Arrow the problem of externality arise because there is a missing market for pollution, because of which the steel mill faces a zero price for pollution produced by it, even though the fishery world be willing to pay to reduce pollution levels.

Thus if we define property rights and allow buying and selling of pollution, the externality problem would be solved and we get the socially optimal level of externality

CASE I Suppose Fishery has right to clean water;

Now fishery would be selling right to pollution to the steel mill. If q is the price per unit of pollution and P is the amount of pollution that the steel mill produces (it buys right to produce P units of pollution at a price of

q per unit from fishery).

Therefore the steel mills profit maximizing problem is;

maxÕ =s P S C s p_s. - _s( , )-q p s p. , ( .q p is additional cost for steel mill)

While the fishery profit maximizing function looks like:

maxÕ =_f P F C F P_f. - _f( , )+q p f p, , ( .q p is additional revenue for fishery)

The profit maximizing solution for steel mill and fishery are;

( , ) ( , ) ( )1

s s s

s s

d o P dc s p o P dc s p

ds ds ds

Õ = Þ - = Þ =

( , ) ( , ) ( )2

s s s

s s

d o P dc s p q o P dc s p q

dp ds ds

Õ = Þ - - = Þ = - =

( , ) ( , ) 3

f f f ( )

f f

d dc f p dc f p

o P o P

df df df

Õ - -

= Þ = Þ =

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

The market for pollution will clear if DP and SS balance. DP price is determined by equation (2) while ss price is given by equation (4).

Therefore at equilibrium

( , ) ( , )

s s

dc s p dc F P

dp dp

- =

This is exactly the same condition as was derived for socially optimal production of pollution.

CASE 2: When the steel mill has right to pollutions.

Now the fishery buys /pays the steel mill to reduce pollution. Suppose without any interaction with the fishery the steel mill is producing P*

units of pollution. Now q becomes the price per unit of pollution reduced.

Now the profit (Õ) maximising problems of steel mill will becomes:

maxÕ =_s P S C S P_s. - _s( , )+q p( *-p)

(Note ( *q P -P)is revenue earned by reducing pollution from P* to P) While the fishery’s Õmaximisation problem is

max .Õ =_f P F C F P_f. - _f( , )-q P( *-P f p) ,

(Note ( *q p -P)is extra cost due to payment made to steel mill reduce pollution from P* to P )

Here again the Õmaximising conditions are;

( , ) ( , ) ( )1

s s s

s s

d o P dc S P o P dc S P

ds ds ds

Õ -

= Þ = Þ = -

( , ) ( , ) 2

( )

s s s

s

d dc S P dc S P

o P q o q

ds ds dp

Õ -

= Þ - = Þ =

( , ) ( , ) 3

f f f ( )

f

d dc F P dc F P

o P o pf

df df df

Õ -

= Þ = Þ

Therefore, these conditions are exactly the same as what we have when property rights are with fishery.

Therefore, irrespective of who has the property rights, the market will generate optimal amount of externality, even though distribution of benefit will depend on who has the property right.

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

10. Tragedy of the commons

This refers to the inefficiency that arises when property rights are not well defined. We consider a common field ( the resource) in a village where villagers graze their cows.

Cost per Cow = Rs. A (MC = AC) Value of milk produced by C cows = f(c)

AP Per Cow ( )

MP of each Cow ( ) f c

c

d f c dc

=

= We consider two saturations:

(i) Suppose there is private ownership of common ground. Then the individual will maximise his total wealth which in turn would mean maximisation of wealth of the village. Therefor his maximisation problem

is; max. ( )f c -ac

and maximisation will occur where ( *) MP c =a The individual would buy c* number of cows.

(ii) Suppose there is common owners of ground;

Now when a villager decides to add a cow to the common his decision will be based on the fact whether the output generated by the cow is greater of lesser than its cost

Suppose currently c cows are grazing and AP ^{f c( )}

= c

Adding another cow world be profitable from a villagers point of view as long as

1 1

( )

f c a C

+ ³ +

Hence the villagers will graze cows till the average product of a cow = a.

Therefore ˆC cows will be grazed where ( )ˆ ( )ˆ ˆ ˆ

ˆ ˆ

( ) , . total profit f c a f c ac

c

f c ac o i e

= Þ =

Þ - =

( )Õ have been driven to zero.

This happens because an individual villager ignores the social cost of his action. When an individual decides to add a cow to the common he only considers the private cost ‘a’ of buying the cow, he ignores the fact that his extra cow will reduce output of all existing cows. Thus each

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PAPER No. : 5- Advance Microeconomics MODULE No. : 22-Externalities

villager ignores the social cost of his action and the common ground gets overgrazed. This can be seen from the figure 22.8 below:

Here ideally number of cows should be ˆcwhere MP = MCbut actually c*

cows graze on the ground because actual number of cows is where .

AP = AC

To prevent overgrazing of field we need some mechanism to restrict use;

(a) One such mechanism is private property. As shown in case (i) above, if ownership of ground is given to an individual, number of cows grazed world be maximising profit.

(b) Government can take out grazing rights and sell them. The number of grazing rights would be c*.

(c) Government can impose a per Unit tax per cow such that ( *)

*

f c t a c + =

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11 Summary

Externality is one of the main reason of market failure. The major source of inefficiency lies in the existence of externalities. As externality arises when a person engage in an activity that influences the well being of another individual and get neither pays or receivers any compensation for these effects. Externalities (positive or negative) are borne by people who are not directly involved in the market exchanges. Thus, an externality is a divergence between private costs and social costs or between private benefits and social benefits when externalities are present, the outcome of a competitive market is unlikely to be pareto efficient.