EC202 Lectures XVII & XVIII

Francesco Nava

London School of

February 2011

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 1/24 Summary

A common cause of Failures are Externalities:

1 Externalities Eg: Pollution (negative) & Research (positive)

2 Consumption Externalities Eg: Tobacco (negative) & Deodorant (positive)

Competitive Outcome is not Pareto Optimal

Solutions to the Problem Taxes & Subsidies Private Solutions: Reorganization Private Solutions: Pseudo-Markets

Coase Theorem (Take 1)

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 2/24 Production & Consumption Externalities

Definition () There is an externality when an agent’sactions directly influence the choice possibilities (production set or consumption set) of another agent.

Definition (Consumption Exernality) There is a consumption externality when an agent’sactions directly influence the consumption set of another agent.

Definition (Production Exernality) There is a production externality when an agent’sactions directly influence the production set of another agent.

Classical example by Meade: beekeeper and nearby orchard, both increase the other agent’sproductivity and production possibilities.

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 3/24 Positive & Negative Externalities

Definition (Positive Exernality) There is a positive externality when an agent’sactions increase the choice possibilities of another agent.

Definition (Negative Exernality) There is a negative externality when an agent’sactions decrease the choice possibilities of another agent.

Common causes of externalities are:

Networking Effects ( in assets that facilitate cooperation) Civic Action (good norms of behavior that benefit others) Undefined Ownership of Resources (excessive use of resources)

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 4/24 A Simple Model with Externalities I

Topic is discussed with a simple example of production externalities:

Two 1, 2 , two firms a, b and one consumer c { } { } Good 1 is polluting while good 2 is not Firm a is situated on river A Consumer c is situated on river B Firm b is situated after the confluence of the two rivers

Firm a Consumer

Firm b

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 5/24 A Simple Model with Externalities II

Firm a produces good 1 using good 2:

a y1 = f (x2 )

Consumer c has preferences for the two goods defined by:

c c U(x1 , x2 )

Firm b produces good 2 using good 1:

b c y2 = g(x1 , y1, x1 )

its output decreases with river pollution which depends on the quantity of good 1 produced and consumed upstream

Let (e1, e2) denote the initial resources of the economy

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 6/24 Pareto Optimum I

The Pareto Optima of this economy are solutions of the following program:

max U(xc , xc ) subject to c c b a 1 2 x1 ,x2 ,y1,y2,x1 ,x2 c b x1 + x1 e1 + y1 (λ1) c a ≤ x2 + x2 e2 + y2 (λ2) ≤ a y1 f (x2 )(µ1) ≤ b c y2 g(x , y1, x )(µ ) ≤ 1 1 2 As production constraints bind this corresponds to:

max U(xc , xc ) subject to c c b a 1 2 x1 ,x2 ,x1 ,x2 c b a x1 + x1 e1 + f (x2 )(λ1) c a ≤ b a c x + x e2 + g(x , f (x ), x )(λ2) 2 2 ≤ 1 2 1

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 7/24 Pareto Optimum II

The Pareto Optima of this economy are solutions of: max U(xc , xc ) subject to c c b a 1 2 x1 ,x2 ,x1 ,x2 a c b e1 + f (x2 ) x1 x1 0 [λ1] b a c − c − a ≥ e2 + g(x , f (x ), x ) x x 0 [λ2] 1 2 1 − 2 − 2 ≥ Taking first order conditions we get that: c U1 λ1 + λ2g3 = 0 [x1 ] − c U2 λ2 = 0 [x2 ] − b λ2g1 λ1 = 0 [x1 ] − a λ1f1 λ2 + λ2f1g2 = 0 [x ] − 2 Solving the system of FOC requires:

U1 1 + g3 = g1 = g2 U2 f1 −

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 8/24 Pareto Optimum III

Thus effi ciency in this economy requires:

U1 1 + g3 = g1 = g2 (PO) U2 f1 − What does the PO condition require?

