M. Ali Khan
Abram Hutzler Professor of Political Economy
I continue to pursue interests in economic interaction, as formalized in general equilibrium theory: models with a representative agent, as well as those with a finite number and a continuum. In particular, those situations in which an individual agent is "numerically negligible" but is nevertheless influenced by actions, or summary statistics of actions, of all other agents in the game, and where individual and social outcomes are uncertain.
Questions of risk and uncertainty have led me to models of asset-pricing, again with an arbitrary index set of assets. In collaboration with Professor Yeneng Sun, I am exploring questions having to do with arbitrage and with the distinction between systematic and idiosyncratic risk. We hope that this work in financial economics will also lead to applications in other applied fields such as cost-benefit analysis for economic development.
I see issues in development economics alongside those in methodology and the history of ideas. Interests in population, education and the environment have led me to consider the robustness of disciplinary boundaries, and more broadly, to the relationship between economic development and cultural change. To me, this subsumes the question of how markets handle, or fail to handle, basic (positive (?), normative (?)) issues of resource allocation; and has thereby led me to the Scottish Enlightenment, and to the "economics of the eighteenth century."
My interests in theory and epistemology are complemented by those in mathematics, where I am working with methods of nonstandard analysis (Loeb spaces), nonsmooth analysis and optimization (Mordukhovich-Ioffe cones), and stochastic processes (law of large numbers with a continuum of random variables).
La concorrenza perfetta come teoria dell'equilibrio, Chapter 25 in La Matematica C. Bartocci and P. Odifreddie (eds.), Volume 4, pp. 875-947, 2012, Guilio Einaudi Editore, Rome.
Turnpike theory: a current perspective, (co-author: A. Piazza), The New Palgrave Dictionary of Economics, S. N. Durlauf and L. E. Blume (eds.), 2012, online edition, Palgrave, Macmillan.
Long run optimal behavior in a two-sector Robinson-Solow-Srinivasan model, (co-author: T. Mitra), Journal of Macroeconomic Dynamics, 16, (2012) 70-85.
Set-valued functions, Lebesgue extensions, and saturated probability spaces, (co-author: Y. Zhang), Advances in Mathematics, 229, (2012) 1080-1103.
The Shapley-Folkman theorem and the range of a bounded measure: an elementary and unified treatment, (co-author: K. P. Rath), Positivity, online.
Large Games with a Bio-Social Typology, (co-authors: K. P. Rath, Y. N. Sun, H. Yu), Journal of Economic Theory, online.
Maharam-types and Lyapunov's theorem for vector measures on Banach spaces, (co-author: N. Sagara), Illinois Journal of Mathematics, forthcoming.
Economics 318 -- Economics in/of the 18th Century:
This seminar traces the extent to which theory, particularly as it pertains to exchange and trade and to economic development, is grounded in and responds to 18th-century texts. The interdisciplinary nature of the writing and its implications for epistemological questions in economics will be emphasized. Students in the humanities and social sciences are welcome. Prerequisite-102 or permission of instructor.
Economics 602 -- Microeconomic Theory:
A more intensive discussion of selected topics than 180.601, emphasizing recent contributions. Prerequisites:180.301-302, or equivalent and Differential Calculus 110.106 or permission of instructor.
Economics 614 -- Mathematical Economics:
The mathematical theory of general static equilibrium. The course will emphasize the formal mathematical expression of economic ideas and the ability to give a loose economic intuition a coherent logical meaning. Different mathematical structures in general equilibrium theory will be isolated and discussed. Prerequisites: 180.601-602 or permission of instructor.
Economics 617 -- Topics in Mathematical Economics:
The subject matter of this course will vary from year to year, according to the interests of the instructor. Such topics as convex analysis, functional equations, and non convex global optimization may be studied. Prerequisite: permission of instructor.
Economics 627 -- Economic Development:
A review of experience in less-developed countries (LDCs) since 1945, theories of development, economic planning in the LDC context, and models of the development process. Corequisites: 180.601, 180.603.