Microeconomic models of a production economy with environmental externalities

  • Marco RognaEmail author


The environmental issue has surely become a central theme in the economic debate. From one side, this is analysed through large empirical models, solved numerically, that describe explicitly production and consumption\utility functions. On the other side, when environmental problems have a multinational dimension or, simply, involve a multiplicity of stakeholders, the game theoretical approach, focused on the strategic dimension of this problem, offers analytic solutions based on simple utility functions having only pollution and\or abatement as arguments. Although there are examples of large-scale empirical models taking into account game theoretical insights, the diversity in representing the same problem constitutes a gap for these two economic approaches to find a better integration. The present paper tries to bridge the mentioned gap by offering a family of models enough simple to be solved analytically, but where production and consumption, together with environmental aspects, are explicitly portrayed. Although the paper does not tackle directly the game theoretical aspect, the aim of the proposed family of models is to be used in game theoretical analysis in order to improve their representation of the economic–environmental linkage. Furthermore, in the proposed models, the negative consequences of pollution are divided into their detrimental effect on production activities and on utility. This last aspect is modelled in a novel way through the direct introduction into the utility function of an hypothetical environmental good whose consumption’s possibilities are diminished by pollution.


Environmental externalities Microeconomic models Optimal taxation Utility 

JEL Classification

D51 D62 



  1. Antimiani, A., Costantini, V., Martini, C., Palma, A., & Tommasino, M. C. (2012). The GTAP-E: Model description and improvements. In V. Costantini & M. Mazzanti (Eds.), The dynamics of environmental and economic systems (pp. 3–24). Dordrecht: Springer.CrossRefGoogle Scholar
  2. Argenziano, R., & Gilboa, I. (2017). Psychophysical foundations of the Cobb–Douglas utility function. Economics Letters, 157, 21–23.CrossRefGoogle Scholar
  3. Barrett, S. (1994). Self-enforcing international environmental agreements. Oxford Economic Papers, 46, 878–894.CrossRefGoogle Scholar
  4. Baumol, W. J. (1972). On taxation and the control of externalities. The American Economic Review, 62, 307–322.Google Scholar
  5. Bosetti, V., Carraro, C., Galeotti, M., Massetti, E., & Tavoni, M. (2006). WITCH a world induced technical change hybrid model. The Energy Journal, 27(Special Issue: Hybrid Modeling of Energy-Environment Policies: Reconciling Bottom-up and Top-down 2006), 13–37.Google Scholar
  6. Bosetti, V., Carraro, C., De Cian, E., Duval, R., Massetti, E., & Tavoni, M. (2009). The incentives to participate in and the stability of international climate coalitions: A game theoretic approach using the witch model. Venice: International Center for Climate Governance.Google Scholar
  7. Buchanan, J. M., & Craig Stubblebine, W. (1962). Externality. Economica, 29(116), 371–384.CrossRefGoogle Scholar
  8. Burfisher, M. E. (2011). Introduction to computable general equilibrium models. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  9. Chander, P., & Tulkens, H. (2006). The core of an economy with multilateral environmental externalities. In P. Chander, J. Drèze, C. K. Lovell, & J. Mintz (Eds.), Public goods, environmental externalities and fiscal competition (pp. 153–175). Boston: Springer.CrossRefGoogle Scholar
  10. d’Aspremont, C., Jacquemin, A., Gabszewicz, J. J., & Weymark, J. A. (1983). On the stability of collusive price leadership. Canadian Journal of economics, 16, 17–25.CrossRefGoogle Scholar
