Element contents
The Spatial Dimension In Environmental and Resource Economics
Published online by Cambridge University Press: 29 April 2026
Summary
Although the spatial dimension is embedded in most issues studied by environmental and resource economics, its incorporation into economic models is not widespread. As a result, significant aspects of important problems remain hidden, which could lead to policy failures. This Element fills this gap by exploring how space can be integrated into environmental and resource economics. The emergence of spatial patterns in economic models through Turing's mechanism is explained and an extension of Pontryagin's maximum principle under spatial dynamics is provided. Examples of the use of spatial dynamics serve to illustrate why space matters in environmental policy design. Moreover, the differentiation of policy when spatial transport mechanisms are considered is made clear. The tools presented, along with their applications, provide foundations for future research in spatial environmental and resource economics in which the underlying spatial dimension – which is very real – is fully taken into account.
Keywords
Information
- Type
- Element
- Information
- Online ISBN: 9781009694407Publisher: Cambridge University PressPrint publication: 11 June 2026
References
Acemoglu, D., Akcigit, U., Hanley, D. & Kerr, W. (2016). Transition to clean technology. Journal of Political Economy, 124(1), 52–104.CrossRefGoogle Scholar
Adda, J., Boucekkine, R. & Thuilliez, J. (2024). Epidemics, mental health and public trust. Working paper. www.researchgate.net/publication/377355964_Epidemics_Mental_Health_and_Public_Trust.Google Scholar
Albers, H. J., Fischer, C. & Sanchirico, J. N. (2010). Invasive species management in a spatially heterogeneous world: Effects of uniform policies. Resource and Energy Economics, 32(4), 483–99.CrossRefGoogle Scholar
Alexeev, V. A. & Jackson, C. H. (2013). Polar amplification: Is atmospheric heat transport important? Climate Dynamics, 41(2), 533–47.Google Scholar
Alexeev, V. A., Langen, P. L. & Bates, J. R. (2005). Polar amplification of surface warming on an aquaplanet in “ghost forcing”: Experiments without sea ice feedbacks. Climate Dynamics, 24(7), 655–66.CrossRefGoogle Scholar
Anderson, E. W., Brock, W. A., Hansen, L. P. & Sanstad, A. (2014). Robust analytical and computational explorations of coupled economic-climate models with carbon-climate response. RDCEP Working Paper no. 13-05.Google Scholar
Anderson, E. W., Hansen, L. P. & Sargent, T. J. (2012). Small noise methods for risk-sensitive/robust economies. Journal of Economic Dynamics and Control, 36(4), 468–500.CrossRefGoogle Scholar
Anthoff, D. & Tol, R. S. J. (2013). The uncertainty about the social cost of carbon: A composition analysis using FUND. Climatic Change, 117, 515–30.CrossRefGoogle Scholar
Arino, J. (2020). Mathematical epidemiology in a data-rich world. Infectious Disease Modelling, 5, 161–88.CrossRefGoogle Scholar
Arnott, R., Hochman, O. & Rausser, G. C. (2008). Pollution and land use: Optimum and decentralization. Journal of Urban Economics, 64(2), 390–407.CrossRefGoogle Scholar
Augeraud-Véron, E., Boucekkine, R., Gozzi, F., Venditti, A. & Zou, B. (2024). Fifty years of mathematical growth theory: Classical topics and new trends. Journal of Mathematical Economics, 111(13), 102966.CrossRefGoogle Scholar
Baldwin, R., Forslid, R., Martin, P., Ottaviano, G. & Robert-Nicoud, F. (2003). Economic Geography and Public Policy, Princeton, NJ: Princeton University Press.Google Scholar
Baldwin, R. E. & Martin, P. (2004). Agglomeration and regional growth. In Henderson, V. and Thisse, J.-F., eds., Handbook of Regional and Urban Economics, vol. 4, Amsterdam: Elsevier, pp. 2671–711.Google Scholar
Barnett, M., Brock, W. A. & Hansen, L. P. (2020). Pricing uncertainty induced by climate change. Review of Financial Studies 33(3), 1024–66.CrossRefGoogle Scholar
Barnett, M., Brock, W. A. & Hansen, L. P. (2022). Climate change uncertainty spillover in the macroeconomy. NBER Macroeconomics Annual 36(1), 253–320.CrossRefGoogle Scholar
Başar, T. & Olsder, G. J. (1995). Dynamic Noncooperative Game Theory, 2nd ed., London: Academic Press.Google Scholar
Behringer, S. & Upmann, T. (2014). Optimal harvesting of a spatial renewable resource. Journal of Economic Dynamics and Control, 42(C), 105–20.10.1016/j.jedc.2014.03.008CrossRefGoogle Scholar
Bekryaev, R. V., Polyakov, I. V. & Alexeev, V. A. (2010). Role of polar amplification in long-term surface air temperature variations and modern Arctic warming. Journal of Climate, 23(14), 3888–906.10.1175/2010JCLI3297.1CrossRefGoogle Scholar
Belik, V., Geisel, T. & Brockmann, D. (2011). Natural human mobility patterns and spatial spread of infectious diseases. Physical Review X, 1(1), 011001.CrossRefGoogle Scholar
Bewley, T. (1982). An integration of equilibrium theory and turnpike theory. Journal of Mathematical Economics, 10(2–3), 233–67.CrossRefGoogle Scholar
Bosetti, V., Carraro, C., Galeotti, M., Massetti, E. & Tavoni, M. (2006). WITCH: A World Induced Technical Change Hybrid model. Energy Journal, 27(SI2), 13–37.CrossRefGoogle Scholar
Boucekkine, R., Camacho, C. & Fabbri, G. (2013). Spatial dynamics and convergence: The spatial AK model. Journal of Economic Theory, 148(6), 2719–36.CrossRefGoogle Scholar
Boucekkine, R., Camacho, C. & Zou, B. (2009). Bridging the gap between growth theory and the new economic geography: The spatial Ramsey model. Macroeconomic Dynamics, 13(1), 20–45.CrossRefGoogle Scholar
Boucekkine, R., Fabbri, G., Federico, S. & Gozzi, F. (2019a). Geographical environmental Kuznets curves: The optimal growth linear-quadratic case. Mathematical Modelling of Natural Phenomena, 14(1): article 105.10.1051/mmnp/2018076CrossRefGoogle Scholar
