Osaka University of Economics Working Paper Series No Optimal Environmental Policy under Monopolistic Provision of Environmental Technology 20

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1 Osaka University of Economics Working Paper Series No Optimal Environmental Policy under Monopolistic Provision of Environmental Technology 27 2 Keisuke Hattori, Osaka University of Economics

2 27 2 / 1 / Jaffe et.al (22)) / 2 Downing and White (1986) 2 *1 Downing and White (1986) Milliman and Prince (1989) / / (FS-53) *1 Kneese and Schultz, 1975; Magat, 1978 Downing and White (1986) 2

3 Fischer et.al (23) / *2 (a) (b) (c) 3 R&D R&D (cost-reducing investment) Ulph (1997), Petrakis-Xepapadeas (1999), Montero (22a, 22b) R&D Montero (22a) (b), (c) (d) Lanjouw and Mody (22) 95 98% (inside supplier) (outside supplier) R&D (outside supplier *2 Fischer et.al (23) 3

4 Goulder (1995) Bovenberg-de Mooji (1994), Goulder et. al (1999) Ulph (1997) (inside supplier (outside supplier n 1 R&D R&D ) R&D R&D 4

5 * *4 X(P ) P (X) n c X R&D P (X) = c + e()t (1) P (X) = c + e(z) t + r (2) P ( ) X (X = nx) x e( ) 1 z R&D t r R&D 1 e() e(z) 1 r R&D 1 z, < e < ; e < ; e > 1 1 e( ) 2 (non-drastic) c + e()t < argmax P {P X(P ) (c + e(z)t)x(p )} *3 Milliman and Prince (1989), Fischer et al. (23) *4 Denicolò (1999) 5

6 2 (c + e()t r Arrow (1962) r = [e() e(z)]t (3) R&D r 2 r R&D r (3) (2) X = X(c + e()t) (4) x x = X(c + e()t)/n X( ) = P 1 ( ) ) z R&D R&D { Π = max z r X(c + e()t) (1 s) z F ]} (5) s R&D F R&D (3) e (z) t X(c + e()t) = 1 s (6) *5 (6) R&D [ dz ] dt = e X + e() t X e t X dz ds = 1 e t X >, dz dc = e X e X < (7) (7) σ e()t [, 1), c + e()t ɛ X (P ) P X [, ) σ ɛ (7) dz dt = e ( ) 1 σ ɛ e t *5 e t X < 6

7 P R&D P M P c + e()t c + e(z)t c P (X) X(c + e()t) MR X 1 R&D 1 (σ) (ɛ) R&D R&D R&D R&D (7) t = X(Pt=) M + (Pt= M c)x (Pt=) M = Pt= M (1) P M t= (7)= P M t= > P (X) (7)> 2 c + e()t < argmax P {P X(P ) c X(P )} c + e()t < argmax {P X(P ) c X(P )} P 2 7

8 1 P M c + e()t 1 R&D R&D R&D (3), (5) dπ dt = [e() e(z)][ X + e()tx ] 1 2 R&D F (5) t = π = F R&D t X z SW = X P (h)dh c X z F D(e(z) X) (8) 3 ψ >, D(ψ) < ; D > ; D > ; D() = (8) X z X = P (X) = c + e(z)d (9) z = e (z) X D = 1 (1) *6 (9) (1) t R&D s (8) = dx ] [e()t e(z)d + dz [ ] 1 s D 1 = (11) t dt dt t = dz [ ] 1 s D 1 = (12) s ds t *7 *6 *7 dz/dt > 8

9 3 t F B = e(z) e() D (13) s F B = e() e(z) e() = e e R&D R&D (13) D ) (13) (6) (12) R&D (14) R&D 1 z % (11) s = = dx ] [(e() e(z))d < (15) t t=d dt = dz [ ] e() t t=t F B ds e(z) 1 > (16) 4 t SB t F B < t SB < D R&D D R&D R&D R&D R&D B Environmental Policy Budget [ ] B = e()t F B X s F B z (14) (17) 9