  11. De Young, R. (1999). Tragedy of the commons. Dordrecht: Kluwer Academic Publishers.Google Scholar
  12. Dellink, R. (2011). Drivers of stability of climate coalitions in the STACO model. Climate Change Economics, 2(02), 105–128.CrossRefGoogle Scholar
  13. Dellink, R. B., Nagashima, M., van Ierland, E. C., Hendrix, E., Sáiz, E., & Weikard, H.-P. (2009). STACO technical document 2: Model description and calibration of STACO-2.1. Mansholt Graduate School Discussion Paper, 49.Google Scholar
  14. Diamantoudi, E., & Sartzetakis, E. S. (2006). Stable international environmental agreements: An analytical approach. Journal of Public Economic Theory, 8(2), 247–263.CrossRefGoogle Scholar
  15. Diamantoudi, E., & Sartzetakis, E. S. (2015). International environmental agreements: Coordinated action under foresight. Economic Theory, 59(3), 527–546.CrossRefGoogle Scholar
  16. Dorfman, R., & Dorfman, N. S. (1972). Economics of the environment: Selected readings. New York: WW Norton.Google Scholar
  17. Easter, R. C., Ghan, S. J., Zhang, Y., Saylor, R. D., Chapman, E. G., Laulainen, N. S., et al. (2004). MIRAGE: Model description and evaluation of aerosols and trace gases. Journal of Geophysical Research: Atmospheres, 109(D20), 1–46.CrossRefGoogle Scholar
  18. Edenhofer, O., Bauer, N., & Kriegler, E. (2005). The impact of technological change on climate protection and welfare: Insights from the model MIND. Ecological Economics, 54(2–3), 277–292.CrossRefGoogle Scholar
  19. Edenhofer, O., Lessmann, K., & Bauer, N. (2006). Mitigation strategies and costs of climate protection: The effects of ETC in the hybrid model MIND. The Energy Journal, 0, 207–222.Google Scholar
  20. Eyckmans, J., & Tulkens, H. (2006). Simulating coalitionally stable burden sharing agreements for the climate change problem. In P. Chander, J. Drèze, C. K. Lovell, & J. Mintz (Eds.), Public goods, environmental externalities and fiscal competition (pp. 218–249). Boston: Springer.CrossRefGoogle Scholar
  21. Finus, M. (2000). Game theory and international environmental co-operation: A survey with an application to the kyoto-protocol. Milan: Fondazione Eni Enrico Mattei.Google Scholar
  22. Gerlagh, R., & Kuik, O. (2014). Spill or leak? Carbon leakage with international technology spillovers: A CGE analysis. Energy Economics, 45, 381–388.CrossRefGoogle Scholar
  23. Grubb, M. (1993). The costs of climate change: Critical elements. In Costs, Impacts, and Benefits of CO2 Mitigation (153–166). IIASA Collaborative Paper Series, CP93-2, Laxenburg, Austria.Google Scholar
  24. Grüning, C., & Peters, W. (2010). Can justice and fairness enlarge international environmental agreements? Games, 1(2), 137–158.CrossRefGoogle Scholar
  25. Hertel, T. W. (1997). Global trade analysis: Modeling and applications. Cambridge: Cambridge University Press.Google Scholar
  26. Jacoby, H. D., Reilly, J. M., McFarland, J. R., & Paltsev, S. (2006). Technology and technical change in the MIT EPPA model. Energy Economics, 28(5–6), 610–631.CrossRefGoogle Scholar
  27. Kehoe, T. J., Levine, D. K., & Romer, P. M. (1992). On characterizing equilibria of economies with externalities and taxes as solutions to optimization problems. Economic Theory, 2(1), 43–68.CrossRefGoogle Scholar
  28. Kypreos, S., & Bahn, O. (2003). A MERGE model with endogenous technological progress. Environmental Modeling & Assessment, 8(3), 249–259.CrossRefGoogle Scholar
  29. Laborde, D., & Valin, H. (2012). Modeling land-use changes in a global CGE: Assessing the EU biofuel mandates with the MIRAGE-BioF model. Climate Change Economics, 3(03), 1250017.CrossRefGoogle Scholar
  30. Luo, Z.-Q., Pang, J.-S., & Ralph, D. (1996). Mathematical programs with equilibrium constraints. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  31. Manne, A., Mendelsohn, R., & Richels, R. (1995). MERGE: A model for evaluating regional and global effects of GHG reduction policies. Energy Policy, 23(1), 17–34.CrossRefGoogle Scholar