Boucekkine, R., Fabbri, G., Federico, S. & Gozzi, F. (2019b). Growth and agglomeration in the heterogeneous space: A generalized AK approach. Journal of Economic Geography, 19(6), 1287–318.CrossRefGoogle Scholar
Boucekkine, R., Fabbri, G., Federico, S. & Gozzi, F. (2022a). Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution. Journal of Mathematical Economics, 98, 102577.10.1016/j.jmateco.2021.102577CrossRefGoogle Scholar
Boucekkine, R., Fabbri, G., Federico, S. & Gozzi, F. (2022b). A dynamic theory of spatial externalities. Games and Economic Behavior, 132, 133–65.CrossRefGoogle Scholar
Broadbridge, P. & Hutchinson, A. J. (2022). Integrable nonlinear reaction-diffusion population models for fisheries. Applied Mathematical Modelling, 102, 748–67.10.1016/j.apm.2021.10.013CrossRefGoogle Scholar
Brock, W. A., Xepapadeas, A. & Yannacopoulos, A. N. (2013). Robust control of a spatially distributed commercial fishery. In Moser, E., Semmler, W., Tragler, G. and Veliov, V. M., eds., Dynamic Optimization in Environmental Economics, Berlin: Springer-Verlag, pp. 215–41.Google Scholar
Brock, W. A., Engström, G. & Xepapadeas, A. (2014). Spatial climate–economic models in the design of optimal climate policies across locations. European Economic Review, 69(C), 78–103.CrossRefGoogle Scholar
Brock, W. A., Engström, G. & Xepapadeas, A. (2015). Energy balance climate models, damage reservoirs, and the time profile of climate change policy. In Bernard, L. and Semmler, W., eds., The Oxford Handbook of the Macroeconomics of Global Warming, Oxford: Oxford University Press, pp. 19–52.Google Scholar
Brock, W. A. & Hansen, L. P. (2019). Wrestling with uncertainty in climate economic models. Working Paper, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3008833.Google Scholar
Brock, W. A. & Starrett, D. (2003). Managing systems with non-convex positive feedback. Environmental and Resource Economics, 26(4), 575–602.CrossRefGoogle Scholar
Brock, W. A. & Xepapadeas, A. (2002). Optimal ecosystem management when species compete for limiting resources. Journal of Environmental Economics and Management, 44(2), 189–230.10.1006/jeem.2001.1206CrossRefGoogle Scholar
Brock, W. A. & Xepapadeas, A. (2005). Spatial analysis in descriptive models of renewable resource management. Swiss Journal of Economics and Statistics, 141(III), 331–54.Google Scholar
Brock, W. A. & Xepapadeas, A. (2008). Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control. Journal of Economic Dynamics and Control, 32(9), 2745–87.CrossRefGoogle Scholar
Brock, W. A. & Xepapadeas, A. (2010). Pattern formation, spatial externalities and regulation in coupled economic–ecological systems. Journal of Environmental Economics and Management, 59(2), 149–64.CrossRefGoogle Scholar
Brock, W. A. & Xepapadeas, A. (2017). Climate change policy under polar amplification. European Economic Review, 94(C), 263–82.CrossRefGoogle Scholar
Brock, W. A. & Xepapadeas, A. (2018). Modeling coupled climate, ecosystems, and economic systems. In Dasgupta, P., Pattanayak, S. K. and Smith, V. K., eds., Handbook of Environmental Economics, vol. 4, Amsterdam: North-Holland, pp. 1–45.Google Scholar
Brock, W. A. & Xepapadeas, A. (2019). Regional climate change policy under positive feedbacks and strategic interactions. Environmental and Resource Economics, 72(1), 51–75.CrossRefGoogle Scholar
Brock, W. A. & Xepapadeas, A. (2020). Spatial heat transport, polar amplification and climate change policy. In Chichilnisky, G. and Rezai, A., eds., Handbook of Climate Change, Cheltenham: Edward Elgar Publishing, pp. 127–66.Google Scholar
Brock, W. & Xepapadeas, A. (2025). Land-use, climate change and the emergence of infectious diseases: A synthesis. Environmental and Resource Economics. doi.org/10.1007/s10640-024-00949-9.CrossRefGoogle Scholar
Brock, W. A., Xepapadeas, A. & Yannacopoulos, A. N. (2013). Robust control of a spatially distributed commercial fishery. In Moser, E., Semmler, W., Tragler, G. and Veliov, V. M., eds., Dynamic Optimization in Environmental Economics, Berlin: Springer-Verlag, pp. 215–41.Google Scholar
Brock, W. A., Xepapadeas, A. & Yannacopoulos, A. N. (2014a). Optimal agglomerations in dynamic economics. Journal of Mathematical Economics, 53(C), 1–15.CrossRefGoogle Scholar
Brock, W. A., Xepapadeas, A. & Yannacopoulos, A. N. (2014b). Optimal control in space and time and the management of environmental resources. Annual Reviews in Resource Economics, 6(1), 33–68.CrossRefGoogle Scholar
Brock, W. A., Xepapadeas, A. & Yannacopoulos, A. N. (2014c). Robust control and hot spots in spatiotemporal economic systems. Dynamic Games and Applications, 4(3), 257–89.10.1007/s13235-014-0109-zCrossRefGoogle Scholar
Brock, W. A., Xepapadeas, A. & Yannacopoulos, A. N. (2014d). Spatial externalities and agglomeration in a competitive industry. Journal of Economic Dynamics and Control, 42(C), 143–74.10.1016/j.jedc.2014.03.010CrossRefGoogle Scholar
Brozović, N., Sunding, D. & Zilberman, D. (2010). On the spatial nature of the groundwater pumping externality. Resource and Energy Economics, 32(2), 154–64.10.1016/j.reseneeco.2009.11.010CrossRefGoogle Scholar
Cai, Y., Brock, W., Xepapadeas, A. & Judd, K. (2019). Climate policy under spatial heat transport: Cooperative and noncooperative regional outcomes. https://arxiv.org/pdf/1909.04009.pdf.Google Scholar
Cai, Y., Brock, W. & Xepapadeas, A. (2023). Climate change impact on economic growth: Regional climate policy under cooperation and noncooperation. Journal of the Association of Environmental and Resource Economists, 10(3), 569–605.CrossRefGoogle Scholar
