# American Institute of Mathematical Sciences

## Water taxes and fines imposed on legal and illegal firms exploiting groudwater

 1 Dipartimento Jonico, "Sistemi Giuridici ed Economici del Mediterraneo: societá, ambiente, culture", University of Bari, Via Duomo 259, 74100 Taranto, Italy 2 Dipartimento di Economia, Management e Territorio, University of Foggia, Via Alberto da Zara 11, 71121 Foggia, Italy 3 Department of Economics and Finance, University of Bari, Largo Abbazia S. Scolastica, 53 70124 Bari, Italy

* Corresponding author: Marta Biancardi

Received  July 2020 Revised  October 2020 Published  December 2020

This paper uses a differential game approach to investigate a model that represents the exploitation of groundwater, taking into account the strategic and dynamic interactions among users of the resource and public authority. Agents' behaviour may influence their gains but also the overexploitation of the aquifer. The effects of legal and illegal firms' actions and the contribution of taxes and penalties imposed by public authorities, are analysed by studying Feedback equilibria in order to capture the problem of non-compliance with resource management regimes and to discuss policy options in a non-cooperative and cooperative context. We show that illegal extractions can be a significant stumbling block on the path towards implementing of better management and environmental policies and we explain how, in order to fight this phenomenon, the public authority must increase controlled activity rather than taxation, but also encourage cooperation between legal firms under appropriate conditions.