The LHS is the Social MRS of consumer c c It accounts for the externality of consuming x1 units of good 1 The RHS is the Social MRT of firm a

It accounts for the externality of producing y1 units of good 1 The central term is simply the MRT of firm b

If externalities are present, PO requires MRS and MRT to be adjusted by their social to account for the external effects of each agent’s decisions have on the rest of the economy (Pigou 1920) Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 9/24 Competitive Equilibrium I

Optimality in a competitive equilibrium agents requires:

U1 1 = g1 = (CE) U2 f1 What does the CE condition require? The LHS is the Private MRS of consumer c c It doesn’taccount for the externality of consuming x1 (over-consumption) The RHS is the Private MRT of firm a

It doesn’taccount for the externality of producing y1 (over-production) The central term is the Private MRT of firm b If externalities are present, CE is not PO because agents only consider for their private MRS and MRT and neglect the social consequences of their behavior Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 10/24 Competitive Equilibrium II

CE condition can be derived by solving the problems of the 3 players: b c b max p2g(x , y1, x ) p1x b 1 1 1 x1 − p2g1 = p1 ⇒

max p f (xa) p xa a 1 2 2 2 x2 − p1f1 = p2 ⇒

max U(xc , xc ) st p xc + p xc < y c c 1 2 1 1 2 2 x1 ,x2 U p 1 = 1 ⇒ U2 p2 Collecting the three FOC, one gets the desired condition:

U1 1 = g1 = (CE) U2 f1

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 11/24 Externalities: Remedies

Several remedies have been proposed to fix Market Failures (CE = PO) due to to externalities: 6

Quotas Subsidies for Depollution Rights to Pollute Pigovian Taxes Integration of Firms Compensation Mechanisms

We say that a mechanism internalizes an externality if it implements the Pareto Optimum in the economy (ie if CE = PO)

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 12/24 Quotas

Quotas are the simplest way to implement PO consumption of good 1:

c Compute PO consumption levels of good 1 (x1, y 1)

Forbid firm a from producing more than y 1 c Forbid consumer c from consuming more than x1

Problems with quotas are:

Computing PO requires a detailed knowledge of the economy It’san authoritarian solution

It’sa commonly used solution (though in a less brutal form), eg:

Limiting quantities of pollutants emitted by firms and consumers

Limits in CO2 emissions of automobiles

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 13/24 Subsidies for Depollution I

Another way to relax the externality is to subsidize firm for depollution:

Assume that firm a can invest z2 units of good 2 in depollution

If so, its pollution drops from y1 to y1 d(z2) − The resource constraint for good 2 consumption becomes:

c a x + x + z2 e2 + y2 2 2 ≤ The production constraint for firm b becomes:

b c y2 g(x , y1 d(z2), x ) ≤ 1 − 1 In which case the PO conditions become

U1 1 1 1 + g3 = g1 = g2 = + (PO) U2 f1 − f1 d1

since FOC with respect to PO z2 imply that g2d1(z2) = 1 − Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 14/24 Subsidies for Depollution II

Consider the CE of this economy if the government subsidizes depollution:

Let s(z2) denote the subsidy of the government With the subsidies in place the program of firm a becomes: max p f (xa) + s(z ) p (xa + z ) a 1 2 2 2 2 2 x2 ,z2 − While the problem of firm b becomes: b c b max p2g(x , y1 d(z2), x ) p1x b 1 1 1 x1 − − Government induces the socially optimal level of depollution by choosing s( ) so that s1(z2) = p2 · However, the CE for this economy still requires:

U1 1 = g1 = U2 f1 and is therefore not PO

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 15/24 Rights to Pollute I

This is the preferred solution by economist (but not by policy makers): In particular consider the following remedy: Firm b (pollutee) sells rights to pollute to firm a and consumer c (the polluters) It receives a r for any pollution right it sells to consumer c It receives a price q for any pollution right it sells to firm a If so, the solution to consumer c’sproblem becomes: U p r 1 = 1 + U2 p2 p2 While the solution to firm a’sproblem becomes: 1 p q = 1 f1 p2 − p2

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 16/24 Rights to Pollute II

The problem of firm b is more complex as it needs to decide: on how much output to produce on how many pollution rights to sell to the polluter