Calvo, E. & Rubio, S. J. (2012). Dynamic models of international environmental agreements: A differential game approach. International Review of Environmental and Resource Economics, 6(4), 289–339.CrossRefGoogle Scholar
Camacho, C. & Pérez-Barahona, A. (2015). Land use dynamics and the environment. Journal of Economic Dynamics and Control, 52(C), 96–118.CrossRefGoogle Scholar
Cantrell, R. S. & Cosner, C. (2003). Spatial Ecology via Reaction-Diffusion Equations. Chichester: John Wiley and Sons.Google Scholar
Cass, D. & Shell, K. eds. (1976). The Hamiltonian Approach to Dynamic Economics. New York: Academic Press.Google Scholar
Castruccio, S., McInerney, D. J., Stein, M. L., Crouch, F. L., Jacob, R. I. & Moyer, E. J. (2014). Statistical emulation of climate model projections based on precomputed GCM runs. Journal of Climate, 27(5), 1829–44.CrossRefGoogle Scholar
Chincarini, L. & Asherie, N. (2008). An analytical model for the formation of economic clusters. Regional Science and Urban Economics, 38(3), 252–70.CrossRefGoogle Scholar
Copeland, B. R. (1996). Pollution content tariffs, environmental rent shifting, and the control of cross-border pollution. Journal of International Economics, 40(3–4), 459–76.CrossRefGoogle Scholar
Copeland, B. R. & Taylor, M. S. (1994). North–South trade and the environment. Quarterly Journal of Economics, 109(3), 755–87.CrossRefGoogle Scholar
Copeland, B. R. & Taylor, M. S. (1995). Trade and transboundary pollution. American Economic Review, 85(4), 716–37.Google Scholar
Cornet, A. & Camacho, C. (2021). Diffusion of soil pollution in an agricultural economy: The emergence of regions, frontiers and spatial patterns. https://ssrn.com/abstract=3977551.Google Scholar
Costello, C. & Polasky, S. (2004). Dynamic reserve site selection. Resource and Energy Economics, 26(2), 157–74.CrossRefGoogle Scholar
Costello, C. & Polasky, S. (2008). Optimal harvesting of stochastic spatial resources. Journal of Environmental Economics and Management, 56(1), 1–18.10.1016/j.jeem.2008.03.001CrossRefGoogle Scholar
Cruz, J. L. and Rossi-Hansberg, E. (2024). The economic geography of global warming. Review of Economic Studies, 91(2), 899–939.10.1093/restud/rdad042CrossRefGoogle Scholar
Cui, R., Li, H., Mei, L. & Shi, J. (2017). Effect of harvesting quota and protection zone in a reaction-diffusion model arising from fishery management. Discrete and Continuous Dynamical Systems - Series B, 22(3), 791–807.CrossRefGoogle Scholar
Deacon, R. T., Kolstad, C. D., Kneese, A. V., Brookshire, D. S., Scrogin, D., Fisher, A. C., Ward, M., Smith, K. & Wilen, J. (1998). Research trends and opportunities in environmental and natural resource economics. Environmental and Resource Economics, 11, 383–97.CrossRefGoogle Scholar
de Frutos, J. & Martín-Herrán, G. (2019). Spatial effects and strategic behavior in a multiregional transboundary pollution dynamic game. Journal of Environmental Economics and Management, 97(C), 182–207.10.1016/j.jeem.2017.08.001CrossRefGoogle Scholar
de Frutos, J., López-Perez, P. M. & Martín-Herrán, G. (2021). Equilibrium strategies in a multiregional transboundary pollution differential game with spatially distributed controls. Automatica, 125, 109411.CrossRefGoogle Scholar
Denant-Boemont, L., Gaigné, C. & Gaté, R. (2018). Urban spatial structure, transport-related emissions and welfare. Journal of Environmental Economics and Management, 89(C), 29–45.10.1016/j.jeem.2018.01.006CrossRefGoogle Scholar
Derzko, N. A., Sethi, S. P. & Thompson, G. L. (1984). Necessary and sufficient conditions for optimal control of quasilinear partial differential systems. Journal of Optimization Theory and Applications, 43(1), 89–101.CrossRefGoogle Scholar
Desmet, K. & Rossi-Hansberg, E. (2009). Spatial growth and industry age. Journal of Economic Theory, 144(6), 2477–502.CrossRefGoogle Scholar
Desmet, K. & Rossi-Hansberg, E. (2010). On spatial dynamics. Journal of Regional Science, 50(1), 43–63.10.1111/j.1467-9787.2009.00648.xCrossRefGoogle Scholar
Desmet, K. & Rossi-Hansberg, E. (2015). On the spatial economic impact of global warming. Journal of Urban Economics, 88(C), 16–27.CrossRefGoogle Scholar
Dockner, E. (1985). Local stability analysis in optimal control problems with two variables. In Feichtinger, G., ed., Optimal Control Theory and Economic Analysis 2, Amsterdam: North-Holland, pp. 89–113.Google Scholar
Dockner, E. J. & Long, N. V. (1993). International pollution control: Cooperative versus noncooperative strategies. Journal of Environmental Economics and Management, 25(1), 13–29.CrossRefGoogle Scholar
Dutta, P. & Radner, R. (2006). A game-theoretic approach to global warming. Advances in Mathematical Economics, 8, 135–53.CrossRefGoogle Scholar
Easterling, W. E. (1997). Why regional studies are needed in the development of full-scale integrated assessment modelling of global change processes. Global Environmental Change, 1(4), 337–56.Google Scholar
Epanchin-Nieli, R. S. & Wilen, J. E. (2012). Optimal spatial control of biological invasions. Journal of Environmental Economics and Management, 63(2), 260–70.Google Scholar
Ferraccioli, F., Stilianakis, N. I. & Veliov, V. M. (2024). A spatial epidemic model with contact and mobility restrictions. Mathematical and Computer Modelling of Dynamical Systems, 30(1), 284-302.CrossRefGoogle Scholar
Flannery, B. P. (1984). Energy balance models incorporating transport of thermal and latent energy. Journal of the Atmospheric Sciences, 41(3), 414–21.2.0.CO;2>CrossRefGoogle Scholar
Francis, J. A. (2017). Why are Arctic linkages to extreme weather still up in the air? Bulletin of the American Meteorological Society, 98(12), 2551–57.10.1175/BAMS-D-17-0006.1CrossRefGoogle Scholar
