Reyer Gerlagh. Tilburg University

Transcription

1 The Green Paradox Tilburg University

2 Introduction Policy questions What is optimal climate change policy? Should we tax carbon dioxide emissions? Now / in the future / ramping up carbon taxes? Should we develop clean energy alternatives for oil / coal / gas? Main insight: Fossil fuels markets are dynamically integrated Expected policies at future time t affect current market (!) Future carbon taxes can backfire if they increase current emissions If we cannot set optimal pollution constraints, we must worry about effect of policy on abundant polluting resource extraction: coal and unconventional oil 04 July

3 Discovery of Climate Change Oil connection Oil crisis: Maedows et al 1972; Solow/Stiglitz/Dasgupta/Heal 1974 Climate change: Earth Summit Rio de Janeiro 1992 High does nothing and rising is worse: carbon taxes should keep declining i to cut harmful emissions i (Sinclair i 1992) On the optimum trend of fossil fuel taxation (Sinclair 1994) The optimal time path of a carbon tax (Ulph and Ulph 1994) Depletion of fossil fuels and the impact of global warming (Hoel and Kverndokk 1996) Fossil fuels, stock externalities, and backstop technology (Tahvonen 1997) 04 July

4 Silence? ( more (more important questions) Shift in attention, from optimal climate change policy connected to exhaustible resources considerations, to distributional question: who pays, who gains: (1) timing of optimal policy (discounting) & (2) international cooperation Act or delay climate change policy? Should we discount future damages? They will only happen after 2100, so why worry? Nordhaus WD (1993), Rolling the DICE: an optimal transition path for controlling greenhouse gases, Resource and Energy Economics 15: We will not be able to cooperate internationally! Barret, S. (1994), Self-enforcing international environmental agreements, Oxford Economic Papers 46: July

5 2008 The oil market matters: The Green Paradox Public policies against global warming: a supply side approach (Sinn 2008) Technology treaties ti and fossil-fuels f l extraction ti (Strand 2008) Bush meets Hotelling: effects of improved renewable energy technology on greenhouse gas emissions (Hoel 2008) Strategic Resource Dependence (Gerlagh and Liski 2011) 04 July

6 2010-now The Green Paradox, revised Too much oil (Gerlagh 2009/2011) Biofuel subsidies and the green paradox (Grafton, Kompas, van Long 2010) Is there really a green paradox? (van der Ploeg and Withagen 2010) Climate change and carbon tax expectations (Hoel 2010) The Supply Side of CO2 with Country Heterogeneity (Hoel 2011) Cutting costs of catching carbon (Hoel and Jensen 2010) Can Brown Backstops undo the GP (Michielsen 2011) 04 July

7 Introduction Overview Aim: connect climate policy questions to resource economics models Gradually build model (add elements) Open research questions 04 July

8 Model I: Sinclair (1992,1994) Fossil fuels & climate change High does nothing and rising is worse: carbon taxes should keep declining to cut harmful emissions (Manchester School 60:41-52) The key decision i of those lucky enough to own oil-wells ll is not so much how much to produce as when to extract it. (1992) Fossil fields are a stock. Coal or oil burnt at one date means that there is less to burn later (1994) Rising carbon taxes, mean lower future profits for fossil fuel owners, and dynamic arbitrage implies they accept lower present prices (at higher supply) ppy) 04 July

9 Model I: Sinclair (1992,1994) Reduced Model Set Up Sinclair has fully closed model (Cobb-Doublas production with utility max) with endogenous interest rate I think that s insubstantial. Main intuition is simple / partial Demand: Qt () = AtDP () ( c()) t = e Pc() t Supply: St () = Et () S(0) = 0 E( t) dt Resource price inclusive i tax: Pc () t = P () t Z () t zt () Zt ()/ Zt () Dynamic Fossil Fuel Policy: Hotelling rule (dynamic arbitrage): at σ P ()/ t P () t = r+ z c c 04 July

10 Model I: Sinclair (1992,1994) Iso-elastic demand Substitution: Total stock: ( z + r ) t at ( z + r ) t P () t = P (0) e E() t = e E(0) e σ c c at σ ( z+ r ) t σ 0 S (0) = E (0) e e dt { a σ ( r+ z)} t E(0) = E (0) 0 e dt = σ ( r+ z) a Present emissions increase with increasing taxes: E(0) = { σ ( z+ r ) a } S(0) Can we do better = more general? 04 July

