Is there really a green paradox? Rick van der Ploeg (Oxford) Cees Withagen (VU University Amsterdam) Paris September 28, 2010 Some evidence Fourth assessment report of IPCC: Global surface temperature increased 0.74 ± 0.18 °C during the 20th century. Most of the observed temperature increase since the middle of the 20th century has been caused by increasing concentrations of greenhouse gases resulting from human activity such as the burning of fossil fuel and deforestation. Climate model projections indicate that the global surface temperature is likely to rise a further 1.1 to 6.4 °C (2.0 to 11.5 °F) during the 21st century. Evidence from rocks 55 million years ago: massive sudden release of carbon from the ocean floors (Paleocene Thermal Maximum). Led to a rise of temperature with 5 -7 degrees Celcius, acidification of oceans, 4-5 meters higher sea level. Lots of species did not survive. Took 200,000 years to recover. The Alpes “Les Alpes, un ‘château d’eau’ ébranlé par le réchauffement du climat” , Le Monde (26 septembre 2010) Less snow, more rain, smaller glaciers, 15% less hydro electricity. Current demand driven policies Curbing demand for fossil fuels: higher petrol taxes, home insulation, lighter cars Green electricity: wind, water, solar, biomass, hybrid cars Nuclear: electricity generation and hydro power Other green energy sources: biodiesel, heat pumps, solar, geothermal Efficient combustion: optimized power plants Hans Werner Sinn Green Paradox: counter- productivity of green policies Sinn, H.-W. (2008). “Public policies against global warming: a supply-side approach”, International Tax and Public Finance , 15, 360-394. Focus on demand for carbon ignores supply of carbon. Anticipation of green policies causes oil sheiks to pump oil faster, which accelerates global warming. Supply side: Exhaustibility of fossil fuels “.. the ‘pure’ mining problem must be coupled with the ‘pure’ pollution problem”. “..run out first: air to breathe or fossil fuels to pollute the air we breathe?” (d’Arge and Kogiku, 1973) Integration of supply of oil and climate Literature Old (without backstop). Sinclair (1992) (ad valorem tax),Ulph and Ulph (1994) (ad valorem tax), W. (1994) (optimal program) Recent ( including backstops). Hoel and Kverndokk (1996) Sinn (2008), Hoel (2008, 2010), Gerlagh (2009), Grafton et al. (2010), Zemel and Smulders (2010), Tsur and Zemel (2010), Long (2010), Smulders et al. (2010), Edenhofer and Kalkuhl (2010), Spinesi (2010) Outline of sequel 1. Basics. Hotelling’s rule 2. From dirty fuel to clean backstop: -optimum+market -cost -monopoly -capital accumulation 3. From dirty to even more dirty 4. Future research 1. Hotelling Two period Hotelling rule 1 max ( p )1( − k)q )1( + ( p )2( − k)q )2( 1+ r + = subject to q )1( q )2( S0 1 ( p(1) − k) > ( p(2) − k) ⇒ q(1) = S ,q(2) = 0 1+ r 0 1 ( p )1( − k) < ( p )2( − k) ⇒ q )1( = ,0 q )2( = S 1+ r 0 1 Supply in both periods requires ( p )1( − k) = ( p )2( − k) 1+ r p )2( − k − ( p )1( − k) or = r : Hotelling' s rule p )1( − k ⇒ shadow price λ Continuous time Hotelling ∞ max ∫e−rt ( p(t) − k)q(t)dt 0 subject to = − = S&(t) q(t), S )0( S0 q(t) ≥ ,0 S(t) ≥ 0 q(t) > 0 ⇒ e−rt ( p(t) − k)= λ constant λ = λ ert Hotelling with backstop price p p' T’ T time Sinn Cash flow tax t(p-G(S)) Ad valorem tax tp Expropriation risk Figure 1: Coal Reserves dominate Gas and Oil Reserves 2. From dirty to clean. Optimum U (q + x) − G(S)q − bx − D(E) 2. From dirty to clean. Optimum U (q + x) − G(S)q − bx − D(E) ∞ max∫ exp(−ρtUqt )[ (() +− xt ()) GStqt (())() −− bxt () DEt ( ())] dt 0 2. From dirty to clean. Optimum U (q + x) − G(S)q − bx − D(E) ∞ max∫ exp(−ρtUqt )[ (() +− xt ()) GStqt (())() −− bxt () DEt ( ())] dt 0 = = Et&( ) qtE ( ), (0) E 0 , given (no decay) (µ) 2. From dirty to clean. Optimum U (q + x) − G(S)q − bx − D(E) ∞ max∫ exp(−ρtUqt )[ (() +− xt ()) GStqt (())() −− bxt () DEt ( ())] dt 0 = = Et&( ) qtE ( ), (0) E 0 , given (no decay) (µ) x( t )≥ 0 2. From dirty to clean. Optimum U (q + x) − G(S)q − bx − D(E) ∞ max∫ exp(−ρtUqt )[ (() +− xt ()) GStqt (())() −− bxt () DEt ( ())] dt 0 = = Et&( ) qtE ( ), (0) E 0 , given (no decay) (µ) x( t )≥ 0 =− ≥ ≥ = λ St&() qtqt (), () 0, St () 0, S (0) S 0 ,given ( ) Necessary conditions Uqt'(()+ xt ()) −≤ b 0, xt () ≥ 0, cs.. Uqtxt'(()+−−− ())λ () t µ () tGSt (()) ≤ 0,() qt ≥ 0, cs .. Preliminary results No simultaneo us use No extraction after some T Suppose S(T) > 0 Use less solar : cost saving b + + Use more oil : extra cost G'(S) D'(E 0 S0-S(T)) Indifferen ce needed for optimality : = + = = − FMD D'(E 0 S0-S(T)) MB