Francis, J. A. & Skific, N. (2015). Evidence linking rapid Arctic warming to mid-latitude weather patterns. Philosophical Transactions of the Royal Society A, 373(2045), 20140170.CrossRefGoogle ScholarPubMed
Francis, J. A., Skific, N. & Vavrus, S. J. (2018). North American weather regimes are becoming more persistent: Is Arctic amplification a factor? Geophysical Research Letters, 45(20), 11414–22.CrossRefGoogle Scholar
Francis, J. A. & Vavrus, S. J. (2014). Evidence for a wavier jet stream in response to rapid Arctic warming. Environmental Research Letters, 10(1), 014005.10.1088/1748-9326/10/1/014005CrossRefGoogle Scholar
Fujita, M., Krugman, P. & Venables, A. J. (1999). The Spatial Economy, Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Fujita, M. & Mori, T. (2005). Frontiers of the new economic geography. Papers in Regional Science, 84(3), 377–405.10.1111/j.1435-5957.2005.00021.xCrossRefGoogle Scholar
Fujita, M. & Ogawa, H. (1982). Multiple equilibria and structural transition of non-monocentric urban configurations. Regional Science and Urban Economics, 12(2), 161–96.CrossRefGoogle Scholar
Fujita, M. & Thisse, J.-F. (2013). The Economics of Agglomeration: Cities, Industrial Location and Globalization, 2nd ed., Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Gasparrini, A., Guo, Y., Hashizume, M. et al. (2015). Mortality risk attributable to high and low ambient temperature: A multicountry observational study. The Lancet, 386(9991), 369–75.CrossRefGoogle ScholarPubMed
Ghil, M. (1976). Climate stability for a sellers-type model. Journal of the Atmospheric Sciences, 33(1), 3–20.2.0.CO;2>CrossRefGoogle Scholar
Ghil, M. & Lucarini, V. (2020). The physics of climate variability and climate change. Reviews of Modern Physics, 92, 1–77.10.1103/RevModPhys.92.035002CrossRefGoogle Scholar
Gisser, M. & Sanchez, D. A. (1980). Competition versus optimal control in groundwater pumping. Water Resources Research, 16(4), 638–42.CrossRefGoogle Scholar
Goetz, R. U. & Zilberman, D. (2000). The dynamics of spatial pollution: The case of phosphorus runoff from agricultural land. Journal of Economic Dynamics and Control, 24(1), 143–63.10.1016/S0165-1889(98)00067-0CrossRefGoogle Scholar
Goetz, R. U. & Zilberman, D. (2007). The economics of land-use regulation in the presence of an externality: A dynamic approach. Optimal Control Applications and Methods, 28(1), 21–43.10.1002/oca.787CrossRefGoogle Scholar
Gozzi, F. & Leocata, M. (2022). A stochastic model of economic growth in time-space. SIAM Journal on Control and Optimization, 60(2), 620-51.CrossRefGoogle Scholar
Grass, D. & Uecker, H. (2017). Optimal management and spatial patterns in a distributed shallow lake model. Electronic Journal of Differential Equations, 2017(1), 1–21.Google Scholar
Hansen, L. P. & Sargent, T. J. (2001). Robust control and model uncertainty. American Economic Review, 91(2), 60–6.CrossRefGoogle Scholar
Hansen, L. P. & Sargent, T. J. (2008). Robustness in Economic Dynamics. Princeton, NJ: Princeton University Press.Google Scholar
Hansen, L. P. & Sargent, T. J. (2019). Macroeconomic uncertainty prices when beliefs are tenuous. NBER Working Paper no. 25781. National Bureau of Economic Research, Cambridge, MA.Google Scholar
Hansen, L. P., Sargent, T. J., Turmuhambetova, G. & Williams, N. (2006). Robust control and model misspecification. Journal of Economic Theory, 128(1), 45–90.CrossRefGoogle Scholar
Hassler, J. & Krusell, P. (2018). Environmental macroeconomics: The case of climate change. In Dasgupta, P., Pattanayak, S. K. and Smith, V. K., eds., Handbook of Environmental Economics, vol. 4, Amsterdam: North-Holland., pp. 333–94.Google Scholar
Hassler, J., Krusell, P. & Smith, A. A. (2016). Environmental macroeconomics. In Taylor, J. B. and Uhlig, H., eds., Handbook of Macroeconomics, vol. 2b, Amsterdam: North-Holland, pp. 1893–2008.Google Scholar
Hastings, A. (1982). Dynamics of a single species in a spatially varying environment: The stabilizing role of high dispersal rates. Journal of Mathematical Biology, 16(1), 49–55.10.1007/BF00275160CrossRefGoogle Scholar
Hastings, A. & Harrison, S. (1994). Metapopulation dynamics and genetics. Annual Review of Ecology and Statistics, 25, 167–88.Google Scholar
Hatzipanayotou, P., Lahiri, S. & Michael, M. S. (2002). Can cross-border pollution reduce pollution? Canadian Journal of Economics, 35(4), 805–18.CrossRefGoogle Scholar
Hatzipanayotou, P., Lahiri, S. & Michael, M. S. (2005). Reforms of environmental policies in the presence of cross-border pollution and public–private clean-up. Scandinavian Journal of Economics, 107(2), 315–33.10.1111/j.1467-9442.2005.00410.xCrossRefGoogle Scholar
Henderson, J. V. (1977). Externalities in a spatial context: The case of air pollution. Journal of Public Economics, 7(1), 89–110.CrossRefGoogle Scholar
Hethcote, H. W. (1989). Three basic epidemiological models. In Levin, S. A., Hallam, T. G. and Gross, L. J., eds., Applied Mathematical Ecology, Berlin: Springer, pp. 119–44.Google Scholar
Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42(4), 599–653.CrossRefGoogle Scholar
High-Level Commission on Carbon Prices (2017). Report of the High-Level Commission on Carbon Prices, Washington, DC: World Bank.Google Scholar
Hope, C. (2006). The marginal impact of CO2 from PAGE2002: An integrated assessment model incorporating the IPCC’s five reasons for concern. Integrated Assessment Journal, 6(1), 566–77.Google Scholar
Hoyle, R. (2006). Pattern Formation. An Introduction to Methods. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hsiang, S., Kopp, R., Jina, A. et al. (2017). Estimating economic damage from climate change in the United States. Science, 356(6345), 1362–69.10.1126/science.aal4369CrossRefGoogle ScholarPubMed