10 R&D B Double Dividend) 2.2 P (X) = A b X, e(z) = e() exp[ α z], D(ψ) = β ψ2 2 A b α R&D β A = 2, b = 1, c = 1, α =.3, β =.1, e() = 1 t F B s F B σ = e()t F B /(c + e()t F B ) 2 Market Size) A R&D 1 R&D R&D 2 β R&D (4) *8 2 b b b R&D *8 R&D R&D 1

11 Tax Subsidy rate Σ and s Tax Subsidy rate Σ and s Market Size A s Slope of Inverse Demand b Σ s Σ Tax Subsidy rate Σ and s Tax Subsidy rate Σ and s Slope of Marginal Damage Β R&D Efficiency Α s Σ Σ s 2 2 R&D α α B 3 X) z) (s σ 3 β) β B 3 b B b 3 α B R&D 3 B 11

12 4 4 Env. Policy Budget B Env. Policy Budget B Market Size A Slope of Marginal Damage Β Env. Policy Budget B Env. Policy Budget B Slope of Inverse Demand b R&D Efficiency Α n Cournot) i (i = 1,, n) { } π N = max P (x + (n 1) x) x c x e() t x x { } π A = max P (x + (n 1) x) x c x e(z) t x r x x π N R&D π A m(x, n) P (nx) + x P (nx) = c + e()t (18) m(x, n) P (nx) + x P (nx) = c + e(z)t + r (19) (18) (19) m(x, n) m x <, m n < 12

13 R&D (18) (19) r r = [e() e(z)]t x (18) x = x(c + e()t, n) x t = e()/m x <, x n = m n /m x < m x < X = X(c + e()t, n) = n x X t <, X n > R&D (z) R&D Π = [e() e(z)] t n x (1 s)z F e (z) t n x(c + e()t, n) = 1 s [ ] dz dt = e x + t xt e (2) t x dz = e [X n ] dn e X > (21) fixed t (2) σ e()t [, 1), c + e()t ɛ m m x x m [, ) ɛ m (2) ( ) dz dt = e e 1 σ t ɛ m 5 σ < ɛ m. ɛ m *9 (21) 6 *9 P = A b(n x) (n + 1)b x/(a (n + 1)b x) (A b n x)/b n x P = (n x) 1/ɛ ɛ 1/ɛ

14 X R&D z Ulph (1997) R&D inside supplier) outside supplier) Ulph (1997) R&D R&D R&D 7 ˆt F B = e(z) e() D + X P (X) e() n = e(z) e() D P MC e() ŝ F B = = e() e(z) e() e() e(z) e() X P (X) e() n D (22) + P MC e() D (23) R&D ((22) ) Ebert (1992) Ebert (1992) R&D R&D 14

15 ˆ t ˆ SW t = dx ] [(e() e(z))d X P < t=d dt = dz [ 1 + t=ˆt F B ds e() D ] e(z) D + X P > ˆt SB ˆt F B < ˆt SB < D R&D B 3 * 1 * 11 *1 OECD (26) *11 EIEP (2) CO 2 15

16 4 R&D R&D - R&D R&D R&D Downing-White (1986), Milliman-Prince (1989), Fischer et. al (23) 16

17 I: adoption subsidy * 12 R&D R&D (3) r = ((e() e(z))t 1 s R&D Π = ((e() e(z))t 1 s X z F (6) II: ˆ SW = nx P (h)dh n c x z F D(e(z)n x) ˆ x = P (n x) c e(z) D = ˆ z = 1 e (z) n x D = ˆ t ˆ z = dx dt n [ = dz ds P (n x) c e(z) D ] + dz dt [ 1 e (z) n x D ] = [ 1 e (z) n x D ] = R&D ˆ t ˆ z = dx dt n [ = dz ds [ e()t e(z)d X P ] s D ] = t n + dz [ dt s D ] = t *12 17

