Externalities Microeconomics 2
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Externalities Microeconomics 2 Bernard Caillaud Master APE - Paris School of Economics January 30, 2017 (Lecture 3) Bernard Caillaud Externalities I. What are externalities { I.1. Classics ! Meade's example of a positive external effect Honey producer H raises bees so as to produce honey Next to H, P has an orchard and produces fruits The more bees, the better the pollination of fruit trees; the larger the orchard, the larger the production of honey Production functions depend on input / output decisions of another agent. Examples of negative externalities also often mentioned Smoking: My utility depends on your consumption of cigarettes Noise: My listening to loud heavy metal impacts your en- joying a quite night GHG emissions: environmental externalities and correspond- ing climate policies (Kyoto protocol, Emission Trading Sys- tems, Carbon taxes,...) Bernard Caillaud Externalities I.2. Definitions of externalities Pigou (1932): "...one person A, in the course of rendering some service, for which payment is made, to a second person B, inci- dentally also renders services or dis-serves to other persons, of such a sort that payment cannot be extracted from the benefited parties or compensation enforced on behalf of the injured parties." Standard definition: "...whenever a decision variable of one eco- nomic agent enters into the utility function or production func- tion of another" Note: "directly enters", i.e. not indirectly through how the price may be modified when decisions change. This last case corresponds to a pecuniary externality Bernard Caillaud Externalities I.2. Definitions of externalities Externalities and markets A and B pump water from a well for their own consumption Given the finite amount of available water, the more A pumps, the more difficult for B to pump: externality If the well were owned by a firm C, that pays A and B a fixed hourly wage to pump water which then C sells, on the water market, to A and B: no externality ...! So the definition at best incomplete Hence later definitions by Meade, Arrow, Heller-Starett: "exter- nalities as nearly synonymous with nonexistence of markets." Bernard Caillaud Externalities I.2. Definitions of externalities Externalities and merger Two firms exert negative pollution externalities on each other If they merge, the cross effect becomes a technical relation- ship within the merged entity; no externality anymore If the economy consisted of one unique economic agent, there would be no externalities Externalities (standard definition) disappear when they are medi- ated by an appropriate market or in specific institutional setting! But micro-economic framework does not endogenize the set of economic agents nor the creation of markets. Take these as given! Bernard Caillaud Externalities I.3. Road map for today Objectives: Impact of externalities in the standard microeconomic frame- work Foundations for public / market intervention Introduction to public economics and environmental eco- nomics Precise roadmap: Definition of externalities Basic market failure in a simple example: Pareto optimum, competitive equilibria, intuition Restoring efficiency: quotas, taxes, mergers, creating new markets (competitive or not) What about remedies under informational problems ? Bernard Caillaud Externalities II. The basic market failure { II.1. A simple economy with externality A simple distribution economy: Two-good economy (1 and 2), two firms (a and b), and one consumer Production of good 2 by firm a affects the production func- tion of firm b a (Differentiable and concave) production functions: y2 = a a b b b a f (y1 ) and y2 = f (y1; y2 ) (Differentiable, increasing and strictly quasi-concave) utility function for the consumer: U(x1; x2) Consumer's initial endowment: (!1;!2) Bernard Caillaud Externalities II.2. Pareto optimal allocation max j U(x1; x2) xh≥0;yh≥0 a b !1 − y1 − y1 − x1 ≥ 0 [λ1] a b !2 + y2 + y2 − x2 ≥ 0 [λ2] a a a f (y1 ) ≥ y2 [µa] b b a b f (y1; y2 ) ≥ y2 [µb] Optimality condition at the optimum X0 = (x0; ya0; yb0): @U b a b a λ1 @x1 @f @f @f @f = @U = b = a + a · a λ2 @y @y @y @y @x2 1 1 2 1 Equalization of MRS to social MRT, where "social" means tak- ing into account all effects, direct and indirect (external) Bernard Caillaud Externalities II.2. Pareto optimal allocation b In the productive sector, dy1 = dy1 induces an increase in output @f b b dy2 = b dy1; no external effect: @y1 b dy2 @f b SMRT1;2 = − b jP rog= b = MRT1;2 dy1 @y1 a In the productive sector, dy1 = dy1 induces an direct increase in a @f a a output via dy2 = a dy1 and an indirect increase in output via @y1 b @f b a dy2 = a dy2 : @y2 a b a b a dy2 @f @f @f a @f @f SMRT1;2 = − a jP rog= a + a · a = MRT1;2 + a · a dy1 @y1 @y2 @y1 @y2 @y1 Bernard Caillaud Externalities II.2. Pareto optimal allocation Another example: externality in consumption Two-good economy, one firm and one consumer Consumption of good 1 by the consumer affects the produc- tion function of the firm : y2 = f(y1; ; x1) Optimality condition: equalization of social MRS and MRT @U + @U · @f λ1 @x1 @x2 @x1 @f = @U = λ2 @y1 @x2 dx yields direct increase @U dx and an increase in output 1 @x1 1 dy = @f dx , used to increase utility further by @U @f dx ; 2 @x1 1 @x2 @x1 1 to compensate, dx yields @U dx 2 @x2 2 @U + @U · @f SMRS = − dx2 = @x1 @x2 @x1 = MRSU + @f 1;2 dx1 @U 1;2 @x1 @x2 Bernard Caillaud Externalities II.3. Competitive equilibrium Competitive equilibrium with externalities Same as without externalities, except that agents take prices AND others' decisions as given: (p∗; x∗; ya∗; yb∗) with: a∗ ∗ a ∗ a a a a y maximizes p1(−y1 ) + p2y2 s.t. y2 ≤ f (y1 ) b∗ ∗ b ∗ b b b b a∗ y maximizes p1(−y1) + p2y2 s.t. y2 ≤ f (y1; y2 ) x∗ maximizes U(x) s.t. p∗ · x ≤ p∗ · ! + Π(p∗) ∗ a∗ b∗ ∗ a∗ b∗ Markets clear: x1 = !1 − y1 − y1 ; x2 = !2 + y2 + y2 Equilibrium: equalization of private MRS and private MRT to ratio of prices: @U @f b @f a p∗ @x1 = = = 1 @U @yb @ya p∗ @x2 1 1 2 Bernard Caillaud Externalities II.3. Competitive equilibrium Inefficiency of competitive equilibrium under externalities In general, the competitive equilibrium is not a Pareto optimum Competitive equilibrium equalizes private MRS and MRT; Pareto optimality requires to equalize social MRS and MRT Hence they are not consistent (except in degenerate cases, @f b e.g. here if for the equilibrium allocation, a = 0) @y2 Too much decentralization of economic decisions Partial equilibrium argument: an agent whose consump- tion / production creates positive (negative) external effects decides typically to consume / produce too little (too much) compared to the Pareto optimum In general equilibrium, though, i.e. through price and revenue effects, this intuitive prediction can be reversed. Bernard Caillaud Externalities II.4. Partial equilibrium reasoning Producing steel imposes additional cost D to society (USD 100 / ton): Equilibrium yields too high production of steel P of steel social marg. cost = SMRT marg. cost = MRT O dem. = MRS = SMRS D E Q of steel Bernard Caillaud Externalities II.4. Partial equilibrium reasoning Smoking causes disutility C to society (USD 40c / pack): Equi- librium yields too much smoking P of cigarettes marg. cost = MRT = SMRT C E dem. = MRS O social marg benefit = SMRS Q of cigarettes Bernard Caillaud Externalities III. Restoring efficiency { III.1. Quotas and taxes Since the competitive market does not lead to an efficient allo- cation, there is scope for government intervention besides pure redistributive purposes First solution: central planner imposes the level of externality- generating activities Impose all externality-generating decisions at their optimal levels Or, depending whether the equilibrium leads to an excessive or an insufficient decision from the agent, impose a maximum quota (ceiling) or a minimum quota (floor) at the optimum level of this activity Not realistic if multiple local decentralized externalities Even if one large externality by multiple heterogeneous ac- tors: information necessary and monitoring of each actor Bernard Caillaud Externalities III.1. Quotas and taxes Distribution of equal quotas to heterogeneous firms vs global quota with tradable permits among firms (perfect competition) cost of pollution reduction A’s mg cost B’s mg cost total mg cost social marg benefit of depollution q 2q reduction of emissions Bernard Caillaud Externalities III.1. Quotas and taxes Second solution: tax the externality-generating activity Normalize p2 = 1 Let τ the ad-valorem personalized tax (subsidy) paid by a- firm on its production of good 2 The total amount of taxes levied is redistributed to the con- sumer as a lump sum payment T (assume consumer takes this transfer as given !): adds up to the consumer's revenue Competitive equilibrium with taxes: choose tax at the level of its marginal externality effect evaluated at the Pareto op- @f b 0 timum, τ = − a (X )(Pigouvian taxes) @y2 Bernard Caillaud Externalities III.1. Quotas and taxes Competitive equilibrium with taxes yields: @U @x1 @U = p1 @x2 a b @f p1 p1 @f = = b and = p1 a @f 0 b @y1 1 − τ 1 + a (X ) @y1 @y2 Therefore, the Pareto optimum X0 is an equilibrium with price: @U (X0) p = @x1 1 @U (X0) @x2 b a b a @f 0 @f 0 @f 0 @f 0 = b (X ) = a (X ) + a (X ) · a (X ) @y1 @y1 @y2 @y1 Bernard Caillaud Externalities III.1. Quotas and taxes In the example, the (unique) competitive equilibrium with these taxes is the Pareto optimum τ = marginal externality at the optimum, i.e.