# American Institute of Mathematical Sciences

November  2021, 26(11): 5787-5806. doi: 10.3934/dcdsb.2021008

## 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  November 2021 Early access  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 and Continuous Dynamical Systems - B, 2021, 26 (11) : 5787-5806. 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). [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. [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. [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. [5] J. Budds, Contested $H_2O$: Science, policy and politics in water resources management in Chile, Geoforum, 40 (2009), 418-430. [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. [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. [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. [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. [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. [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. [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. [13] M. Gisser and D. A. Sanchez, Competition versus optimal control in groundwater pumping, Water Resources Research, 16 (1980), 638-642. [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. [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. [16] D. H. Negri, The common property aquifer as a differential game, Water Resources Research, 25 (1989), 9-15.  doi: 10.1029/WR025i001p00009. [17] E. Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action, Cambridge University Press, 1990. [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. [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. [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. [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. [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. [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.

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). [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. [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. [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. [5] J. Budds, Contested $H_2O$: Science, policy and politics in water resources management in Chile, Geoforum, 40 (2009), 418-430. [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. [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. [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. [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. [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. [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. [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. [13] M. Gisser and D. A. Sanchez, Competition versus optimal control in groundwater pumping, Water Resources Research, 16 (1980), 638-642. [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. [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. [16] D. H. Negri, The common property aquifer as a differential game, Water Resources Research, 25 (1989), 9-15.  doi: 10.1029/WR025i001p00009. [17] E. Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action, Cambridge University Press, 1990. [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. [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. [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. [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. [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. [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.
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 $c_0 = 1$
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