In particular firm b solves the following program:

b c b c max p2g(x , y1, x ) p1x + rx + qy1 b c 1 1 1 1 x1 ,y1,x1 − Optimality conditions for this program require:

p1 q r g1 = & g2 = & g3 = p2 − p2 − p2 Solving FOC for all three players implies effi ciency since:

U1 1 + g3 = g1 = g2 U2 f1 −

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 17/24 Rights to Pollute III

The creation of markets for rights to pollute therefore: implements the Pareto Optimum requires less information than quotas as the government does not need to know preferences and technologies of all individuals and firms

Further consideration: Not all individuals pay the same price for the same right to pollute b c b c In our example q = r only if g(x1 , y1, x1 ) = G (x1 , y1 + x1 ) In our example there is only one supplier and buyer in each open pollution market. To avoid strategic considerations it would be better if there were more. We have discussed a "polluters pays" scheme. Similar arguments work if "depollution rights" markets are opened where pollutees buy from polluters. Of course the of equilibrium would differ.

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 18/24 Pigovian Taxes

A different way to solve the externality problem is through taxes:

One could tax production of good 1 at rate T One could tax consumption of good 1 at rate t Where T = q and t = r (from the previous remedy)

Such tax rates would:

solve the externality problem since PO = CE require a lot of information to be computed exactly

These tax levels are often called Pigovian taxes in honor of Pigou who first wrote about them in 1928.

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 19/24 Integration of Firms

For convenience assume that consumer c does not pollute: g3 = 0. Another remedy to the externality problem is to have both firms merge. In which case the merged firm solves the following problem:

a b a b a max p1f (x ) + p2g(x , f (x )) p1x p2x b a 2 1 2 1 2 x1 ,x2 − − The solution to this problem implies PO since FOC require:

p1 1 = g1 = g2 p2 f1 − This is not the preferred solution since: It disregards considerations of market power Big firms usually extract higher rents It disregards property rights Firms may prefer not to merge

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 20/24 A Compensation Mechanism

Compensating Mechanisms have been designed to internalize externalities whenever:

the firms and consumers know all fundamentals of the economy while the government does not

Such mechanism guarantee that the government can:

elicit the Pigovian tax rates from producers and consumers set such effective tax rates so that PO = CE

The limitations to this approach (suggested in Varian 1994) are that:

it requires a lot of knowledge on the part of consumers and producers it does no better than markets for pollution rights

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 21/24 Coase Theorem I

In a seminal paper of 1960, Coase doubted the necessity of any government intervention in presence of externalities. His argument proceeded as follows: Let b(q) denote the benefit to the polluter of q units of pollution Let c(q) denote the cost to the pollutee of q units of pollution

Assume that b0 > 0, b00 < 0, c0 > 0, c00 > 0

Effi cient pollution q would require b0(q ) = c0(q ) ∗ ∗ ∗ If pollution q0 is ineffi cient it must be that b0(q0) < c0(q0) If so, the pollutee can ask the polluter:

1 to reduce pollution by some small number ε to q0 ε − 2 in exchange of a transfer tε where t (b (q0), c (q0)) ∈ 0 0 Such benefits the polluter since t > b0(q0)

Such trade also benefits the pollutee since t < c0(q0)

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 22/24 Coase Theorem II

The previous argument can be repeated so long as b0 < c0

Moreover a similar argument works for the case in which b0 > c0 Thus Coase concluded that the following result had to hold: Theorem If property rights are clearly defined and transaction costs are negligible, the parties affected by an externality succeed in eliminating any ineffi ciency through the simple recourse of negotiation.

The two essential ingredients for his claim are:

1 Negligible transaction costs

2 Well defined property rights

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 23/24 Coase Theorem III

Limitations of the Coase Theorem are due:

1 Non-negligible transaction costs In fact the result fails:

1 If a lawyer is needed and if he charges more than ε(c b ) 0 − 0 2 If information about costs and benefits is private [Myerson et al 1983]

2 Well defined property rights In fact the result fails when rights are not well defined:

1 As with open water fishing 2 As for pollution But several examples have been reported in which such bargaining occurs Cheung 1973 shows that in US arrangement with side payments between beekeepers and orchards are common.

Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 24/24