Ioannides, Y. M. & Overman, H. G. (2007). Spatial evolution and the U.S. urban system. Journal of Economic Geography, 4(2), 131–56.Google Scholar
IPCC (2013). Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, T, F. Stocker, Qin, D., Plattner, G.-K.r et al., eds., Cambridge: Cambridge University Press.Google Scholar
IPCC (2021). Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, Masson-Delmotte, V., Zhai, P., Piraniet, A. et al., eds., Cambridge: Cambridge University Press.Google Scholar
Jorgensen, S., Martín-Herrán, G. & Zaccour, G. (2010). Dynamic games in the economics and management of pollution. Environmental Modeling and Assessment, 15(6), 443–67.10.1007/s10666-010-9221-7CrossRefGoogle Scholar
Kaitala, V., Pohjola, M. & Tahvonen, O. (1992). Transboundary air pollution and soil acidification: A dynamic analysis of an acid rain game between Finland and the USSR. Environmental and Resource Economics, 2(2), 161–81.10.1007/BF00338241CrossRefGoogle Scholar
Kamien, M. I. & Schwartz, N. L. (1991). Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management, 2nd ed., Amsterdam: Elsevier.Google Scholar
Kendall, D. G. (1957). Discussion of ‘Measles periodicity and community size’ by M. S. Bartlett. Journal of the Royal Statistical Society, A120, 64–76.Google Scholar
Kendall, D. G. (1965). Mathematical models of the spread of infection. In: Mathematics and Computer Science in Biology and Medicine, London: Medical Research Council, pp. 213–25.Google Scholar
Knutti, R. (2013). Relationship between global emissions and global temperature rise. Working Group I Contribution to the IPCC Fifth Assessment Report. Presentation. https://unfccc.int/sites/default/files/7_knutti.reto.3sed2.pdf.Google Scholar
Knutti, R. & Rogelj, J. (2015). The legacy of our CO 2 emissions: A clash of scientific facts, politics and ethics. Climatic Change, 133(3), 361–73.10.1007/s10584-015-1340-3CrossRefGoogle Scholar
Kolstad, C. (1987). Uniformity versus differentiation in regulating externalities. Journal of Environmental Economics and Management, 14(4), 386–99.10.1016/0095-0696(87)90029-5CrossRefGoogle Scholar
Kossioris, G., Plexousakis, M. A., Xepapadeas, A. & de Zeeuw, A. (2011). On the optimal taxation of common-pool resources. Journal of Economic Dynamics and Control, 35(11), 1868–79.CrossRefGoogle Scholar
Kossioris, G., Plexousakis, M. A., Xepapadeas, A., de Zeeuw, A. & Mäler, K.-G. (2008). Feedback Nash equilibria for non-linear differential games in pollution control. Journal of Economic Dynamics and Control, 32(4), 1312–31.10.1016/j.jedc.2007.05.008CrossRefGoogle Scholar
Krugman, P. R. (1996). The Self-Organizing Economy, Cambridge, MA: Blackwell Publishers.Google Scholar
Krugman, P. R. (1998). Space: The final frontier. Journal of Economic Perspectives, 12(2), 161–74.10.1257/jep.12.2.161CrossRefGoogle Scholar
Krusell, P. & Smith, A. A. (2022). Climate change around the world. NBER Working Paper no. 30338 and CEPR Discussion Paper no. 17522.10.3386/w30338CrossRefGoogle Scholar
Kurz, M. (1968). The general instability of a class of competitive growth processes. Review of Economic Studies, 35(2), 155–74.10.2307/2296545CrossRefGoogle Scholar
Kuwayama, Y. & Brozović, N. (2013). The regulation of a spatially heterogeneous externality: Tradable groundwater permits to protect streams. Journal of Environmental Economics and Management, 66(2), 364–82.10.1016/j.jeem.2013.02.004CrossRefGoogle Scholar
Kyriakopoulou, E. & Xepapadeas, A. (2013). Environmental policy, first nature advantage and the emergence of economic clusters. Regional Science and Urban Economics, 43(1), 101–16.10.1016/j.regsciurbeco.2012.05.006CrossRefGoogle Scholar
Kyriakopoulou, E. & Xepapadeas, A. (2017). Atmospheric pollution in rapidly growing industrial cities: Spatial policies and land use patterns. Journal of Economic Geography, 17(3), 607–34.Google Scholar
Langen, P. L. & Alexeev, V. A. (2007). Polar amplification as a preferred response in an idealized aquaplanet GCM. Climate Dynamics, 29(2–3), 305–17.10.1007/s00382-006-0221-xCrossRefGoogle Scholar
La Torre, D., Liuzzi, D. & Marsiglio, S. (2015). Pollution diffusion and abatement activities across space and over time. Mathematical Social Sciences, 78, 48–63.10.1016/j.mathsocsci.2015.09.001CrossRefGoogle Scholar
La Torre, D., Liuzzi, D. & Marsiglio, S. (2021). Transboundary pollution externalities: Think globally, act locally? Journal of Mathematical Economics, 96, 102511.10.1016/j.jmateco.2021.102511CrossRefGoogle Scholar
La Torre, D., Liuzzi, D. & Marsiglio, S. (2022). Geographical heterogeneities and externalities in an epidemiological-macroeconomic framework. Journal of Public Economic Theory, 24(5), 1154–81.10.1111/jpet.12576CrossRefGoogle Scholar
La Torre, D., Liuzzi, D. & Marsiglio, S. (2024). Epidemic outbreaks and the optimal lockdown area: A spatial normative approach. Economic Theory, 77(1), 349–411.10.1007/s00199-023-01517-wCrossRefGoogle Scholar
Leduc, M., Matthews, H. D. & de Elía, R. (2016). Regional estimates of the transient climate response to cumulative CO2 emissions. Nature Climate Change, 6(5), 474–78.10.1038/nclimate2913CrossRefGoogle Scholar
Lenton, T. M., Held, H., Kriegler, E. et al. (2008). Tipping elements in the Earth’s climate system. PNAS, 105(6), 1786–93.10.1073/pnas.0705414105CrossRefGoogle ScholarPubMed
Levin, S. A. (1974). Dispersion and population interactions. American Naturalist, 108(960), 207–28.10.1086/282900CrossRefGoogle Scholar
Levin, S. A. (1976). Population dynamic models in heterogeneous environments. Annual Review of Ecology and Systematics, 7(1), 287–310.10.1146/annurev.es.07.110176.001443CrossRefGoogle Scholar
