The pricing of assets — and hence the allocation of investment — is central to macroeconomics. My paper with Joe Stiglitz in the QJE (1967) and with Chris Caton in the RES (1971) show how the apparent plethora of perfect-foresight equilibria is substantially reduced by boundary conditions arising from the non-negativity of prices.
My paper in the RES (1969) with Sidrauski and Stiglitz shows how different “money models” can be from “real models.” Boundary conditions do rule out hyper-deflation, but they do not rule out hyperinflation. For this reason, multiplicity of equilibrium trajectories is more likely in monetary economies. The phase-diagram analysis in Shell-Sidrauski-Stiglitz (1969) is the same as in the later bubble analysis of Tirole (1985). Conraria and Shell (2005, 2006) have extended the analysis of Shell-Stiglitz to OG economies with a focus on bursting bubbles.
Perfect-foresight economies generate perturbed Hamiltonian dynamical systems. My work with Dave Cass on Hamiltonian dynamics is in part an outgrowth of his work with Stiglitz and Sidrauski. Cass and Shell (1976) showed how the geometry of the Hamiltonian function generating the perturbed Hamiltonian dynamical system determines the long-run development of the economy.
- “The Allocation of Investment in a Dynamic Economy” (with Joseph E. Stiglitz) Quarterly Journal of Economics, Vol. 81(325), November 1967, 592-609.
- “Capital Gains, Income, and Saving” (with Miguel Sidrauski and Joseph E. Stiglitz), The Review of Economic Studies, Vol. 36(1) No. 105, January 1969, 15-26.
- “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.”)
- “Public Debt, Taxation, and Capital Intensiveness” (with Edmund S. Phelps), Journal of Economic Theory, Vol. 1(3), October 1969, 330-346. See also “Erratum,” Journal of Economic Theory, Vol. 2(2), June 1970, 209. Reprinted in Studies in Macroeconomic Theory, Vol. 2, Redistribution and Growth (E.S. Phelps, ed.), New York: Academic Press, 1980, 24-45.
- “An Exercise in the Theory of Heterogeneous Capital Accumulation” (with Christopher Caton), The Review of Eocnomic Studies, Vol. 37(1), No. 113, January 1971, 13-22.
- “On Competitive Dynamical Systems” in Differential Games and Related Topics (H.W. Kuhn and G.P. Szegö, eds.), Amsterdam: North-Holland, 1972, 449-476.
- “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. Reidal 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.
- “Growth Dynamics and Returns to Scale: A Bifurcation Analysis” (with Gaetano Antinolfi and Todd Keister), Journal of Economic Theory, Vol. 96(1), January 2001, 70-96. (doi:10.1006/jeth.1999.2632)
- “Capital Gains: Blue Machines and Red Machines” (with Luís Francisco Aguiar-Conraria), Singapore Economic Review, Vol. 50 (Special Issue No.1), 2005, 437-448.
- “Capital Gain” (with Luís Francisco Aguiar-Conraria), International Journal of Economic Theory, (doi:10.1111/j.1742-7363.2006.0039.x), Vol. 2(3-4), September/December 2006, 331-349.