11 Model I: Sinclair (1992,1994) General demand Assume competitive market = Hotelling rule: Stock = cumulative supply = cumulative demand ( r + z ) t 0 Δ S = ( P, Z, z) = D( e Z P ) dt ΔP < 0; Δ 0; 0 0 Z < Δ 0 z < Change in future tax (z), must be offset by change in initial iti price ds d dp dz dp0 ΔP dz Δ z 0 0= 0 = Δ = Δ P + Δ = < z Future higher carbon tax (dz>0) implies lower current price (dp 0 <0) implies higher current emissions (de 0 >0). 04 July

12 Model I: Sinclair (1992,1994) Policy implications Sinclair emphasizes that to study climate change requires closed economy, as climate change causes major damages. Otherwise, his analysis would resemble too much Dasgupta & Heal (1979) but his analysis is unclear (who understands 1992, eq (2)+(7)?) Moreover, I wonder whether closed economy + strong unrealistic assumption on damages is better then partial economy Main climate change damages ages after 2100, main fossil fuel use before 2100 separation? Conclusion stands: High does nothing and rising is worse: carbon taxes should keep declining to cut harmful emissions [discuss] Declining refers to ad valorem tax as price factor, per volume tax can increase 04 July

13 Model II: Ulph and Ulph (1994) Efficient carbon tax = NPV marginal damage Fundamental principle: Optimal carbon tax = Pigouvian tax = NPV marginal damage As CO2 levels l increase, and damages are convex, marginal damages are increasing in CO2 marginal damages increasing over time Sinclair (1992) cannot be correct. Sinclair assumes (Z 0,z) policy, optimal policy must be more complicated ca Use partial analysis (utility of resource use), no closed economy Use linear demand and marginal damages to solve explicitly 04 July

14 Model II: Ulph and Ulph (1994) Increasing tax = decreasing tax? Is there a fundamental difference in result? Optimal carbon tax = NPV marginal damage = increasing per volume To delay fossil fuel extraction, carbon tax must be decreasing as percentage of rent value As rent prices increase with interest rate, both can be satisfied Numerical illustration U&U suggest optimal carbon tax that is hump-shaped (increasing-decreasing) as percentage of value Intuition: optimal carbon tax tries to smooth damages, shave off large concentration levels (convex damages), more early emissions (2010), more late emissions (>2100), less peak emissions (2050). 04 July

15 Model II: Ulph and Ulph (1994) Model set up Benefits of resource use U(E) ( ) (net of extraction costs), damages of pollution stock D(M) rt Max W = 0 e { UEt ( ( )) Ω ( Mt ( ))} dt λ: St () = Et () τ: Mt () = Et () δ Mt () Hamiltonian: H= UEt ( ()) Ω ( Mt ()) λ() tet () τ()( t Et () δmt ()) FOC: 0 = H ; rλ = H + λ; rτ = H + τ E S M 04 July

16 Model II: Ulph and Ulph (1994) Main results FOC: U'( E ) = λ + τ λ = rλ τ = ( r + δ ) τ Ω '( M) Marginal productive value of FF = Hotelling rent + Pigouvian tax Hotelling rent increases with interest rate Pigouvian tax: (i) Pollution depreciation present emissions maximally exploits nature s capacity to neutralize! Favour high current use High future taxes (ii) Increasing marginal damages of stock present pollution increases future marginal damages smooth emissions high present taxes At initial low concentrations (2010), (i) dominates, at peak concentrations (2050), (ii) dominates optimal carbon taxes will first increase fast, then curve back 04 July

17 Model II: Ulph and Ulph (1994) Graphical representation BAU vs Optimal Policy Concentrations (M) Emissions i (E) Optimal policy tries to avoid peak concentration with peak marginal damages Total cumulative emissions not affected 04 July

18 Model II: Ulph and Ulph (1994) Linear demand and damages (1) U ue= λ + τ T (2) S 0 = 0 Edt (3) M = E δ M (4) λ = rλ (5) τ = ( r+ δτ ) ωm Given M(0), choose λ(0) and τ(0) such that (2) is met, where demand d should be zero at final date T, and Pigouviani tax satisfies (6) λ( T) + τ ( T) = U r ( t T ) ( δ + r ) t ω MT ( ) (7) τ ( T) = T e ωmtdt ( ) = ωmt ( ) 0 e dt= δ + r 04 July