Levin, S. A. & Segel, L. A. (1985). Pattern generation in space and aspect. SIAM Review, 27(1), 45–67.10.1137/1027002CrossRefGoogle Scholar
Levin, S. A. & Xepapadeas, A. (2017). Transboundary capital and pollution flows and the emergence of regional inequalities. Discrete and Continuous Dynamical Systems - Series B, 22(3), 913-22.10.3934/dcdsb.2017046CrossRefGoogle Scholar
Lin, J., Andreasen, V., Casagrandi, R. & Levin, S. A. (2003). Traveling waves in a model of influenza A drift. Journal of Theoretical Biology, 222(4), 437–45.10.1016/S0022-5193(03)00056-0CrossRefGoogle Scholar
Liu, Y. & Sims, C. (2016). Spatial-dynamic externalities and coordination in invasive species control. Resource and Energy Economics, 44, 23–38.10.1016/j.reseneeco.2016.01.001CrossRefGoogle Scholar
Lucas, R. E., Jr. (2001). Externalities and cities. Review of Economic Dynamics, 4(2), 245–74.10.1006/redy.2000.0108CrossRefGoogle Scholar
Lucas, R. E., Jr. & Rossi-Hansberg, E. (2002). On the internal structure of cities. Econometrica, 70(4), 1445–76.10.1111/1468-0262.00338CrossRefGoogle Scholar
MacDougall, A. H. & Friedlingstein, P. (2015). The origin and limits of the near proportionality between climate warming and cumulative CO2 emissions. Journal of Climate, 28(10), 4217–30.10.1175/JCLI-D-14-00036.1CrossRefGoogle Scholar
MacDougall, A. H., Swart, N. C. & Knutti, R. (2017). The uncertainty in the transient climate response to cumulative CO2 emissions arising from the uncertainty in physical climate parameters. Journal of Climate, 30(2), 813–27.10.1175/JCLI-D-16-0205.1CrossRefGoogle Scholar
Mäler, K.-G. (1989). The acid rain game. In Folmer, H. and van Ierland, E., eds., Valuation Methods and Policy Making in Environmental Economics, vol. 36, Amsterdam: Elsevier, pp. 231–52.Google Scholar
Mäler, K.-G. & de Zeeuw, A. (1998). The acid rain differential game. Environmental and Resource Economics, 12(2), 167–84.10.1023/A:1008273509255CrossRefGoogle Scholar
Mäler, K.-G., Xepapadeas, A. & de Zeeuw, A. (2003). The economics of shallow lakes. Environmental and Resource Economics, 26(4), 603–24.10.1023/B:EARE.0000007351.99227.42CrossRefGoogle Scholar
Matthews, H. D., Gillett, N. P, Stott, P. A. & Zickfield, K. (2009). The proportionality of global warming to cumulative carbon emissions. Nature, 459(7248), 829–33.10.1038/nature08047CrossRefGoogle ScholarPubMed
Matthews, H. D., Solomon, S. & Pierrehumbert, R. (2012). Cumulative carbon as a policy framework for achieving climate stabilization. Philosophical Transactions of the Royal Society A, 370, 4365–79.Google ScholarPubMed
McKenzie, L. W. (1976). Turnpike theory. Econometrica, 44(5), 841–65.10.2307/1911532CrossRefGoogle Scholar
Merlis, T. M. & Henry, M. (2018). Simple estimates of polar amplification in moist diffusive energy balance models. Journal of Climate, 31(15), 5811–24.10.1175/JCLI-D-17-0578.1CrossRefGoogle Scholar
Milner, F. A. & Zhao, R. (2008). S-I-R model with directed spatial diffusion. Mathematical Population Studies, 15(3), 160-81.10.1080/08898480802221889CrossRefGoogle Scholar
Murray, J. D. (2002). Mathematical Biology, I: An Introduction, 3rd ed., Berlin: Springer.10.1007/b98868CrossRefGoogle Scholar
Murray, J. D. (2003). Mathematical Biology, II: Spatial Models and Biomedical Applications, 3rd ed., Berlin: Springer.10.1007/b98869CrossRefGoogle Scholar
Nagase, Y. & Silva, E. C. D. (2007). Acid rain in China and Japan: A game-theoretic analysis. Regional Science and Urban Economics, 37(1), 100–20.10.1016/j.regsciurbeco.2006.08.001CrossRefGoogle Scholar
Negri, D. H. (1989). The common property aquifer as a differential game. Water Resources Research, 25(1), 9–15.10.1029/WR025i001p00009CrossRefGoogle Scholar
Nordhaus, W. D. (2011). Estimates of the social cost of carbon: Background and results from the RICE-2011 model. NBER Working Paper no. 17540. National Bureau of Economic Research, Cambridge, MA.10.3386/w17540CrossRefGoogle Scholar
Nordhaus, W. D. (2014). Estimates of the social cost of carbon: Concepts and results from the DICE-2013R model and alternative approaches. Journal of the Association of Environmental and Resource Economists, 1(1/2), 273–312.10.1086/676035CrossRefGoogle Scholar
Nordhaus, W. D. (2017). Revisiting the social cost of carbon. Proceedings of the National Academy of Sciences, 114(7), 1518–23.10.1073/pnas.1609244114CrossRefGoogle ScholarPubMed
Nordhaus, W. D. & Sztorc, P. (2013). DICE 2013-R: Introduction and User’s Manual, Yale University, New Haven, CT.Google Scholar
Nordhaus, W. D. & Yang, Z. (1996). A regional dynamic general-equilibrium model of alternative climate-change strategies. American Economic Review, 86(4), 741–65.Google Scholar
North, G. R. (1975a). Analytical solution to a simple climate model with diffusive heat transport. Journal of the Atmospheric Sciences, 32(7), 1301–07.10.1175/1520-0469(1975)032<1301:ASTASC>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
North, G. R. (1975b). Theory of energy-balance climate models. Journal of the Atmospheric Sciences, 32(11), 2033–43.10.1175/1520-0469(1975)032<2033:TOEBCM>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
North, G. R., Cahalan, R. F. & Coakley, J. A. Jr. (1981). Energy balance climate models. Reviews of Geophysics and Space Physics, 19(1), 91–121.10.1029/RG019i001p00091CrossRefGoogle Scholar
North, G. R. & Kim, K.-Y. (2017). Energy Balance Climate Models. Hoboken, NJ: Wiley.10.1002/9783527698844CrossRefGoogle Scholar
Pfeiffer, L. & Lin, C. Y. (2012). Groundwater pumping and spatial externalities in agriculture. Journal of Environmental Economics and Management, 64(1), 16–30.10.1016/j.jeem.2012.03.003CrossRefGoogle Scholar
