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Externalities EC202 Lectures XVII & XVIII

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Externalities EC202 Lectures XVII & XVIII Externalities EC202 Lectures XVII & XVIII Francesco Nava London School of Economics February 2011 Nava (LSE) EC202 —Lectures XVII & XVIII Feb2011 1/24 Summary A common cause of Market Failures are Externalities: 1 Production 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 (Externality) 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 (investment 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 goods 1, 2 , two firms a, b and one consumer c f g f g 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 (l1) c a ≤ x2 + x2 e2 + y2 (l2) ≤ a y1 f (x2 )(m1) ≤ b c y2 g(x , y1, x )(m ) ≤ 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 )(l1) c a ≤ b a c x + x e2 + g(x , f (x ), x )(l2) 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 [l1] b a c c a ≥ e2 + g(x , f (x ), x ) x x 0 [l2] 1 2 1 2 2 ≥ Taking first order conditions we get that: c U1 l1 + l2g3 = 0 [x1 ] c U2 l2 = 0 [x2 ] b l2g1 l1 = 0 [x1 ] a l1f1 l2 + l2f1g2 = 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 value 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 price 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.
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