  32. Morris, J., Paltsev, S., & Reilly, J. (2012). Marginal abatement costs and marginal welfare costs for greenhouse gas emissions reductions: Results from the EPPA model. Environmental Modeling & Assessment, 17(4), 325–336.CrossRefGoogle Scholar
  33. Nagashima, M., Dellink, R., Van Ierland, E., & Weikard, H.-P. (2009). Stability of international climate coalitions: A comparison of transfer schemes. Ecological Economics, 68(5), 1476–1487.CrossRefGoogle Scholar
  34. Nijkamp, P., Wang, S., & Kremers, H. (2005). Modeling the impacts of international climate change policies in a CGE context: The use of the GTAP-E model. Economic Modelling, 22(6), 955–974.CrossRefGoogle Scholar
  35. Nordhaus, W. D. (1991). To slow or not to slow: The economics of the greenhouse effect. The Economic Journal, 101(407), 920–937.CrossRefGoogle Scholar
  36. Olesen, J. E., & Bindi, M. (2002). Consequences of climate change for European agricultural productivity, land use and policy. European Journal of Agronomy, 16(4), 239–262.CrossRefGoogle Scholar
  37. Ortiz, R. A., & Markandya, A. (2009). Integrated impact assessment models of climate change with an emphasis on damage functions: A literature review, Working Paper, 06-2009, Basque Center for Climate Change, Spain.Google Scholar
  38. Paltsev, S., Reilly, J. M., Jacoby, H. D., Eckaus, R. S., McFarland, J. R., Sarofim, M. C., Asadoorian, M. O., & Babiker, M. H. M. (2005). The MIT emissions prediction and policy analysis (EPPA) model: Version 4. Technical report, MIT Joint Program on the Science and Policy of Global Change.Google Scholar
  39. Perman, R., Ma, Y., McGilvray, J., & Common, M. (2003). Natural resource and environmental economics (3rd ed.). London: Pearson Education.Google Scholar
  40. Piao, S., Ciais, P., Huang, Y., Shen, Z., Peng, S., Li, J., et al. (2010). The impacts of climate change on water resources and agriculture in China. Nature, 467(7311), 43.CrossRefGoogle Scholar
  41. Rogna, M. (2016). Cooperative game theory applied to IEAs: A comparison of solution concepts. Journal of Economic Surveys, 30(3), 649–678.CrossRefGoogle Scholar
  42. Sartzetakis, E. S., & Strantza, S. (2013). International environmental agreements: An emission choice model with abatement technology. Technical report 5/2013, University of Macedonia.Google Scholar
  43. Schlenker, W., & Lobell, D. B. (2010). Robust negative impacts of climate change on African agriculture. Environmental Research Letters, 5(1), 014010.CrossRefGoogle Scholar
  44. Tol, R. S. J. (2009). The economic effects of climate change. Journal of Economic Perspectives, 23(2), 29–51.CrossRefGoogle Scholar
  45. Varian, H. R. (1994). A solution to the problem of externalities when agents are well-informed. The American Economic Review, 84, 1278–1293.Google Scholar
  46. Vrontisi, Z., Abrell, J., Neuwahl, F., Saveyn, B., & Wagner, F. (2016). Economic impacts of EU clean air policies assessed in a CGE framework. Environmental Science & Policy, 55, 54–64.CrossRefGoogle Scholar
  47. Wei, W., Wen, C., Cui, Q., & Xie, W. (2018). The impacts of technological advance on agricultural energy use and carbon emission: An analysis based on GTAP-E model. Journal of Agrotechnical Economics, 2, 003.Google Scholar
  48. Yu, L., & Peng, S. (2017). Assessment and prediction of the impact of trade liberalization on China’s carbon emission: Empirical studies based on the GTAP-MRIO model and the GTAP-E model. Journal of International Trade, 8, 011.Google Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Economics and ManagementFree University of Bolzano-BozenBolzano-BozenItaly

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