Citation: Marta Biancardi, Lucia Maddalena, Giovanni Villani. Water taxes and fines imposed on legal and illegal firms exploiting groudwater. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021008
##### References:
 [1] D. Agnew, D. J. Pearce, G. Pramod, T. Peatman, R. Watson, J. Beddington and T. Pitcher, Estimating the worldwide extent of illegal fishing, PLoSONE, 4 (2009). Google Scholar [2] M. Biancardi and L. Maddalena, Competition and cooperation in the exploitation of the groudwater resource, Decis. Econ. Finance, 41 (2018), 219-237.  doi: 10.1007/s10203-018-0217-0.  Google Scholar [3] M. Biancardi and L. Maddalena, Groundwater Management and Agriculture, International Scientific Conference on IT, Tourism, Economics, Management and Agriculture, (2019). doi: 10.31410/itema.2018.992.  Google Scholar [4] M. Biancardi, L. Maddalena and G. Villani, Groundwater extraction among overlapping generations: A differential game approach, Decisions in Economics and Finance, (2020) On Line First. doi: 10.1007/s10203-020-00292-w.  Google Scholar [5] J. Budds, Contested $H_2O$: Science, policy and politics in water resources management in Chile, Geoforum, 40 (2009), 418-430.   Google Scholar [6] H. S. Burness and T. C. Brill, The role for policy in common pool groundwater use, Resource and Energy Economics, 23 (2001), 19-40.  doi: 10.1016/S0928-7655(00)00029-4.  Google Scholar [7] B. Crettez, N. Hayek and G. Zaccour, Non-deceptive counterfeiting and consumer welfare: A differential game approach, Annals of the International Society of Dynamic Games, 17 (2020), 253-296.  doi: 10.1007/978-3-030-56534-3_11.  Google Scholar [8] L. De Stefano and and E. Lopez-Gunn, Unauthorized groundwater use: Institutional, social and ethical considerations, Water Policy, 14 (2012), 147-160.  doi: 10.2166/wp.2012.101.  Google Scholar [9] T. Dworak, G. Schmidt, L. De Stefano, E. Palacios and M. Berglund, Background Paper to the Conference: Application of EU Water Related Policies at Farm Level, Report for the European Commission - DG Environment, 2010. Google Scholar [10] K. Erdlenbruch, M. Tibdall and G. Zaccour, Quantity-quality management of a groundwater resource by a water agency, Environmental Science and Policy, 44 (2014), 201-214.  doi: 10.1016/j.envsci.2014.08.002.  Google Scholar [11] E. Esteban and J. Albiac, Groundwater and ecosystems damages: Questioning the Gisser-Sanchez effect, Ecological Economics, 70 (2011), 2062-2069.  doi: 10.1016/j.ecolecon.2011.06.004.  Google Scholar [12] E. Esteban and A. Dinar, Modeling sustainable groundwater management: Packaging and sequencing of policy interventions, Journal of Environmental Management, 119 (2013), 93-102.  doi: 10.1016/j.jenvman.2012.12.047.  Google Scholar [13] M. Gisser and D. A. Sanchez, Competition versus optimal control in groundwater pumping, Water Resources Research, 16 (1980), 638-642.   Google Scholar [14] P. Koundouri, Current issues in the economics of groundwater resource management, Journal of Economic Surveys, 18 (2004), 703-740.  doi: 10.1111/j.1467-6419.2004.00234.x.  Google Scholar [15] P. Martinez-Santos, M. Ramón Llamas and P. Martinez-Alfaro, Vulnerability assessment of groundwater resources: A modelling-based approach to Mancha Occidental aquifer, Spain, Environmental Modelling & Software, 23 (2008), 1145-1162.   Google Scholar [16] D. H. Negri, The common property aquifer as a differential game, Water Resources Research, 25 (1989), 9-15.  doi: 10.1029/WR025i001p00009.  Google Scholar [17] E. Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action, Cambridge University Press, 1990.   Google Scholar [18] C. R. Palma, Joint quantity/quality management of groundwater, Current Issues in the Economics of Water Resource Management, 23 (2002), 151-170.  doi: 10.1007/978-94-015-9984-9_8.  Google Scholar [19] C. Palmer, The extent and causes of illegal logging: An analysis of a major cause of tropical deforestation in Indonesia, Centre for Social and Economic Research on the Global Environment, CSERGE, 2000. Google Scholar [20] B. Provencher and O. Burt, The externalities associated with the common property exploitation of groundwater, Journal of Environmental Economics and Management, 24 (1993), 139-158.  doi: 10.1006/jeem.1993.1010.  Google Scholar [21] S. J. Rubio and B. Casino, Competitive versus efficient extraction of a common property resource. The groundwater case, J. Econom. Dynam. Control, 25 (2001), 1117-1137.  doi: 10.1016/S0165-1889(99)00047-0.  Google Scholar [22] S. J. Rubio and B. Casino, Strategic Behavior and efficiency in the common property extraction of groundwater, Current Issues in the Economics of Water Resource Management, 23 (2002), 105-122.  doi: 10.1007/978-94-015-9984-9_6.  Google Scholar [23] A. Xepapadeas, Regulation and evolution of compliance in common pool resources, Scandinavian Journal of Economics, 107 (2005), 583-599.  doi: 10.1111/j.1467-9442.2005.00424.x.  Google Scholar

