Optimal Growth

My Varenna Lectures (1969) and my edited MIT Press book (1967) were widely used in the 1960’s and 1970’s as how-to-do-it sources for applications of the calculus of variations and Pontryagin’s maximum principle. The non-necessity of the so-called “transversality condition” for the unbounded-horizon problem was pointed out in the Varenna lectures. With Duncan Foley and Miguel Sidrauski, we analyzed optimal fiscal and monetary policy in a macro-growth model (1969). Dave Cass and I, in a 1976 JET symposium, provided geometric sufficient conditions on the Hamiltonian function for the global asymptotic stability of optimal growth when boundary conditions are included. Extensions of our approach by Jess Benhabib, Tapan Mitra, Kazuo Nishimura, Aldo Rustichini, and others have also led to conditions for multiplicity, for periodicity, and chaotic behavior of optimal growth dynamics.

References

Essays on the Theory of Optimal Economic Growth (Editor), Cambridge, Massachusetts: MIT Press (hardcover and softcover), 1967.
“Optimal Programs of Capital Accumulation for an Economy in which there is Exogenous Technical Change” in Essays on the Theory of Optimal Economic Growth, (K. Shell, ed.), Cambridge, Massachusetts: MIT Press, 1967, Chapter I, 1-30.
“Technological Knowledge and Economic Growth” in Planning for Advanced Skills and Technologies, Industrial Planning and Programming Series No. 3, United Nations, New York: United Nations Industrial Development Organization, 1969, 79-90.
“Applications of Pontryagin’s Maximum Principle to Economics” in Mathematical Systems Theory and Economics, I (H.W. Kuhn and G.P. Szegö, eds.), Berlin: Springer Verlag, 1969, 241-292. (The “Varenna Lectures.”)
“Optimal Fiscal and Monetary Policy, and Economic Growth” (with Duncan K. Foley and Miguel Sidrauski), Journal of Political Economy, Vol. 77(4), Part II, July/August 1969, 698-719. Appears in Italian as “La Politica Monetaria e Fiscale per lo Sviluppo Economico Ottimale” (translated by D. Martellato), in Lo sviluppo economico ottimale: teoria della planificazione (I. Musu, ed.), Milano: Franco Angeli Editore, 1974, 238-264.
“The Theory of Hamiltonian Dynamical Systems, and an Application to Economics” in The Theory and Application of Differential Games (J.D. Grote, ed.), Dordrecht-Holland: D. Reidel Publishing Company, 1975, 189-200.
“Neoclassical Growth Models” in Modern Economic Thought (S. Weintraub, ed.), Philadelphia: University of Pennsylvania Press, 1976, 347-367.
The Hamiltonian Approach to Dynamic Economics (Editor with David Cass), New York: Academic Press, 1976. ISBN: 012163650X.
“Introduction to Hamiltonian Dynamics in Economics” (with David Cass), Journal of Economic Theory, Vol. 12(1), February 1976, 1-10. Reprinted as Essay I in The Hamiltonian Approach to Dynamic Economics (D. Cass and K. Shell, eds.), New York: Academic Press, 1976, 1-10.
“The Structure and Stability of Competitive Dynamical Systems” (with David Cass), Journal of Economic Theory, Vol. 12(1), February 1976, 31-70. Reprinted as Essay III in The Hamiltonian Approach to Dynamic Economics (D. Cass and K. Shell, eds.), New York: Academic Press, 1976, 31-70.
“Hamiltonians” in The New Palgrave: A Dictionary of Economics (J. Eatwell, M. Milgate and P. Newman, eds.), Vol. 2, New York: Macmillan, 1987, 588-590.