Pindyck, R. S. (2007). Uncertainty in environmental economics. Review of Environmental Economics and Policy, 1(1), 45–65.10.1093/reep/rem002CrossRefGoogle Scholar
Pindyck, R. S. (2011). Fat tails, thin tails, and climate change policy. Review of Environmental Economics and Policy, 5(2), 258–74.10.1093/reep/rer005CrossRefGoogle Scholar
Pindyck, R. S. (2012). Uncertain outcomes and climate change policy. Journal of Environmental Economics and Management, 63(3), 289–303.10.1016/j.jeem.2011.12.001CrossRefGoogle Scholar
Pindyck, R. S. (2013). Climate change policy: What do the models tell us? Journal of Economic Literature, 51(3), 860–72.10.1257/jel.51.3.860CrossRefGoogle Scholar
Provencher, B. & Burt, O. (1993). The externalities associated with the common property exploitation of groundwater. Journal of Environmental Economics and Management, 24(2), 139–58.10.1006/jeem.1993.1010CrossRefGoogle Scholar
Quah, D. T. (1996). Empirics for economic growth and convergence. European Economic Review, 40(6), 1353–75.10.1016/0014-2921(95)00051-8CrossRefGoogle Scholar
Quah, D. T. (1997). Empirics for growth and distribution: Stratification, polarization, and convergence clubs. Journal of Economic Growth, 2(1), 27–59.10.1023/A:1009781613339CrossRefGoogle Scholar
Quah, D. T. (2002). Spatial agglomeration dynamics. AEA Papers and Proceedings, 92(2), 247–52.Google Scholar
Ramanathan, V., Crutzen, P. J., Mitra, A. P. & Sikka, D. (2002). The Indian Ocean experiment and the Asian brown cloud. Current Science, 83(8), 947–54.Google Scholar
Rassweiler, A., Costello, C. & Siegel, D. A. (2012). Marine protected areas and the value of spatially optimized fishery management. Proceedings of the National Academy of Sciences, 109(29), 11884–9.10.1073/pnas.1116193109CrossRefGoogle ScholarPubMed
Redding, S. J. & Rossi-Hansberg, E. (2017). Quantitative spatial economics. Annual Review of Economics, 9(1), 21–58.10.1146/annurev-economics-063016-103713CrossRefGoogle Scholar
Regnier, C. & Legras, S. (2018). Urban structure and environmental externalities. Environmental and Resource Economics, 70(1), 31–52.10.1007/s10640-016-0109-0CrossRefGoogle Scholar
Rossi-Hansberg, E. & Sarte, P.-D. (2012). Economics of housing externalities. International Encyclopedia of Housing and Home, 2, 47–50.10.1016/B978-0-08-047163-1.00102-8CrossRefGoogle Scholar
Rossi-Hansberg, E., Sarte, P.-D. & Owens, R. III. (2010). Housing externalities. Journal of Political Economy, 118(3), 485–535.10.1086/653138CrossRefGoogle Scholar
Ruan, S. (2007). Spatial-temporal dynamics in nonlocal epidemiological models. In Takeuchi, Y., Iwasa, Y. and Sato, K., eds., Mathematics for Life Science and Medicine, Berlin: Springer, pp. 97–122.Google Scholar
Saak, A. E. & Peterson, J. M. (2007). Groundwater use under incomplete information. Journal of Environmental Economics and Management, 54(2), 214–28.10.1016/j.jeem.2006.12.005CrossRefGoogle Scholar
Sanchirico, J. N. & Wilen, J. E. (2005). Optimal spatial management of renewable resources: Matching policy scope to ecosystem scale. Journal of Environmental Economics and Management, 50(1), 23–46.10.1016/j.jeem.2004.11.001CrossRefGoogle Scholar
Sanchirico, J. N. & Wilen, J. E. (1999). Bioeconomics of spatial exploitation in a patchy environment. Journal of Environmental Economics and Management, 37(2), 129–50.10.1006/jeem.1998.1060CrossRefGoogle Scholar
Sanchirico, J. N. & Wilen, J. E. (2001). A bioeconomic model of marine reserve creation. Journal of Environmental Economics and Management, 42(3), 257–76.10.1006/jeem.2000.1162CrossRefGoogle Scholar
Sanchirico, J. N. & Wilen, J. E. (2005). Optimal spatial management of renewable resources: Matching policy scope to ecosystem scale. Journal of Environmental Economics and Management, 50(1), 23–46.10.1016/j.jeem.2004.11.001CrossRefGoogle Scholar
Schindler, M., Caruso, G. & Picard, P. (2017). Equilibrium and first-best city with endogenous exposure to local air pollution from traffic. Regional Science and Urban Economics, 62(C), 12–23.10.1016/j.regsciurbeco.2016.10.006CrossRefGoogle Scholar
Sellers, W. D. (1969). A global climatic model based on the energy balance of the Earth-atmosphere system. Journal of Applied Meteorology, 8(3), 392–440.10.1175/1520-0450(1969)008<0392:AGCMBO>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Sigman, H. (2005). Transboundary spillovers and decentralization of environmental policies. Journal of Environmental Economics and Management, 50(1), 82–101.10.1016/j.jeem.2004.10.001CrossRefGoogle Scholar
Silva, E. C. D. & Caplan, A. J. (1997). Transboundary pollution control in federal systems. Journal of Environmental Economics and Management, 34(2), 173–86.10.1006/jeem.1997.1008CrossRefGoogle Scholar
Smith, M. D., Sanchirico, J. N. & Wilen, J. E. (2009). The economics of spatial-dynamic processes: Applications to renewable resources. Journal of Environmental Economics and Management, 57(1), 104–21.10.1016/j.jeem.2008.08.001CrossRefGoogle Scholar
Smith, M. D. & Wilen, J. E. (2003). Economic impacts of marine reserves: The importance of spatial behavior. Journal of Environmental Economics and Management, 46(2), 183–206.10.1016/S0095-0696(03)00024-XCrossRefGoogle Scholar
Stiglitz, J. E. (2019). Addressing climate change through price and non-price interventions. European Economic Review, 119, 594–612.10.1016/j.euroecorev.2019.05.007CrossRefGoogle Scholar
Tsangaris, S., Xepapadeas, A., Yannacopoulos, A. N. & Salvati, L. (2024). Spatial externalities, R&D spillovers, and endogenous technological change. Regional Science and Urban Economics, 109, 104055.10.1016/j.regsciurbeco.2024.104055CrossRefGoogle Scholar
Turing, A. M. (1952). The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London B, 237(641), 37–72.10.1098/rstb.1952.0012CrossRefGoogle Scholar