19 Model II: Ulph and Ulph (1994) Conclusions Even linear model is too difficult to say much about path, analytically. Numerical illustrations ti suggest increasing i ad valorem tax, initially, iti curving back, later. 04 July

20 Model III: Hoel and Kverndokk (1996) & Tahvonen (1997) Economic exhaustion of fossil fuels (1) Extraction costs depend on cumulative extraction: we go into deep-water oil wells (Gulf of Mexico) as we run out of cheap oil. Oil exhaustion is economic, not physical cumulative emissions i depend on economy & policy + (2) future energy supply when running out of oil depends on substitute = backstop Use similar partial equilibrium framework as Ulph & Ulph Main result: carbon taxes should delay part of fossil fuel use to long-term, overlap fossil fuels and clean energy (backstop) era 04 July

21 Model III: Hoel and Kverndokk (1996) & Tahvonen (1997) Model set up Benefits of energy use U(E+B) ( ) (with backstop), extraction costs c(s), ( ) (c'<0 as stocks decrease), damages of pollution stock D(M) rt Max W = 0 e { UEt ( () + Bt () ) c ( St ()) Et ( ) ψ B ( t ) Ω ( M () t )} dt Hamiltonian: H= U ( E+ B ) c ( SE ) ψ B Ω ( M ) λ E τ ( E δ M ) FOC: U'( E+ B ) cs ( ) λ + τ E 0 U'( E+ B ) ψ B 0 λ = rλ + c'( SE ) τ = ( r+ δτ ) Ω'( M) 04 July

22 Model III: Hoel and Kverndokk (1996) & Tahvonen (1997) Long-term steady state Economically viable resources are used: E( )=0; ( ) S( )=S( ) ; λ( )=0( ) All pollution has decayed: M( )=0 No Pigouvian tax needed: τ( )=0 Marginal value of energy = marginal costs for substitute: U'( )=ψ marginal extraction costs = marginal value: U'( )=c(s( )) Cumulative fossil fuel use independent of climate change problem! But what is economic counterpart of mathematical convergence? 04 July

23 Model III: Hoel and Kverndokk (1996) & Tahvonen (1997) Transition to long-term steady state Available backstop sets limit to fossil fuel extraction costs c(s) U'(E+B) λ τ and U'(E+B) ψ => c(s) ψ τ When backstop is in use, and pollution decays (τ decreases), fossil fuels will slowly be further depleted BAU vs Optimal Policy Emissions (E) July

24 Sinclair, Ulph&Ulph, Hoel & Kverndokk, Tahvonen: Summary Dasgupta-Heal (1979): constant ad-valorem taxes don t change resource extraction Sinclair i (1992,1994): 1994) to reduce climate change, we must delay fossil fuel extraction high upfront taxes, decreasing over time Ulph & Ulph (1994): we must reduce peak climate change, smooth fossil fuel use through high taxes at peak Hoel and Kverndokk (1996) & Tahvonen (1997): use all fossil fuel reserves but extend fossil fuel era to overlap with backstop era 04 July

25 Model IV: Sinn (2008) The Green Paradox Climate change policy has looked at demand side only: reducing demand for fossil fuels. But demand-side policy doesn t carry far if supply is inelastic. Result 1: 100% carbon leakage: environmental sinners to consume what the Kyoto countries have economized on Result 2: Green paradox: gradual greening of Kyoto policies will advance a fossil fuel extraction Fossil fuels about 4,000 GtC 1200 ppmv very hot 04 July

26 Model IV: Sinn (2008) Dynamics: extraction vs. stock Nice math: consider movement in (E,S)-space: de/ds Notice that E= ds/dt, y-value is speed to left If E=f(S) is continuously differentiable, then curves cannot cross If all scenarios go through (0,0) 0) and Scenario I has higher de/ds, then resource is exhausted earlier 04 July