show all references

##### References:
 [1] D. Agnew, D. J. Pearce, G. Pramod, T. Peatman, R. Watson, J. Beddington and T. Pitcher, Estimating the worldwide extent of illegal fishing, PLoSONE, 4 (2009). Google Scholar [2] M. Biancardi and L. Maddalena, Competition and cooperation in the exploitation of the groudwater resource, Decis. Econ. Finance, 41 (2018), 219-237.  doi: 10.1007/s10203-018-0217-0.  Google Scholar [3] M. Biancardi and L. Maddalena, Groundwater Management and Agriculture, International Scientific Conference on IT, Tourism, Economics, Management and Agriculture, (2019). doi: 10.31410/itema.2018.992.  Google Scholar [4] M. Biancardi, L. Maddalena and G. Villani, Groundwater extraction among overlapping generations: A differential game approach, Decisions in Economics and Finance, (2020) On Line First. doi: 10.1007/s10203-020-00292-w.  Google Scholar [5] J. Budds, Contested $H_2O$: Science, policy and politics in water resources management in Chile, Geoforum, 40 (2009), 418-430.   Google Scholar [6] H. S. Burness and T. C. Brill, The role for policy in common pool groundwater use, Resource and Energy Economics, 23 (2001), 19-40.  doi: 10.1016/S0928-7655(00)00029-4.  Google Scholar [7] B. Crettez, N. Hayek and G. Zaccour, Non-deceptive counterfeiting and consumer welfare: A differential game approach, Annals of the International Society of Dynamic Games, 17 (2020), 253-296.  doi: 10.1007/978-3-030-56534-3_11.  Google Scholar [8] L. De Stefano and and E. Lopez-Gunn, Unauthorized groundwater use: Institutional, social and ethical considerations, Water Policy, 14 (2012), 147-160.  doi: 10.2166/wp.2012.101.  Google Scholar [9] T. Dworak, G. Schmidt, L. De Stefano, E. Palacios and M. Berglund, Background Paper to the Conference: Application of EU Water Related Policies at Farm Level, Report for the European Commission - DG Environment, 2010. Google Scholar [10] K. Erdlenbruch, M. Tibdall and G. Zaccour, Quantity-quality management of a groundwater resource by a water agency, Environmental Science and Policy, 44 (2014), 201-214.  doi: 10.1016/j.envsci.2014.08.002.  Google Scholar [11] E. Esteban and J. Albiac, Groundwater and ecosystems damages: Questioning the Gisser-Sanchez effect, Ecological Economics, 70 (2011), 2062-2069.  doi: 10.1016/j.ecolecon.2011.06.004.  Google Scholar [12] E. Esteban and A. Dinar, Modeling sustainable groundwater management: Packaging and sequencing of policy interventions, Journal of Environmental Management, 119 (2013), 93-102.  doi: 10.1016/j.jenvman.2012.12.047.  Google Scholar [13] M. Gisser and D. A. Sanchez, Competition versus optimal control in groundwater pumping, Water Resources Research, 16 (1980), 638-642.   Google Scholar [14] P. Koundouri, Current issues in the economics of groundwater resource management, Journal of Economic Surveys, 18 (2004), 703-740.  doi: 10.1111/j.1467-6419.2004.00234.x.  Google Scholar [15] P. Martinez-Santos, M. Ramón Llamas and P. Martinez-Alfaro, Vulnerability assessment of groundwater resources: A modelling-based approach to Mancha Occidental aquifer, Spain, Environmental Modelling & Software, 23 (2008), 1145-1162.   Google Scholar [16] D. H. Negri, The common property aquifer as a differential game, Water Resources Research, 25 (1989), 9-15.  doi: 10.1029/WR025i001p00009.  Google Scholar [17] E. Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action, Cambridge University Press, 1990.   Google Scholar [18] C. R. Palma, Joint quantity/quality management of groundwater, Current Issues in the Economics of Water Resource Management, 23 (2002), 151-170.  doi: 10.1007/978-94-015-9984-9_8.  Google Scholar [19] C. Palmer, The extent and causes of illegal logging: An analysis of a major cause of tropical deforestation in Indonesia, Centre for Social and Economic Research on the Global Environment, CSERGE, 2000. Google Scholar [20] B. Provencher and O. Burt, The externalities associated with the common property exploitation of groundwater, Journal of Environmental Economics and Management, 24 (1993), 139-158.  doi: 10.1006/jeem.1993.1010.  Google Scholar [21] S. J. Rubio and B. Casino, Competitive versus efficient extraction of a common property resource. The groundwater case, J. Econom. Dynam. Control, 25 (2001), 1117-1137.  doi: 10.1016/S0165-1889(99)00047-0.  Google Scholar [22] S. J. Rubio and B. Casino, Strategic Behavior and efficiency in the common property extraction of groundwater, Current Issues in the Economics of Water Resource Management, 23 (2002), 105-122.  doi: 10.1007/978-94-015-9984-9_6.  Google Scholar [23] A. Xepapadeas, Regulation and evolution of compliance in common pool resources, Scandinavian Journal of Economics, 107 (2005), 583-599.  doi: 10.1111/j.1467-9442.2005.00424.x.  Google Scholar
