AAEC 6524: Environmental Theory and Policy Analysis. Outline. Environmental Policy with Pre-existing Distortions Part B. Klaus Moeltner Spring 2017

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1 under AAEC 6524: Environmental Theory and Analysis Environmental with Pre-existing Part B Klaus Moeltner Spring 2017 March 2, / 31 Outline under under 2 / 31

2 Closer look at MIE under, continued Note: X = X (w, p), so dx = ( X (.) / p) dp Re-write FOC as: ( u X (.) C (.) + (1 + λ) N MIE depends on: / X (.) ) wm } p {{ p } MIE 1. size of labor supply elasticity ɛ L (via λ) = D (X ) 2. relationship between N and X (complements, substitutes) 3. price elasticity of demand for X 3 / 31 Another look at MIE under, continued Define ɛ X = η XN = X (.) w X (.) p p X (1 m)w X By Slutsky symmetry: Then: own-price elasticity of X elasticity of substitution between X and N N(.) p = ( ) MIE = (1 + λ) ηxn ɛ X p m 1 m X (.) w 4 / 31

3 Summary under, continued If G is raised only through tax on labor: (a) Marginal social cost of reducting X (and thus E) is higher (lower) than in first-best when X, N are substitutes (complements) (b) Optimal X is larger (smaller) than in first-best when X, N are substitutes (complements) (c) The difference between first- and second-best pollution level is larger (in absolute terms) when: (i) labor supply is more elastic (ii) demand for X is less price-responsive, and / or (iii) complement / substitute relationship between X and N is stronger. 5 / 31 under, continued New government budget constraint: G = wm (T N) + τx Social planner chooses τ, m X, N, p determined via: u X (X, N) = p u N (X, N) = (1 m) w C (X ) = p τ Government extracts τ = p C (X ) from firm 6 / 31

4 Regulator problem under, continued max τ,m U (X, N) + Z D (X ) + px C (X ) τx s.t. w m (T N) + τx = G As before G returned to consumer: Z = (1 m) w (T N) px + G = w (T N) px + τx max τ,m U (X, N) + w (T N) D (X ) C (X ) + λ (w m (T N) + X (p C (X )) G) 7 / 31 FOCs under, continued FOC for m same as before FOC for τ: ( N (.) / ) X (.) u X (.) C (.)+(1 + λ) wm τ τ }{{} MIE D (X ) ( +λ / ) X τ + X = τ }{{} MRE Note: / N(.) X (.) τ τ / = N(.) X (.) p p 8 / 31

5 Marginal Revenue Effect under, continued ( / ) X MRE = λ τ + X τ / X τ + X τ = change in revenue raised as X changes Scale this by λ to obtain marginal welfare value of this change. Interpret MRE as or in the social cost of a unit of X. This extra cost is due to or in public funds that need to be raised in the (distorted) labor market. 9 / 31 Sign of MRE under, continued Over full range of X, can be positive or negative Starting at τ = 0, incremental reduction in X increases revenue, so MRE < 0 However, as X continues to, tax base shrinks (less X ) At some point subsequent reduction in X leads to marginal in revenue from the pollution charge, and MRE > 0 10 / 31

6 Sign of MRE under, continued Assuming C (X ) = c, we can express MRE as: ( ) MRE = λ τ + p ɛ X MRE < 0 when τ <<< p and/or demand for X is inelastic (ɛ X small) 11 / 31 Sign of MRE under, continued Suppose for a moment N (.) / p = 0 (no MIE effect) u X (.) C (X ) + MRE = D (X ) We can then study the MRE effect in isolation 12 / 31

7 MRE and ɛ X 42 Figure 7.4 $ X(p,w) under, continued P RE p τ 0 X RE X * X c C (X)+D (X) C (X)=c X $ ux C (X)+MRE X RE D (X) ux C (X)=MAC 0 X X c MRE 13 / 31 Edited June 24, 2014 Summary under, continued Assume G is raised through tax on labor and emission Assume MIE = 0 (no interaction effect with labor market) Optimal X differs from first-best X via revenue effect MRE, where: (a) MRE is smaller (perhaps even < 0) when demand for X less price-elastic (b) MRE is smaller when τ is small relative to p (c) MRE lowers soc. cost of abatement when it s negative (X RE < X ) (d) MRE increases soc. cost of abatement when it s positive (X RE > X ) 14 / 31