27 Model IV: Sinn (2008) The economy Welfare with non-constant interest rate (r(t)=r'(t)),( ) ( ) fossil fuel extraction, and climate damages with no depreciation: Rt () 0 { ( ) ( ) Ω ( 0 )} W = e U E c S E S S dt S = E FOC E: P(t) U'(E(t))=c(S(t))+λ(t) FOC λ = rλ+ c'( S ) E Ω'( S S ) Substitution: P = λ c ' E = r ( P c ) Ω ' ˆ c Ω ' P= r(1 ) P P 0 ( c' < 0; Ω ' > 0) 04 July

28 Model IV: Sinn (2008) Demand side Competitive energy demand market for fossil fuels: U'(E) ( ) = P(E) ( ) From demand: U'' E= P de E ˆ P ' = = E= U = σ ( E) Pˆ ds S EU'' P Pareto optimal path: de c Ω ' = σ ( E ){ r (1 ) } ds P P Efficient Market equilibrium: de c = σ ( Er ) (1 ) ds P 04 July

29 Model IV: Sinn (2008) Supply side with insecure property rights Insecure property rights: hazard rate of loosing ownership π: λ = ( r+ π) λ+ c'( S) E Substitution in rents: P = ( r+ π )( P c( S)) Substitution in demand-side dynamics de ds c ( S ) = σ ( E )( π + r )(1 ) P( E) Extraction goes up with π. 04 July

30 Model IV: Sinn (2008) Green policies Assume government taxes fossil fuel rents at factor Z, growing at constant rate Z Rt () πt PEE ( ) cse ( ) 0 Λ = e dt Z 1 Rt () ( π+ zt ) = 0 e { P( E) E c( S) E} dt Z(0) The tax just works as extra time discounting: P = ( r+ π + z)( P c( S)) 04 July

31 Model IV: Sinn (2008) Green Paradox Benchmark: Market with full property rights Insecure property rights speed up extraction Green policies with increasing taxes further speed up extraction! While PE policy would be to delay 04 July

32 Model IV: Sinn (2008) Robust policies? A gloomy picture High upfront carbon taxes Politically impropable Safer property rights Practically difficult in many countries Binding supply quantity constraints Needs rigid global agreement Would kill fossil fuel rents! Technical means to decouple the accumulation of carbon dioxide from carbon consumption Afforestation insufficient CCS dangerous to trust on 04 July

33 Model V: Strand (2008) Can technology cooperation save us? International negotiators search for acceptable solutions to combat climate change Politicians i don t like carbon taxes, and emission i quota. They do like technology fixes If we jointly search for competitive clean energy = marginal costs < extraction costs for fossil fuels, and find one, we solve the climate change problem. obe Or do we? The perspective of future cheap clean energy, will drive extraction up. 04 July

34 Model V: Strand (2008) Model set up Demand without substitute: D(P) ( ) Demand after technology breakthrough: 0 Break through hazard rate π ( r+ π) t Supply: Λ = 0 e { P( E) E c( S) E} dt Dynamics very much the same as in Sinn (2008) (not known to Strand) de c( S) = σ ( E )( π + r )(1 ) ds P( E) Implication: Technology agreement will speed up fossil fuel use, and dif successful, reduce cumulative use 04 July

35 Model V: Strand (2008) Result Emissions go up If lucky, we may solve the problem If unlucky, we may have added to climate change BAU vs Technology agreement Emissions i (E) July

36 Model VI: Hoel (2008) Bush meets Hotelling: cheap clean energy Cheap clean energy has the advantage that it doesn t cost jobs (or votes, as taxes do) If we develop a competitive clean energy = marginal costs < extraction costs for fossil fuels, and find one, we solve the climate change problem. Or do we? The perspective of future cheap clean energy, will drive extraction up, increasing climate damages. ages Cheaper clean energy may reduce welfare! Model specifics: continuum of countries ordered with respect to willingness to pay for reducing emissions 04 July

37 Model VI: Hoel (2008) Model set up, case I As in Sinclair (1992), define cumulative demand up to time T: T ( r+ z) t 0 = 0 0 Δ( P, T) D( e P ) dt But realize that termination date T is determined by substitute (choke) price: P(T)=ψ Δ(P 0,ψ) with Δ P <0, Δ ψ >0 Change in substitute price (ψ), must be offset by change in initial price ds dδ Δ dp Δ dψ dp0 Δ dψ Δ ψ 0 0= 0 = = P 0+ = > 0 0 ψ Cheaper substitute (dψ<0) implies lower price at every period! (dp t <0) implies higher cumulative emissions at every T (de T >0). P 04 July

