Multiple distortions and second best environmental policy Economics 573 Brian Copeland 1. The model with only one distortion Preferences: Representative consumer Expenditure function E(p,u,z), E z is Marginal damage Assume E z (p,u,z) > 0. (ie pollution is bad) 1
Technology: National income function G(p,v,z) { } G ( p , v , z ) = max py : y ∈ T ( v , z ) y where v is an endowment vector and T is the technology set for the economy (see Copeland and Taylor's 2003 book, p. 37-45.) Note that ∑ ∑ G ( p , v , z ) = p i y i = w j v j + τ z i j where y i are outputs, w j are factor prices, and τ is the price of an emissions permit. Also note that price of emission permit is: τ = G z ( p , v , z ) . Assume the economy is small and open so that p is fixed by world markets. 2
Budget constraint of consumer: (1) for given z: E ( p , u , z ) = G ( p , v , z ) (0) (2) If pollution taxes used, τ is fixed by the government, and the supply of permits z is endogenous. E ( p , u , z ) = G ( p , v , z ) G z ( p , v , z ) = τ If there is no regulation, the equilibrium is given by the above two equations with τ = 0. Find the efficient level of pollution: E p dp + E u du + E z dz = G p dp + G z dz Rearranging: E u du = ( G p − E p ) dp + ( G z − E z ) dz . But since the economy is small and open (p fixed), and recalling that τ = G z , this reduces to: E u du = ( τ − E z ) dz 3
If fixing the level of permits: du dz = τ − E z = 0, → τ = E z E u If choosing the optimal pollution tax: du d τ = ( τ − E z ) dz d τ = 0, → τ = E z E u In either case, the optimal policy is to ensure that the price that firms pay for the right to pollute is equal to marginal damage. Standard result, but now using GE model. 4
2. Two types of pollution Now suppose there are two pollutants, z 1 and z 2 . Modifying our model (by treating z as a vector) the equilibrium conditions are now: E ( p , u , z 1 , z 2 ) = G ( p , v , z 1 , z 2 ) G z 1 ( p , v , z 1 , z 2 ) = τ 1 G z 2 ( p , v , z 1 , z 2 ) = τ 2 (a) First best policy E u du = ( τ 1 − E z 1 ) dz 1 + ( τ 2 − E z 2 ) dz 2 Optimal policy: τ 1 = E z 1 τ 2 = E z 2 5
(b) Second best policy when one pollutant cannot be regulated: Suppose now that type 2 pollution is not regulated. Choose the optimal tax for pollutant 1, under the constraint that τ 2 = 0: ∂ u = ( τ 1 − E z 1 ) ∂ z 1 + ( τ 2 − E z 2 ) ∂ z 2 = 0 E u ∂ τ 1 ∂ τ 1 ∂ τ 1 Noting that τ 2 = 0, and rearranging, we obtain: ∂ z 2 / ∂ τ 1 τ 1 = E z 1 + E z 2 (1) ∂ z 1 / ∂ τ 1 If the two types of pollutants are substitutes, then expect: ∂ z 2 > 0 ∂ τ 1 in which case (1) implies: τ 1 < E z 1 Pollution tax on type 1 pollution is less than the marginal damage caused by type 1 pollution. 6
(c) Taxes vs quotas. Suppose now that both types of pollutants are regulated, but regulation is too lax: τ 1 < E z 1 and τ 2 < E z 2 Government tightens up regulation for type 1 pollution but not type 2 pollution. Taxes: ∂ u = ( τ 1 − E z 1 ) ∂ z 1 + ( τ 2 − E z 2 ) ∂ z 2 E u ∂ τ 1 ∂ τ 1 ∂ τ 1 (3) ( − ) ( − ) ( − ) ( + ) Net effect on welfare could go either way. Quotas: Change type 1 quota; E u du = ( τ 1 − E z 1 ) dz 1 + ( τ 2 − E z 2 ) dz 2 Output of type 2 pollution fixed if quota binds: ∂ u = τ 1 − E z 1 < 0 E u ∂ z 1 7
Reducing the supply of type 1 pollutants will raise welfare even though type 1 and 2 pollutants are substitutes, and type 2 pollution is under-regulated. (d) Lessons 1. If there is more than one distortion in the economy, then trying to fix one distortion can have adverse side effects elsewhere because the other distortions may be exacerbated. 2. With multiple distortions, some of which cannot be internalized, then simple rules such as setting the pollution tax equal to marginal damage may not apply. 3. With multiple distortions, optimal second best policy may not be equivalent across taxes and quotas. 8
3. Monopoly Representative consumer partial equilibrium Let I be the exogenous level of income generated by the rest of the economy (not including monopoly profits or tax revenue). Let output be y and suppose that the inverse demand function is given by p(y). The firm's cost function is c(y,z). (a) Pollution taxes Assume that the government uses a pollution tax. The monopolist's profits are given by π = p ( y ) y − c ( y , z ) − τ z Profit maximization by the firm implies: π y = 0 → p y + p − c y = 0 ′ (4) π z = 0 → − c z = τ 9