b G (' S(T)) Partial exhaustion ≤ + + ρ b G )0( D (' E0 S0 /) b − G(S(T)) − b G(S0 ) + ρ D'(E 0 S0-S(T)) / ST S0 S(T ) Comparative statics Lower backstop price lowers MB: Higher remaining stock If global warming is acute: Higher remaining stock More patience: Higher remaining stock Full exhaustion > + + ρ b G )0( D (' E0 S0 /) b − G(S(T )) − b G(S0 ) + ρ D'(E 0 S0-S(T)) / ST S(T ) No extraction at all < + ρ b GS(0 ) DE '( 0 ) / > ⇒ S( T ) S 0 Green welfare What happens to Green Welfare if the backstop price changes? Green Welfare decreases if the backstop becomes cheaper if and only if > + + ρ bG(0) DE '(0 S 0 )/ Intuition Marginal changes in b. High b, exhaustion, lower b, earlier exhaustion (T decreases) Low b, no exhaustion, lower b, more left in the ground (T decreases) Comparative statics (example) T increases as initial pollution stock is larger initial resource stock is larger extraction the last drop of oil is more expensive demand is smaller Policy recommendations Perfect competition Taxes and subsidies on oil and backstop are feasible . →Do not give subsidy on solar, but tax oil according to marginal damage. No carbon tax; constant subsidy Full exhaustion if the backstop is relatively expensive: b−σ > G (0) Partial exhaustion if the backstop becomes < −σ < cheap enough: GS(0 ) b G (0) GST( ( )) = b − σ No extraction if the backsto p is always −σ < cheaper:b G( S 0 ) Second-best constant subsidy Suppose carbon tax is politically infeasible Parameterize damage function κD( E ) Taxing the backstop enhances welfare if b> G (0) and κ large Subsidy on backstop enhances welfare if G(0)> b and κ large Taxing backstop can boost social welfare Subsidizing backstop can boost social welfare Increasing marginal costs Welfare U (q(t) + x(t)) − G(S (t)) q(t) − B(x(t)) − D(E(t)) =ψ + 1 π 2 Example : B(x) x 2 x Interval with oil and solar use : If q > 0 and x = 0 then U (' q) ≤ B )0( If q = 0 and x > 0 then U (' x) = B(x) ⇒ jump in energy use, which is suboptimal . Generic sequence There exist T1 and T2 such that ≤ ≤ only oil for 0 t T1 ≤ ≤ oil and solar simultaneo usly for T1 t T2 ≥ only solar for t T2 a. With simultaneo us use U (' q + x) = B (' x). Hence q and S not too large .b B (' xˆ) = U (' xˆ). Define b = B (' xˆ) Result: small initial oil stock CASE :1 low b Simultaneo us use from the outset forever Stock approaches a positive stock No Green Paradox CASE :2 high b Simultaneo us use initially until exhaustion Backstop takes over after finite time. No Green Paradox Result: large initial oil stock CASE :3 low b Initially only oil Simultaneo us use forever th ereafter No Green Paradox CASE :4 high b Initially only oil Then oil and solar until exhaustion Solar take s over after finite time. Green Paradox Hotelling monopoly (Hoel) price p p' T’ T time Results A period of limit pricing, i.e. marginally below the cost of the backstop, before switching to the backstop. Green Paradox, if backstop relatively expensive Otherwise, more oil left in situ. Green Paradox need not occur. Capital accumulation Ramsey Solow Capital accumulation ∞ max ∫e−ρt (U (C(t)) − D(E(t))) dt 0 Capital accumulation ∞ max ∫e−ρt (U (C(t)) − D(E(t))) dt 0 subject to = + − − −δ − = K& F(K, x q) bx G(S)q K C, K )0( K0 Capital accumulation ∞ max ∫e−ρt (U (C(t)) − D(E(t))) dt 0 subject to = + − − −δ − = K& F(K, x q) bx G(S)q K C, K )0( K0 = − = S& q, S )0( S0 Capital accumulation ∞ max ∫e−ρt (U (C(t)) − D(E(t))) dt 0 subject to = + − − −δ − = K& F(K, x q) bx G(S)q K C, K )0( K0 = − = S& q, S )0( S0 = = E& q, E )0( E0 Capital accumulation ∞ max ∫e−ρt (U (C(t)) − D(E(t))) dt 0 subject to = + − − −δ − = K& F(K, x q) bx G(S)q K C, K )0( K0 = − = S& q, S )0( S0 = = E& q, E )0( E0 Ramsey : D ≡ x ≡ q ≡ 0 DHSS : D ≡ x ≡ 0 Krautkraem er : x ≡ 0 consumption constant consumption capital C* constant = ρ + δ FK (K *) capital Preliminary result For low initial capital stocks, first only oil then only backstop Reason: low consumption, high marginal utility, no bother about climate change, build up of capital. EKC Result For high initial capital possibly simultaneous use But maybe first only oil Or only solar Initial oil stock Only oil use No initial oil use Initial capital 3 Dirty backstops Dirty backstop Shale oil, tar sands, coal, Exploitation energy intensive and polluting Analytical representation t Et()=+−+ ESStYt () (), Et& () =+ qt ()ψ xt () and Yt() ≡ ψ xss ()d, 0 0 ∫0 Optimum 1 Define = + + − + H(S,Y) ρ(G(S) D'(E 0 S0 S Y)/ ρ − − + − + b ψD'(E 0 S0 S Y)/ ρ) Assume U'( 0 ) is large enough < < CASE :1 H )0,0( ,0 H (S0 ,0) 0 Oil ⇒ Backstop.