Dynamic models for environmental economics

Course description
The aim of the course is to deliver an overview of the extant debate on the impact of firms’ behaviour on global warming and natural resources, both renewables and non-renewables, including investment in green technologies and exploration/repopulation, and the design of regulatory tools.
The exposition encompasses the analysis of the tragedy of commons dating back to the Lotka-Volterra model and the Hotelling model, related to renewables and non-renewbles, respectively. The course is open to any doctoral students interested in this issues across the PhD programmes activated by the University of Bologna. With this in mind, although the course belongs to the PhD in Economics, the exposition will have a transdisciplinary flavour.
The early stage of the course will include a short exposition of basic notions concerning optimal control and differential game theory, and the related solution concepts. However, some prior knowledge of optimal control theory would be a desirable prerequisite.
The syllabus contains essential readings in support of lectures and some hints for essays.

1. Monopoly models, solved through Hamiltonian functions and HJB equations
2. Getting acquainted with differential games: open-loop, memoryless closed-loop and feedback solutions
3. Oligopoly and polluting emissions
4. Oligopoly and natural resources
5. Two eggs in one basket: resource extraction and global warming

Teaching methods
The focus of Sections 1-2 is essentially methodological, while Sections 3-5 mostly rely on selected papers.

Assessment methods
The final mark has the following composition: 20% class participation, 30% essay, 50% exam in class. The theme of the essay (which may be coauthored) has to be agreed upon with the lecturer.
The exam in class (2 hrs) consists of a menu of four questions related to the material of the course, from which the candidate has to pick two questions according to her/his liking.

Benchekroun, H. and N.V. Long (1998), “Efficiency Inducing Taxation for Polluting Oligopolists”, Journal of Public Economics, 70, 325-42.

Benchekroun, H. (2008), “Comparative Dynamics in a Productive Asset Oligopoly”, Journal of Economic Theory, 138, 237-61.

Colombo, L., and P. Labrecciosa (2015), “On the Markovian Efficiency of Bertrand and Cournot Equilibria”, Journal of Economic Theory, 155, 332-58.

Fujiwara, K. (2008), “Duopoly Can Be More Anti-Competitive Than Monopoly”, Economics Letters, 101, 217–19.

Groot, F., C. Withagen and A. de Zeeuw (2003), “Strong Time-Consistency in the Cartel-versus- Fringe Model”, Journal of Economic Dynamics and Control, 28, 287–306.

Lambertini, L. (2013), Oligopoly, the Environment and Natural Resources, London, Routledge, chs 8 and 9.

Lambertini, L. and A. Mantovani (2014), “Feedback Equilibria in a Dynamic Renewable Resource Oligopoly: Pre-emption, Voracity and Exhaustion”, Journal of Economic Dynamics and Control, 47, 115-22.

Lambertini, L. (2018), Differential Games in Industrial Economics, Cambridge, Cambridge University Press, chs 1, 2 and 7.

Lambertini, L. and G. Leitmann (2019), “On the Attainment of the Maximum Sustainable Yield in the Verhulst-Lotka-Volterra Model”, Automatica, 110, article 108555, 1-5.

Tahvonen, O. and J. Kuuluvainen (1993), “Economic Growth, Pollution and Renewable Resources”, Journal of Environmental Economics and Management, 24, 101-18.