Targets of Environmental Policy

ERE9: Targets of Environmental Policy • Optimal targets – Flow pollution – Stock pollution • When location matters • Steady state – Stock-flow pollutant • Steady state • Dynamics • Alternative targets Last week • Valuation theory • Total economic value • Indirect valuation methods – Hedonic pricing – Travel cost method • Direct valuation methods Environmental & Resource Economics • Part 1: Introduction – Sustainability – Ethics – Efficiency and optimality • Part 2: Resource economics – Non-renewables – Renewables • Part 3: Environmental economics – Targets – Instruments • Part 4: Miscellaneous – Valuation (next course) – International environmental problems (next course) – Environmental accounting Pollution • Pollution is an externality, that is, the unintended consequence of one‘s production or consumption on somebody else‘s production or consumption • Pollution damage depends on – – – – Assimilative capacity of the environment Existing loads Location Tastes and preferences of affected people • Pollution damage can be – Flow-damage pollution: – Stock-damage pollution: – Stock-flow-damage pollution: D=D(M); M is the flow D=D(A); A is the stock D=D(M,A) Economic activity, residual flows and environmental damage Efficient Flow Pollution • Damages of pollution D=D(M) • Benefits of pollution B=B(M) • Net benefits NB=B(M)-D(M) • Efficient pollution Max NB ∂NB ∂B ∂D ∂B ∂D = − =0⇔ = ∂M ∂M ∂M ∂M ∂M Efficient level of flow pollution emissions D(M) B(M) D(M) B(M) Total damage and benefit functions Maximised net benefits M dD dM µ* dB dM M* Marginal damage and benefit functions M The economically efficient level of pollution minimises the sum of abatement and damage costs Costs, benefits Marginal X benefit Marginal damage A Y D C B M M* M’ Quantity of pollution emission per period Types of externalities • Area B: Optimal level of externality • Area A+B: Optimal level of net private benefits of the polluter • Area A: Optimal level of net social benefits • Area C+D: Level of non-optimal externality that needs regulation • Area C: Level of net private benefits that are unwarranted • M*: Optimal level of economic activity • M‘: Level of economic activity that maximises private benefits Efficient Flow Pollution (2) • Optimal pollution is greater than zero • The laws of thermodynamics imply that zero pollution implies zero activity, unless there are thresholds (e.g., assimilative capacity) • Optimal pollution is greater than the assimilative capacity • Pollution greater than the optimal pollution arises from discrepancies between social and private welfare Steady State (2) ∂D ∂B ∂A = ∂M r +α • Marginal benefit of the polluting activity equals the net present value of marginal pollution damages • Benefits of pollution are current only • Damages of pollution are a perpetual annuity • The decay rate ( ) acts as a discount rate α Steady State (3) ∂D ∂B ∂D ∂B ∂B ∂D ∂B ∂B r ∂ A = ⇔ = α+ r⇔ = + ∂M r +α ∂A ∂M ∂M ∂A α ∂M ∂M α A= M ∂D ∂D ⇒ = α ∂M α ∂A ⇒ ∂D ∂B = ∂M ∂M 1 + r   ÷  α Distinguish four cases: r=0 r>0 imperfectly persistant pollutant perfectly persistant pollutant α>0 A B α=0 C D Steady state: Case A • Case A r = 0, α > • Equation collapses to ∂D ∂B = ∂M ∂M • In the absence of discounting, an efficiency steady-state rate of emissions requires that – the marginal benefits of pollution should equal the marginal costs of the pollution flow – which equals the marginal costs of the pollution stock divided by its decay rate ∂D ∂D ∂B = = ∂M ∂A α ∂M Steady state: Case A (2) dD dM dB dM µ* M* ˆ M In the steady-state, A will have reached a level at which αA*=M* M Steady state: Cases A and B dB  r 1 +  dM  α dD dM dB dM µ** µ* M* M** Case A: r = 0, α > Case B: r > 0, α > ˆ M M Steady State: Cases C and D Case C: r > 0, α = Case D: r = 0, α = The pollutant is perfectly persistent In the absence of assimilation, the steady state can only be reached if emissions go to zero • Clean-up expenditures might allow for some positive level of emissions • • • • Efficient Stock-Flow Pollution • Pollution flows are related to the extraction and use of a nonrenewable resource – For example, brown coal (lignite) mining • What is the optimal path for the pollutant? • Two kind of trade offs – Intertemporal trade-off – More production generates more pollution • Pollution damages through – utility function – production function + U = U (C , E ) + • E is an index for environmental pressure • V is defensive expenditure − + − Q = Q (R , K , E ) + + E = E (R , A ) + F = F (V ) The optimisation problem maxW = Ct ,Rt ,Vt ∞ − ρt U ( C , E ( R , A )) e dt ∫ t t t t=0 subject to S& t = −Rt A& t = M (Rt ) − α At − F (Vt ) • Current value Hamiltonian: K& t = Q (Kt , Rt , E (Rt , At )) − Ct − G (Rt ) −Vt H = U (Ct , E (Rt , At )) + Pt ( −Rt ) + λt (M (Rt ) − αAt − F (Vt )) • Control variables: C, R, V • State variables: S,tK, A t • Co-state variables: P, ω, λ +ω (Q (K , Rt , E (Rt , At )) − Ct − G (Rt ) −Vt ) Static Efficiency H = U (Ct , E (Rt , At )) + Pt ( −Rt ) + λt (M (Rt ) − αAt − F (Vt )) +ωt (Q (Kt , Rt , E (Rt , At )) − Ct − G (Rt ) −Vt ) ∂H = UC − ω = ⇔ UC = ω ∂C ∂H = UE ER − P + ωQR + ωQE ER − ωGR + λMR = ∂R ∂H = −ω − λFV = ⇔ ω = −λFV ∂V Dynamic Efficiency H = U (Ct , E (Rt , At )) + Pt ( −Rt ) + λt (M (Rt ) − αAt − F (Vt )) +ωt (Q (Kt , Rt , E (Rt , At )) − Ct − G (Rt ) −Vt ) ∂H & P =− + ρ P ⇔ P&= ρ P ∂S ∂H ω&= − + ρω ⇔ ω&= ρω − ωQK ∂K ∂H & λ=− + ρλ ⇔ λ&= ρλ + α − UE EA − ωQE EA ∂A Shadow Price of Resource ∂H = UE ER − P + ωQR + ωQE ER − ωGR + λMR = ⇔ ∂R ωQR = P + ωGR − UE ER − ωQE ER − λMR • Gross price = Net price + extraction costs + disutility of flow damage + loss of production due to flow damage + value of stock damage • Flow and stock damages need to be internalised! Optimal time paths for the variables of the pollution model Pt+ωGR-UEER-ωQEER-λMR Pt+ωGR-UEER-ωQEER Units of utility Pt+ωGR-UEER Stock damage Production flow damage Utility flow damage Gross price Marginal extraction cost Pt+ωGR Pt = net price Net price τ time, t A competitive market economy where damage costs are internalised Units of utility Stock damage tax Pollution flow damage tax Utility damage tax Pt+ωGR= Gross price Social costs Marginal extraction cost Private costs Pt = net price Net price τ time, t Efficient Clean-up ∂H = −ω − λFV = ⇔ ω = −λFV ∂V • The shadow price of capital equals the shadow price of stock pollution times the marginal productivity of the clean-up activity • Ergo, environmental clean-up (defensive expenditure) is an investment like all other investments Alternative Standards • Optimal pollution is but one way of setting environmental standards and not the most popular • The main difficulty lies in estimating the disutility of pollution • Alternatives – Arbitrary standards – Safe minimum standards – Best available technology (not exceeding excessive costs) – Precautionary principle [...]