18 ˆt F B = e(z) e() D + X P (X) e() n ŝ F B = e() e(z) e() X P (X) e() n D [1] K. Arrow, (1962) Economic welfare and the allocation of resources for invention, in R. Nelson (ed.), The rate and direction of innovative activity, Princeton Univ. Press, Princeton, N.J. [2] A.L. Bovenberg and R.A. de Mooji, (1994) Environmental Levies and Distortionary Taxation, American Economic Review 84, [3] V. Denicolò, (1999) Pollution-Reducing Innovations under Taxes or Permits, Oxford Economic Papers [4] P.B. Downing and L.J. White, (1986) Innovation in Pollution Control, Journal of Environmental Economics and Management [5]. Ebert, (1992) Pigouvian Taxes and Market Structure: The Case of Oligopoly and Different Abatement Technologies Finanzarchiv 49, [6] EIEP, (2) The Carbon Tax to Reduce GHGs Emission. Report to the Study Group on Economic Instruments in Environmental Policies. [7] C. Fischer, I.W.H. Parry and W. Pizer, (23) Instrument Choice for Environmental Protection when Technological Innovation is Endogenous, Journal of Environmental Economics and Management [8] L.H. Goulder, (1995) Environmental Taxation and the Double Dividend: A Reader s Guide, International Tax and Public Finance 2, [9] L.H. Goulder, I.W.H. Parry, R.C. Williams III and D. Burtraw, (1999) The Cost-Effectiveness of Alternative Instruments for Environmental Protection in a Second-Best Setting, Journal of Public Economics [1] A.B. Jaffe, R.G. Newell and R.N. Stavins, (22) Environmental Policy and Technological Change, Environmental and Resource Economics [11] Y. Katsoulacos and A. Xepapadeas, (1996) Emission taxes and market structure in C. Carraro, Y. Katsoulacos and A. Xepapadeas, (ed.), Environmental Policy and Market Structure, Dordrecht, Kluwer. [12] A. Kneese and C. Schultz, (1975) Pollution, Price and Public Policy, Brookings Institution, Washington, USA. [13] J.O. Lanjouw and M. Ashoka, (1996) Innovation and the International Diffusion of Environmentally Responsive Technology, Research Policy 25, pp [14] D.R. Lee, (1975) Efficiency of Pollution Taxation and Market Structure Journal of Environmental Economics and Management 2,

19 [15] W.A. Magat, (1978) Pollution Control and Technological Advance: A Dynamic Model of the Firm, Journal of Environmental Economics and Management [16] S.R. Milliman and R. Prince, (1989) Firm Incentives to Promote Technological Change in Pollution Control, Journal of Environmental Economics and Management [17] J.-P. Montero, (22a) Market Structure and Environmental Innovation, Journal of Applied Economics [18] J.-P. Montero, (22b) Permits, Standards, and Technology Innovation, Journal of Environmental Economics and Management [19] OECD, (26) The Political Economy of Environmentally Related Taxes, OECD, Paris. [2] E. Petrakis and A. Xepapadeas, (1999) Does Government Precommitment Promote Environmental Innovation?, in E. Petrakis, E.S. Sartzetakis and A. Xepapadeas (ed.), Environmental Regulation and Market Power, Edward Elgar Pub., M.A. [21] D. Ulph, (1997), Environmental Policy and Technological Innovation, in C. Carraro and D. Siniscalco, (ed.), New Directions in the Economic Theory of the Environment,Cambridge Univ. Press, Cambridge, UK. 19

Title 最適年金の理論 Author(s) 藤井, 隆雄 ; 林, 史明 ; 入谷, 純 ; 小黒, 一正 Citation Issue Date Type Technical Report Text Version publisher URL

Title 最適年金の理論 Author(s) 藤井, 隆雄 ; 林, 史明 ; 入谷, 純 ; 小黒, 一正 Citation Issue 2012-06 Date Type Technical Report Text Version publisher URL http://hdl.handle.net/10086/23085 Right Hitotsubashi University Repository