Consumer's budget constraint is: E ( p , z , u ) = I + π + τ z Totally differentiating (recalling I is exogenous by our partial equilibrium assumption) yields: E u du = − E p ′ p dy − E z dz + ( ′ p y + p − c y ) dy − c z dz But using both of the first order conditions (4), we can simplify this to: E u du = ( τ − E z ) dz + ( p − c y ) dy (5) To find the optimal policy, we set du/d τ = 0. τ = E z − ( p − c y ) dy / d τ < E z dz / d τ ( + ) ( + ) Optimal pollution tax is less than marginal damage. (b) Other instruments Besanko (J Public Economics 1987) uses a simple oligopoly model to compare a pollution quota with a design standard (a requirement that firms install a certain level of abatement equipment). Using simulations, he shows that the design standard can dominate the pollution quota when the market is not competitive. 10
4. Trade liberalization Two goods: X and Y. X is imported and good Y is exported. Y is numeraire (so that its price is 1), World price of X by p. Country is small, p fixed X is initially protected with a tariff. Domestic price of X is p+t. Y pollutes during production; pollution is directly proportional to Y output. X does not generate pollution. Consumption does not pollute Representative consumer's budget constraint: E ( p + t , u , z ) = G ( p + t , v , z ) + tM where M = E p − G p (6) denotes imports. 11
Change tariffs (liberalize trade), leaving pollution tax unchanged: E u du = − ( E p − G p ) dt + tdM + Mdt + ( G z − E z ) dz Using (6) and recalling that τ = G z , we have: du dt = ( τ − E z ) dz dt + t dM E u (7) dt ( − ) ( − ) (?) If pollution is optimally regulated, then τ = E z , and (7) reduces to: du dt = t dM dt < 0 for t > 0. E u Trade liberalization raises welfare Free trade optimal. If pollution regulations are too weak ( τ < E z ): Liberalizing trade may raise or lower welfare. 12
To find the optimal tariff, set (7) equal to zero, and solve for t: t = − ( τ − E z ) dz / dt dM / dt > 0. ( − ) ( − ) ( + ) The optimal tariff is positive if τ < E z . By promoting the clean industry, the government draws resources out of the dirty industry and reduces pollution. This will be welfare improving if there is inadequate pollution policy. Other scenarios: If import-competing industry X pollutes, and the export industry Y is clean, then freer trade is good for the environment and also raises welfare 13
(5) Labour supply Labour supply is endogenous s . Denote income tax by m and labour supply by Labour time endowment L Labour is the only factor of production. Good X generates pollution during consumption, and we denote its fixed world price by p. Wage is w; assume fixed (Ricardian model will do this). Assume all tax revenue is rebated to the representative agent The consumer's budget constraint is: E ( p + τ , w − m , u , z ) = ( w − m ) L + m s + τ x Recall that E w is be the compensated demand for leisure. 14
Raise pollution tax: d τ + m d s du d τ = ( τ − E z ) dz E u d τ Two effects. Pollution falls, but it also affects labour supply. Supply of labour depends on the real wage. Pollution tax raises the price of consumption goods, and therefore lowers the real wage. If labour supply is an increasing function of the real wage (which the evidence supports), then we expect an increase in the pollution tax to reduce labour supply. Hence the optimal pollution tax is below marginal damage: τ = E z − m d s / d τ dz / d τ < E z Labour supply initially too low. Pollution tax exacerbates this distortion by reducing labour supply even more 15
Double Dividend Fixed government budget constraint: τ x + m s = R where R is the fixed revenue requirement. Key result in this literature (see Bovenberg and de Mooij AER 1994) is that the logic in the previous example above continues to apply, even when the income tax can be lowered in response to the higher pollution tax. Reduction in the income tax made possible by the higher pollution tax is not enough to offset the fall in the real wage caused by the increase in the pollution tax. Hence optimal pollution tax is still below marginal damage. Weak "double dividend" 16
Conclusion Introducing pollution policy to fix one market failure can exacerbate market failures elsewhere. Second best optimal pollution policy takes into account the effects of pollution policy on the other distortions. Better policy would have the government try to fix all distortions - broad based, rather than piecemeal reform Not always possible to correct all distortions Policymaker needs to be aware of the potential side effects of a proposed policy reform, and may need to take action to mitigate the side effects. Presence of multiple distortions affects choice between pollution regulatory instruments. 17
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