... Price of Resource ∂H = UE ER − P + ωQR + ωQE ER − ωGR + λMR = 0 ⇔ ∂R ωQR = P + ωGR − UE ER − ωQE ER − λMR • Gross price = Net price + extraction costs + disutility of flow damage + loss of production due to flow damage + value of stock damage • Flow and stock damages need to be internalised! Optimal time paths for the variables of the pollution model Pt+ωGR-UEER-ωQEER-λMR Pt+ωGR-UEER-ωQEER Units of utility... the absence of assimilation, the steady state can only be reached if emissions go to zero • Clean-up expenditures might allow for some positive level of emissions • • • • Efficient Stock-Flow Pollution • Pollution flows are related to the extraction and use of a nonrenewable resource – For example, brown coal (lignite) mining • What is the optimal path for the pollutant? • Two kind of trade offs – Intertemporal... D Steady state: Case A • Case A r = 0, α > 0 • Equation collapses to ∂D ∂B = ∂M ∂M • In the absence of discounting, an efficiency steady-state rate of emissions requires that – the marginal benefits of pollution should equal the marginal costs of the pollution flow – which equals the marginal costs of the pollution stock divided by its decay rate ∂D ∂D 1 ∂B = = ∂M ∂A α ∂M Steady state: Case A (2) dD... internalised Units of utility Stock damage tax Pollution flow damage tax Utility damage tax Pt+ωGR= Gross price Social costs Marginal extraction cost Private costs Pt = net price Net price τ time, t Efficient Clean-up ∂H = −ω − λFV = 0 ⇔ ω = −λFV ∂V • The shadow price of capital equals the shadow price of stock pollution times the marginal productivity of the clean-up activity • Ergo, environmental clean-up... M α • Steady state ∂B = −µ ∂M ∂D ∂D ∂B ∂ A −r µ = + αµ ⇒ − µ = = ∂A r + α ∂M Steady State (2) ∂D ∂B ∂A = ∂M r +α • Marginal benefit of the polluting activity equals the net present value of marginal pollution damages • Benefits of pollution are current only • Damages of pollution are a perpetual annuity • The decay rate ( ) acts as a discount rate α Steady State (3) ∂D ∂B ∂D ∂B ∂B ∂D 1 ∂B ∂B r ∂ A... environmental clean-up (defensive expenditure) is an investment like all other investments Alternative Standards • Optimal pollution is but one way of setting environmental standards and not the most popular • The main difficulty lies in estimating the disutility of pollution • Alternatives – Arbitrary standards – Safe minimum standards – Best available technology (not exceeding excessive costs) – Precautionary... with short lifetime: When location matters Wind direction and velocity R1 R2 S1 S2 R4 S: Source R: Urban area R3 Stock pollutants with longer lifetime: Efficient pollution • Damages of pollution Dt = D (At ) • Benefits of pollution Bt = B (Mt ) • Stock A& t = Mt − α At with decay rate 0 < α < 1 • Net current benefits NB = B (M ) − D (A ) • Efficient pollution Max NPVNB • Hamiltonian: H = B (M ) − D...Stock pollutants lifetime pre-industrial concentration CO2 (carbon dioxide) CH4 (methane) N2O (nitrous oxide) CFC-11 (chloroflouro carbon-11) HFC-23 (hydrofluoro carbon-23) concentration in 1998 atmospheric lifetime ca 280 ppm 365 ppm 5-200 yr ca 700 ppb 1745 ppb 12 yr ca 270 ppb 314 ppb 114 yr zero 268 ppt 45 yr zero 14 ppt 260 yr Sulphur... example, brown coal (lignite) mining • What is the optimal path for the pollutant? • Two kind of trade offs – Intertemporal trade-off – More production generates more pollution • Pollution damages through – utility function – production function + U = U (C , E ) + • E is an index for environmental pressure • V is defensive expenditure − + − Q = Q (R , K , E ) + + E = E (R , A ) + F = F (V ) The optimisation