38 Model VI: Hoel (2008) Model set up, case II Assume some countries have willingness to pay not to use fossil fuels above ψ. Alternative, assume that substitute has supply curve and ψ is inverse measure of technology: D(P,ψ) ( with D P<0, D ψ>0 Cheaper substitute (dψ<0) ψ still implies lower fossil fuel price at every period (dp t <0). But as cheaper substitute reduces demand as well, the effect on emissions at every t is ambiguous (de t >?0). Current emissions decrease if energy substitute is immediately used. Current emissions increase if energy substitute is mostly a future option. 04 July

39 Sinn, Strand & Hoel: 2008 Summary: Green Paradox everywhere Sinn (2008): market is distorted towards advanced extraction. Carbon tax plans worsen the problem Strand (2008): International ti agreement for clean energy breakthrough will increase emissions, and if unsuccessful, worsen climate change Hoel (2008): cheap clean energy causes a green paradox as much as carbon tax plans, especially if clean energy e is a future u option o and not immediately available 04 July

40 Model VII: Gerlagh (2011) Too Much Oil (Fossil Fuels) We cannot tolerate all fossil fuels to be used Hence, we must either implement strong climate policy or we must develop competitive clean energy = marginal costs < future extraction costs for fossil fuels If we do so, carbon tax or further improving i cheap energy will reduce cumulative fossil fuel use Analysis focuses on developing cheap clean energy (no tax) Models: simple linear demand & supply Message: urgent call for strong market intervention; ti justified as there is no Green Paradox 04 July

41 Model VII: Gerlagh (2011) Model features From Ulph and Ulph (1996): Linear demand & supply functions, so that path is linear combination of eigenvectors. Et Extraction ti costs linear in S(t): Argument: the amount of fossil fuels is too much to accept full depletion (Sinn 2008, Allen et al. 2009). Consequence: cumulative emissions are endogenous Linear clean energy supply Argument: clean energy has decreasing returns to scale (Pacala & Sokolow 2004). Consequence: cheaper clean energy reduces current fossil fuel demand (Hoel 2008) 04 July

42 Model VII: Gerlagh (2011) Redefining Green Paradoxes Weak Green Paradox: current emissions go up Strong Green Paradox: NPV total damages go up If cumulative emissions are constant, then Weak = Strong If cumulative emissions decrease, but current emissions increase? rt Total damages: Γ = 0 e Ω( Mt ()) dt= 0 e τ() tetdt () + Γ0 ( r+ δ) τ Where τ() t = t e Ω'( M( τ)) dt Assume damages increase not too fast. E.g. M(t) increases not too fast, Ω(t) not too convex Ω ˆ ' < r Marginal damages increase not too fast: ˆ τ < r Necessary condition for Strong Green Paradox: increases (Lemma 1) rt rt 0 e E() t dt 04 July

43 Model VII: Gerlagh (2011) Intermezzo: Lemma 1 Lemma 1. Given ˆ τ < r then rt implies 0 e E0() t dt> 0 e E1() t dt Proof: rt rt 0 0 > 0 1 rt e τ() te() tdt e τ() te() tdt 04 July

44 Model VII: Gerlagh (2011) Base model Linear energy demand: Et () = DPt ( ()) = E+ DPt ' () Constant extraction costs: Pt () = rpt ( () c) Extraction dynamics: S = E c E= D' P = r( E+ E) DD ' When clean energy becomes cheaper (dψ<0), then de/ds decreases throughout h t emissions i increase for every t both Weak and Strong Green Paradox 04 July

45 Model VII: Gerlagh (2011) Phase Diagram: replicating Sinn/Strand/Hoel E = 0 S = 0 Im mproving backs stop E S Phase diagram: S = E c E= D' P = r( E+ E) D' c E = 0 E= E+ + D ' Condition: S(0)=S 0 E(T) =D(ψ) (maximal rent) Cheaper clean energy moves path up iff D(ψ)>0 04 July

