Numerical modelling of cooperative and noncooperative three transboundary pollution problems under learning by doing in Three Gorges Reservoir Area
Abstract
In this paper, we investigate cooperative and noncooperative three transboundary pollution problems in Three Gorges Reservoir Area where emission permits trading and abatement costs under learning by doing are considered. The abatement cost depends on two key factors: the level of pollution abatement and the experience of using pollution abatement technology. We use the optimal control theory to study the optimal emission paths and the optimal pollution abatement strategies under cooperative and noncooperative three transboundary pollution problems, respectively. By using the actual economic data of Wanzhou District, Kaizhou District and Yunyang County, we obtain the abatement level and the pollution stock of cooperative and noncooperative three transboundary pollution problems based on the four order Runge-Kutta method. We also discuss the influence of the change of parameter for the abatement level and the pollution stock.
Keyword : three transboundary pollution problem, learning by doing, emission permits trading, Three Gorges Reservoir Area, four order Runge-Kutta method
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
L. Argotte and D. Epple. Learning curves in manufacturing. Science, 247(4945):920–924, 1990. https://doi.org/10.1126/science.247.4945.920
N. Baloff. Extension of the learning curve–some empirical results. Oper. Res. Quart., 22(4):329–340, 1971. https://doi.org/10.1057/jors.1971.77
H. Benchekroun and A. Chaudhuri. A transboundary pollution and clean technologies. Resour. Energy Econ., 36(2):601–619, 2014. https://doi.org/10.1016/j.reseneeco.2013.09.004
L. Bertinelli, C. Camacho and B. Zou. Carbon capture and storage and transboundary pollution: A differential game approach. European J. Oper. Res., 237(2):721–728, 2014. https://doi.org/10.1016/j.ejor.2014.02.025
Y. Bramoulle and L. Olson. Allocation of pollution abatement under learning by doing. J. Pub. Econom., 89(9–10):1935–1960, 2005. https://doi.org/10.1016/j.jpubeco.2004.06.007
S. Chang, W. Qin and X. Wang. Dynamic optimal strategies in transboundary pollution game under learning by doing. Physica A, 490:139–147, 2018. https://doi.org/10.1016/j.physa.2017.08.010
S. Chang, X. Wang and Z. Wang. Modeling and computation of transboundary industrial pollution with emission permits trading by stochastic differential game. Plos One, 10(9):1–29, 09 2015. https://doi.org/10.1371/journal.pone.0138641
N. Hall. Transboundary pollution: Harmonizing international and domestic law. Univ. Michigan J. Law Reform, 40(4):681–746, 2006.
N. Hatch and D. Mowery. Process innovation and learning by doing in semiconductor manufacturing. Manage. Sci., 44(11):1461–1477, 1998. https://doi.org/10.1287/mnsc.44.11.1461
G. Janssens and G. Zaccour. Strategic price subsidies for new technologies. Automatica, 50(8):1999–2006, 2004. https://doi.org/10.1016/j.automatica.2014.05.017
V. Kaitala, M. Pohjola and O. Tahvonen. Transboundary air pollution and soil acidification: A dynamic analysis of an acid rain game between finland and the ussr. Environ. Resour. Econ., 2(2):161–181, 1992.
S. Li. A differential game of transboundary industrial pollution with emission permits trading. J. Optim. Theory Appl., 163(2):642–659, 2014. https://doi.org/10.1007/s10957-013-0384-7
S. Li. Dynamic optimal control of pollution abatement investment under emission permits. Oper. Res. Lett., 44(3):348–353, 2016. https://doi.org/10.1016/j.orl.2016.03.006
S. Li and X. Pan. A dynamic general equilibrium model of pollution abatement under learning by doing. Econom. Lett., 122(2):285–288, 2014. https://doi.org/10.1016/j.econlet.2013.12.002
J.A. List and C.F. Mason. Optimal institutional arrangements for transboundary pollutants in a second best world: evidence from a differential game with asymmetric players. J. Environ. Econ. Manag., 42(3):277–296, 2000. https://doi.org/10.2139/ssrn.212488
Z. Lu, S. Chang, L. Li, L. Cao and Y. Yang. Fitted finite volume method of three transboundary pollution of three gorges reservoir area with emission permits trading by cooperative stochastic differential game. Adv. Appl. Math. Mech., 10(3):690–709, 2018. https://doi.org/10.4208/aamm.OA-2017-0082
N. Rivers and M. Jaccard. Choice of environmental policy in the presence of learning by doing. Energy Econ., 28(2):223–242, 2006. https://doi.org/10.1016/j.eneco.2006.01.002
K.E. Rosendahl. Cost-effective environmental policy: implications of induced technological change. J. Environ. Econ. Manage., 48(3):1099–1121, 2004. https://doi.org/10.1016/j.jeem.2003.12.007
O. Tahvonen. Carbon dioxide abatement as a differential game. Eur. J. Polit. Econ., 10(4):685–705, 1994. https://doi.org/10.1016/0176-2680(94)90033-7
K. Xu, W.Y.K. Chang and L. Liang. Dynamic pricing and channel efficiency in the presence of the cost learning effect. Int. Trans. Oper. Res., 18(5):579–604, 2011. https://doi.org/10.1111/j.1475-3995.2011.00816.x
D. Yeung. Dynamically consistent cooperative solution in a differential game of transboundary industrial pollution. J. Optim. Theory Appl., 134(1):143–160, 2007. https://doi.org/10.1007/s10957-007-9240-y
D. Yeung and L. Petrosyan. Dynamically consistent cooperative solution in a differential game of transboundary industrial pollution. Automatica, 44(6):1532– 1544, 2008. https://doi.org/10.1016/j.automatica.2008.03.005