Uecker, H. (2016). Optimal harvesting and spatial patterns in a semiarid vegetation system. Natural Resource Modeling, 29(2), 229–58.10.1111/nrm.12089CrossRefGoogle Scholar
Ulph, A. (1997). International trade and the environment: A survey of recent economic analysis. In Folmer, H. and Tietenberg, T., eds., The International Yearbook of Environmental and Resource Economics 1997/1998: A Survey of Current Issues, Cheltenham: Edward Elgar, pp. 205–42.Google Scholar
van der Ploeg, F. & de Zeeuw, A. J. (1992). International aspects of pollution control. Environmental and Resource Economics, 2(2), 117–39.10.1007/BF00338239CrossRefGoogle Scholar
Verhoef, E. T. & Nijkamp, P. (2002). Externalities in urban sustainability: Environmental versus localization-type agglomeration externalities in a general spatial equilibrium model of a single-sector monocentric industrial city. Ecological Economics, 40(2), 157–79.10.1016/S0921-8009(01)00253-1CrossRefGoogle Scholar
Verhoef, E. T. & Nijkamp, P. (2003). Externalities in the urban economy. Tinbergen Institute Discussion Paper no. 2003-078/3. https://ssrn.com/abstract=457580.Google Scholar
Verhoef, E. T. & Nijkamp, P. (2005). Spatial externalities and the urban economy. In Capello, R. and Nijkamp, P., eds., Urban Dynamics and Growth: Advances in Urban Economics, Leeds: Emerald Group Publishing Limited, pp. 88–120.10.1108/S0573-8555(2005)0000266005CrossRefGoogle Scholar
Voss, R., Quaas, M. F., Schmidt, J. O. et al. (2018). Quantifying the benefits of spatial fisheries management: An ecological-economic optimization approach. Ecological Modelling, 385, 165–72.10.1016/j.ecolmodel.2018.07.012CrossRefGoogle Scholar
Wagener, F. O. O. (2003). Skiba points and heteroclinic bifurcations, with applications to the shallow lake system. Journal of Economic Dynamics and Control, 27(9), 1533–61.10.1016/S0165-1889(02)00070-2CrossRefGoogle Scholar
Wilen, J. E. (2007). Economics of spatial-dynamic processes. American Journal of Agricultural Economics, 89(5), 1134–44.10.1111/j.1467-8276.2007.01074.xCrossRefGoogle Scholar
Wu, B. & Francis, J. A. (2019). Summer Arctic cold anomaly dynamically linked to East Asian heat waves. Journal of Climate, 30(4), 1137–50.Google Scholar
Xabadia, A., Goetz, R. & Zilberman, D. (2004). Optimal dynamic pricing of water in the presence of waterlogging and spatial heterogeneity of land. Water Resources Research, 40(7), W07S02.10.1029/2003WR002215CrossRefGoogle Scholar
Xabadia, A., Goetz, R. & Zilberman, D. (2006). Control of accumulating stock pollution by heterogeneous producers. Journal of Economic Dynamics and Control, 30(7), 1105–30.10.1016/j.jedc.2005.04.002CrossRefGoogle Scholar
Xabadia, A., Goetz, R. & Zilberman, D. (2008). The gains from differentiated policies to control stock pollution when producers are heterogeneous. American Journal of Agricultural Economics, 90(4), 1059–63.10.1111/j.1467-8276.2008.01168.xCrossRefGoogle Scholar
Xepapadeas, A. (2022). On the optimal management of environmental stock externalities. Proceedings of the National Academy of Sciences, 119(24), e2202679119.10.1073/pnas.2202679119CrossRefGoogle ScholarPubMed
Xepapadeas, A. & Yannacopoulos, A. N. (2016). Spatial growth with exogenous saving rates. Journal of Mathematical Economics, 67, 125–37.10.1016/j.jmateco.2016.09.010CrossRefGoogle Scholar
Xepapadeas, A. & Yannacopoulos, A. N. (2023). Spatial growth theory: Optimality and spatial heterogeneity. Journal of Economic Dynamics and Control, 146, 104584.10.1016/j.jedc.2022.104584CrossRefGoogle Scholar
Yang, Z. (2008). Strategic Bargaining and Cooperation in Greenhouse Gas Mitigations: An Integrated Assessment Modeling Approach. Cambridge, MA: MIT Press.10.7551/mitpress/9780262240543.001.0001CrossRefGoogle Scholar
Accessibility standard: WCAG 2.1 AA
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
The HTML of this element
complies with version 2.1 of the
Web Content Accessibility Guidelines
(WCAG), covering newer accessibility requirements and improved
user experiences and achieves the intermediate
(AA)
level of WCAG compliance, covering a wider range of accessibility requirements.
Content Navigation
Table of contents navigation
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Reading Order & Textual Equivalents
Single logical reading order
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
Short alternative textual descriptions
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
Full alternative textual descriptions
You get more than just short alt text: you have comprehensive text equivalents, transcripts, captions, or audio descriptions for substantial non‐text content, which is especially helpful for complex visuals or multimedia.
You get more than just short alt text: you have comprehensive text equivalents, transcripts, captions, or audio descriptions for substantial non‐text content, which is especially helpful for complex visuals or multimedia.
Visual Accessibility
Use of colour is not sole means of conveying information
You will still understand key ideas or prompts without relying solely on colour, which is especially helpful if you have colour vision deficiencies.
You will still understand key ideas or prompts without relying solely on colour, which is especially helpful if you have colour vision deficiencies.
Structural and Technical Features
ARIA roles provided
You gain clarity from ARIA (Accessible Rich Internet Applications) roles and attributes, as they help assistive technologies interpret how each part of the content functions.
You gain clarity from ARIA (Accessible Rich Internet Applications) roles and attributes, as they help assistive technologies interpret how each part of the content functions.