8 Definition of under, continued Weak form: Welfare if revenues raised via env. policy are used to offset distortionary taxation, rather than refunded as lump sum. This is always true. Strong form: Emission fee should be set above its partial equilibrium level more pollution reduced, more revenue raised. At same time, reduce labor tax. 15 / 31 Requirements under, continued From our model: MSC = u X (.) C (X ) + MIE + MRE = MAC + MIE + MRE Strong form of DD requires MSC < MAC, i.e. MIE + MRE < 0 Means: spillover effects of env. policy reduce marg. social cost. 16 / 31

9 Requirements under, continued Strong DD implies X GE < X ( GE = general equilibrium) MIE and MRE serve to reduce MSC of abatement relative to the partial equilibrium. Three possibilities: 1. MIE < 0, MRE < 0 2. MIE < 0, MRE > 0, MIE > MRE 3. MIE > 0, MRE < 0, MIE < MRE 17 / 31 Requirements under, continued First two s require N, X to be complements (p X, N ) Generally, empirical evidence suggests otherwise More promising: MIE > 0, MRE < 0, MIE < MRE 18 / 31

10 Closer look under, continued Assume C (X ) = c for simplicity (MC of producing X is constant) ( ) Then MRE = λ τ + p ɛ X MRE < 0 λ p τλ ɛ X > 0 DD if MIE/ MRE < 1 Unlikely to hold for reasonable values of m, λ, ɛ X, τ, p 19 / 31 Optimal second-best pollution level under, continued Under labor market distortions, we can only achieve a second-best optimum using environmental policy This entails rent extraction from firms to reduce distortionary taxes Resulting optimal X could be larger or smaller than in absence of distortion. Relative magnitude depends on signs and relative magnitude of MIE, MRE 20 / 31

11 Optimal X under MIE Figure > 50, MRE < 0, MIE > MRE under, continued $ u X C (X)+MIE+MRE u X C (X)+MIE MAC D (X) 0 X * X GE X IE X c X 21 / 31 under properties of env. policy instruments now become important Not just for welfare distribution, but for societal efficiency. 22 / 31

12 Pollution tax under Consider a decentralized emissions tax policy Firm profits: Π = px C (X ) τx Firm FOC: p = C (X ) + τ Consumer FOC: u X (X ) = p 23 / 31 Pollution Tax under Recall: MSC = u X (.) C (X ) + MIE + MRE Set τ = D (X ) MIE MRE to obtain u X (.) C (X ) + MIE + MRE = D (X ) Get second-best welfare-maximizing outcome X GE Raise τx GE in revenue 24 / 31

13 Auctioned Permits under Set X = X GE Permit price will evolve as σ = D (X ) MRE MIE Get second-best welfare-maximizing outcome X GE Raise σx GE in revenue 25 / 31 Freely distributed permits under Set X = X GE, distribute freely amongst firms Permit price will evolve as σ = D (X ) MRE MIE Price for X rises. Leisure demand adjusts accordingly. BUT: MRE = 0 - no revenue recycling effect. Overall welfare cost is higher than under tax or auctioned permits. 26 / 31

14 Command-and-control under Single firm: Same outcome as under freely distributed permits Firm retains scarcity rent p C ( X GE ) Multiple heterogeneous firms: Worse! Marg. abatement costs will be inefficiently high p will increase even more Larger interaction effect with (distorted) labor market. 27 / 31 Subsidies under Even worse. Need to be covered from additional distortions in the labor market. Highest social cost of abatement of all instruments. 28 / 31

15 under U = u (X, N, E) + Z Damage function becomes u E (X, N, E) Implies: depend on private choices and shape of u (.) Demands X (p, w, E), N (p, w, E) - depend on level of emission. 29 / 31 under Consider again spillover, but w/o revenue raising (regulator chooses X ) FOC w.r.t X : ( u X (.) + u E (.) C (.) + (1 + λ) ) wm N (.) X }{{} MIE = D (X ) 30 / 31

16 under New: / N X = N(.) X (.) p p And ( MIE = (1 + λ) + N(.) E N(.) p / X (.) p ) N(.) E wm Second term can change sign of MIE, depends on how abatement affects leisure. If N(.) E < 0 (complements) MIE increases. Example: More recreation in reaction to better site quality 31 / 31