William Brock

Vilas Research Professor, Emeritus of Economics, University of Wisconsin, Madison

Research Professor, University of Missouri, Columbia

Areas of Expertise:

  • Complex dynamics in economics
  • Mathematical economics

Brock is the Vilas Research Professor of Economics, Emeritus at the University of Wisconsin, Madison, where he has taught economics since 1975. Brock received his PhD in Mathematics from the University of California, Berkeley. He is well known for his contributions to the theory of optimal growth, the breadth of applications of the intertemporal model to economics, and other aspects of nonlinear dynamics.

Brock has been a Fellow of the Academy of Arts and Sciences since 1992, a member of the National Academy of Sciences since 1998,  and a Distinguished Fellow of the American Economics Association since 2004.

Research Projects

Robustness in Economic Models with Climate Change |  Heat Balance Climate Models


Recent Publications


William Brock, Lars Peter Hansen Wrestling with Uncertainty in Climate Economic Models, October 9, 2017, SSRN. (lecture on this paper here)


Brock, W. and A. Xepapadeas. 2017. Climate Change Policy Under Polar Amplification.  European Economic Review 94:263-282.


Cai, Y., W. Brock, and A. Xepapadeas. 2016. Climate Change Economics and Heat

Transport Across the Globe: Spatial-DSICE. In 2017 Allied Social Science Association

(ASSA) Annual Meeting, January 6-8, 2017, Chicago, Illinois, 251833. Agricultural and

Applied Economics Association


Anderson, E. W., W. A. Brock, and A. Sanstad. 2016. Robust Consumption and Energy

Decisions. Working paper, SSRN.


Evan Anderson et al. "Robust analytical and computational explorations of coupled economic-climate models with carbon-climate response." RDCEP Working Paper No. 14-05, January 2014.


W A Brock et al. “Energy balance climate models, damage reservoirs, and the time profile of climate change policy.” Oxford Handbook of the Macroecon. of Global Warming, Ox U Press 2014. Ch 3 p 1952


*Brock, William, Gustav Engstrom, and Anastasios Xepapadeas. "Spatial climate-economic models in the design of optimal climate policies across locations." European Economic Review 69 (2014): 78-103.



Carpenter, S., Brock, W., Folke, C., Van Ness, E., Scheffer, M., 2015,

 “Allowing variance may enlarge the safe operating space for exploited

ecosystems,” Proceedings of the National Academy of Sciences, USA, 112(46):14384-14389


William Brock and Steven Durlauf. 2015, On sturdy policy evaluation,.  Journal of Law and Economics, 44,S2.



*William A. Brock et al. "Energy balance climate models and general equilibrium optimal mitigation policies." Journal of Economic Dynamics and Control 37, no. 12 (2013): 2371-2396.



William A Brock et al. Optimal control in space and time and the management of environmental resources. Annu. Rev. Resour. Econ., 6(1):33–68, 2014.


William A Brock, Anastasios Xepapadeas, and Athanasios N Yannacopoulos. Spatial externalities and agglomeration in a competitive industry. Journal of Economic Dynamics and Control, 42:143–174, 2014.


William A Brock, Anastasios Xepapadeas, and Athanasios N Yannacopoulos. Optimal agglomerations in dynamic economics. Journal of Mathematical Economics, 53:1–15, 2014


William Brock, Anastasios Xepapadeas, et al. Modeling coupled climate, ecosystems, and economic systems.Technical report, Athens University of Economics and Business, 2015. Revised, 2017,

forthcoming in Handbook of Environmental Economics, Partha Dasgupta et al., eds., Elsevier: North Holland.


Brock, William A., Anastasios Xepapadeas, and A. N. Yannacopoulos. "Robust control and hot spots in spatiotemporal economic systems." Dynamic Games and Applications, (2014): 1-33.


W A Brock et al. “Robust control of a spatially distributed commercial fishery.” Dynamic Optimization in Environmental Economics, E. Moser et al, editors, Springer, 2014. Pgs 215–241.


William A. Brock et al. "Spatial externalities and agglomeration in a competitive industry." Journal of Economic Dynamics and Control 42 (2014): 143-174.



Stephen R Carpenter, William A Brock, Jonathan J Cole, and Michael L Pace. A new approach for rapid detection of nearby thresholds in ecosystem time series. Oikos, 123(3):290–297, 2014.



James J Elser, Timothy J Elser, Stephen R Carpenter, and William A Brock. Regime shift in fertilizer commodities indicates more turbulence ahead for food security. PloS one, 9(5):e93998, 2014



S. Kefi et al. Early warning signals of ecological transitions: methods for spatial patterns. PloS one, 2014.