46 Model VII: Gerlagh (2011) New: Linear extraction costs Linear fossil fuel demand: Et () = DPt ( ()) = E+ DPt ' () Linear extraction costs: P(t) = c(s 0 S(t))+λ(t) Gerlagh (2011) inverts S from remaining stock to cumulative extraction, we don t Competitive supply: Pt ( ) = rpt ( ( ) cs ( 0 St ( ))) Extraction dynamics: S = E c(s S ( 0 ) E= D' P= r ( E + E ) c D' Locus E = 0 E= E + ( S S0 ) D' 04 July

47 Model VII: Gerlagh (2011) Graphics, Phase Diagram S = 0 E E = 0 S Phase diagram: S = E cs ( 0 S ) E = D' P = r( E+ E) D' c E = 0 E= E+ ( S S0) D' ED' Sinn (2008): S0 < c 04 July

48 Model VII: Gerlagh (2011) Stable and Unstable balanced paths E E = 0 S = 0 S 04 July

49 Model VII: Gerlagh (2011) Equilibrium path (Sinn (2008) assumption) E E = 0 Equilibrium path = linear combination of stable and unstable balanced growth Condition: S = 0 S S(0)=S 0 E(T) =0 (maximal rent at final period, no backstop) 04 July

50 Model VII: Gerlagh (2011) Equilibrium path (a backstop) E E = 0 Equilibrium path = linear combination of stable and unstable balanced growth Condition: S = 0 S S(0)=S 0 E(T) =D(ψ) (maximal rent at final period) When backstop is cheap, fossil fuel is abundant: λ(t)=0 04 July

51 Model VII: Gerlagh (2011) Equilibrium path (Too much fossil fuels) E E = 0 Equilibrium path = stable balanced growth Abstract t from backstop Condition: S(0)=SS 0 (large) E( ) =0 (no rent at infinite horizon) S = 0 S 04 July

52 Model VII: Gerlagh (2011) Equilibrium path (with backstop) S = 0 E E = 0 S Equilibrium path = stable balanced growth Condition: S(0)=S 0 (large) λ(t)=0 P(T) =cs (no rent at final period) Improving backstop = moving T along the red curve E increases, cumulative E decreases 04 July

53 Model VII: Gerlagh (2011) Linear clean energy supply, cnsnt extrn costs Linear energy demand: Et () = DPt ( ()) = E+ DPt ' () Linear clean energy supply (renewables with DRS): N(t) = AP(t) Fossil fuel demand: Et () = Et () Nt () = E ( A D') P( t) Constant extraction costs: Pt () = rpt ( () c) Extraction dynamics: S = E c E= ( A D') P = r( E+ E) A D' When clean energy becomes more productive (da>0), then de/ds decreases throughout emissions decrease for every t no Weak nor Strong Green Paradox 04 July

54 Model VII: Gerlagh (2011) Phase Diagram: no backstop E = 0 Phase diagram: E S = E c E= ( A+ D') P = r( E+ E) A + D' c E = 0 E= E+ A + D' Condition: S = 0 S S(0)=S 0 E(T) =0 (maximal rent) Cheaper clean energy changes path iff c>0 04 July

55 Model VII: Gerlagh (2011) Graphics, Phase Diagram E = 0 S = 0 E S Recall Sinn (2008): de c = σ ( Er ) (1 ) ds P Cheaper clean energy need not change elasticity of demand for fossil fuels, but just lowers demand lower price, hence, lowers slope. 04 July

56 Model VII: Gerlagh (2011) Conclusions Cheaper current clean energy replace fossil fuels and don t lead to Green Paradox. Cheaper future clean energy imply that fossil fuel price decreases current emissions increase + fossil fuels are earlier replaced NPV damages decrease As there is much-too-much coal + nonconventional oil, we must develop clean energy that is competitive In this context, no need to worry for Green Paradox 04 July

57 Model V: Grafton, Kompas, van Long (2010) Biofuels Can biofuel subsidies help reduce cumulative emissions? Supply curve for biofuel, as opposed to backstop First result (Prop 1) equals Gerlagh (2011): no extraction costs & linear demand no effect. Positive constant extraction costs & linear demand Green Orthodox de c Then consider non-linear demand. Sinn (2008): = σ ( Er ) (1 ) ds P Question is: does biofuel subsidy increase or decrease elasticity of fossil fuel demand? If energy demand and biofuel supply are linear, then fossil fuel demand elasticity, σ(e), remains unaffected. But if energy demand is iso-elastic 04 July