Pumping levels $\omega_l(t)$ and $\omega_i(t)$ and water table trajectory $H(t)$ assuming $\sigma = 2$
Pumping levels $\omega_l(t)$ and $\omega_i(t)$ and water table trajectory $H(t)$ assuming $\sigma = 2$
Pumping levels $\omega_l(t)$ and $\omega_i(t)$ and water table trajectory $H(t)$ assuming $\delta = 0.10$
Pumping levels $\omega_l(t)$ and $\omega_i(t)$ and water table trajectory $H(t)$ assuming $\delta = 0.10$
Profits of legal and illegal firms when sanction $\sigma$ changes
Profits of legal and illegal firms assuming $\sigma = 2$ and the water tax $\delta$ changes
Comparison among $H_c(t)$ with several value of $L$
Comparison between water level of $H(t)$ and $H_c(t)$ when $L$ changes with $c_0 = 0.60$
Comparison between water level of $H(t)$ and $H_c(t)$ when $L$ changes with $c_0 = 1$
 [1] Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2677-2692. doi: 10.3934/dcdsb.2020200 [2] Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006 [3] Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209 [4] Vakhtang Putkaradze, Stuart Rogers. Numerical simulations of a rolling ball robot actuated by internal point masses. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 143-207. doi: 10.3934/naco.2020021 [5] Hailing Xuan, Xiaoliang Cheng. Numerical analysis and simulation of an adhesive contact problem with damage and long memory. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2781-2804. doi: 10.3934/dcdsb.2020205 [6] Meiqiao Ai, Zhimin Zhang, Wenguang Yu. First passage problems of refracted jump diffusion processes and their applications in valuing equity-linked death benefits. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021039 [7] Gheorghe Craciun, Abhishek Deshpande, Hyejin Jenny Yeon. Quasi-toric differential inclusions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2343-2359. doi: 10.3934/dcdsb.2020181 [8] José Raúl Quintero, Juan Carlos Muñoz Grajales. On the existence and computation of periodic travelling waves for a 2D water wave model. Communications on Pure & Applied Analysis, 2018, 17 (2) : 557-578. doi: 10.3934/cpaa.2018030 [9] Ying Yang. Global classical solutions to two-dimensional chemotaxis-shallow water system. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2625-2643. doi: 10.3934/dcdsb.2020198 [10] Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277 [11] Nizami A. Gasilov. Solving a system of linear differential equations with interval coefficients. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2739-2747. doi: 10.3934/dcdsb.2020203 [12] Yila Bai, Haiqing Zhao, Xu Zhang, Enmin Feng, Zhijun Li. The model of heat transfer of the arctic snow-ice layer in summer and numerical simulation. Journal of Industrial & Management Optimization, 2005, 1 (3) : 405-414. doi: 10.3934/jimo.2005.1.405 [13] Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056 [14] Wolf-Jüergen Beyn, Janosch Rieger. The implicit Euler scheme for one-sided Lipschitz differential inclusions. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 409-428. doi: 10.3934/dcdsb.2010.14.409 [15] Xianming Liu, Guangyue Han. A Wong-Zakai approximation of stochastic differential equations driven by a general semimartingale. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2499-2508. doi: 10.3934/dcdsb.2020192 [16] Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175 [17] Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213 [18] Xiaoming Wang. Quasi-periodic solutions for a class of second order differential equations with a nonlinear damping term. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 543-556. doi: 10.3934/dcdss.2017027 [19] Abdulrazzaq T. Abed, Azzam S. Y. Aladool. Applying particle swarm optimization based on Padé approximant to solve ordinary differential equation. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021008 [20] Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825

2019 Impact Factor: 1.27