58 Model V: Grafton, Kompas, van Long (2010) Iso-elastic energy dem + linear biofuel supply Energy demand: En = βp ε Biofuel supply (with subsidy z): N= Fossil fuel demand: E= βp ε zp Elasticity of demand: ε de P εp zp (1 + ε zp σ ( E ) = = = ε ) dp E E E Increasing with z: d d d ε d ε d σ ( E) zp = ( P E) = P P > 0 dz dz dz dz dz zp E= cnst E E E 04 July

59 Model V: Grafton, Kompas, van Long (2010) Illustration biofuel subsidy moves you up, as in Sinn (2008) de ds c = σ ( Er ) (1 ) P but for different reason Same results holds if one country out of two subsidizes And if fossil fuel supply is monopolistic 04 July

60 Model V: Grafton, Kompas, van Long (2010) Increasing extraction costs Assumed that fossil fuels remain scarce, λ(t)>0, ( ) which means that the last drop of oil is cheaper to extract than marginal value of energy, then same results continue to hold (no change of cumulative emissions) Similar to Sinn (2008), contrasts Gerlagh who poses that we can t afford to exhaust fossil fuels (must ensure λ( )=0) 04 July

61 Model V: Grafton, Kompas, van Long (2010) Linear extraction costs + biofuels Condition: S = 0 S(0)=S 0 E(T) 0 (maximal rent at final period) E E = 0 E(T) =0 (maximal rent at S Cheaper biofuels reduce fossil fuel demand and delay exhaustion 04 July

62 Van der Ploeg and Withagen (2009) Add welfare to the analysis Green Paradox occurs if the backstop is relatively expensive and full exhaustion of fossil fuels is optimal Add welfare analysis: Without a carbon tax, taxing the backstop might enhance social welfare if fossil fuel reserves are fully exhausted. Without a carbon tax, subsidizing the backstop might enhance social welfare if fossil fuel reserves are not fully exhausted. If backstops are already used, a lower cost of the backstop will postpone fossil fuel exhaustion or leave more fossil fuel in situ, thus boosting green welfare Add monopolistic supply ppy 04 July

63 Model IX: van der Ploeg and Withagen (2009) Equilibrium path (a backstop) S = 0 Green Orthodox E Green Paradox E = 0 S Green Paradox occurs if the backstop is relatively expensive and full exhaustion of fossil fuels is optimal What matters is whether λ(t)=0 Green Paradox: carbon tax & backstop subsidy decreases welfare Green Orthodox: might increase welfare 04 July

64 Model IX: van der Ploeg and Withagen (2009) Backstops in use E = 0 S = 0 E S Recall Sinn (2008): de c = σ ( Er ) (1 ) ds P Recall Gerlagh (2011): Cheaper clean energy need not change elasticity of demand for fossil fuels, but just lowers demand lower price, hence, lowers slope. 04 July

65 Gerlagh; Grafton, Kompas & van Long; vd Ploeg & Withagen Summary: Green Paradox not everywhere Gerlagh (2011): cannot afford to use all fossil fuels fossil fuel rent must be zero at end no full exhaustion Cheap clean energy = no full fossil fuel exhaustion no green paradox carbon tax & clean energy subsidy might increase welfare (vdp&w) Clean energy in use green orthodox if linear demand (G) / green paradox ado if iso-elastic eas cdemand d(g (GKvL) carbon tax & clean energy e subsidy might increase welfare (vdp&w) 04 July

66 What s in it for you? Past future research Country Heterogeneity What if countries differ wrt resource endowments / substitute endowments / carbon tax policy (Hoel) Carbon Capture and Sequestration What if the resource itself offers a clean option (H&Jensen)? Resource heterogeneity What if various resources compete (Michielsen)? Integrate coal, oil, gas & unconventional oil as exh. resources 04 July

67 Learn from the best Intuition From Hoel (2011) 2 countries: Country A has high h carbon tax. Country B has low carbon tax, but increases its tax to the level in Country A Result: Green Paradox ado 04 July

68 What s in it for you? Suggestions for future research Broadening Consider jointly interspatial & intertemporal market integration Deepening Exploration: resources versus reserves Future policies may affect current expected reserves? Endogenous substitute development what if taxes affect R&D into substitute? t Alternatives Alternatives ti for the simple exhaustible resource model any sign for oil price increase with interest rate ? 04 July