Adaptive rolling plans are good

Adaptive rolling plans are good


Piotr Maćkowiak


Keywords: indirect utility function, good plans, adaptive rolling planning, multisector model


Summary: Here we prove the goodness property of adaptive rolling plans in a multisector optimal growth model under decreasing returns in deterministic environment. Goodness is achieved as a result of fast convergence (at an asymptotically geometric rate) of the rolling plan to balanced growth path. Further on, while searching for goodness, we give a new proof of strong concavity of an indirect utility function - this result is achieved just with help of some elementary matrix algebra and differential calculus.



Bala, V., Majumdar, M., Mitra, T., Decentralized evolutionary mechanism for intertemporal economies: A possibility result, “Journal of Economics” 53, pp. 1-29, 1991.

Benhabib, J., Nishimura, K., On the uniqueness of steady states in an economy with heterogeneous capital goods, “International Economic Review” 20, pp. 59-82, 1979a.

Benhabib, J., Nishimura, K., The Hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth, “Journal of Economic Theory” 21, pp. 421-444, 1979b.

Benhabib, J., Nishimura, K., Stability of equilibrium in dynamic models of capital theory, “International Economic Review” 22, pp. 275-293, 1981.

Gale, D., On optimal development in a multi-sector economy, “Review of Economic Studies” 34, pp. 1-18, 1967.

Goldman, S., Optimal growth and continual planning revision, “Review of Economic Studies” 35, pp. 145-154, 1968

Hirota, M., Kuga, K., On an intrinsic joint production, “International Economic Review” 12, pp. 87-98, 1971.

Kaganovich, M., Rolling planning: Optimality and decentralization, “Journal of Economic Behavior and Organization” 29, pp. 173-185, 1996.

Kaganovich, M., Decentralized evolutionary mechanism of growth in a linear multi-sector model, “Metroeconomica” 49, pp. 349-363, 1998.

Lancaster, K., Mathematical economics. Macmillan, 1968.

Lancaster, P., Tismenetsky, M., The theory of matrices. Academic Press, 1985.

Lucas, R., Stokey, N., Recursive methods in economic dynamics. Harvard University Press, 1989.

McKenzie, L., Classical general equilibrium. MIT Press, 2002.

Nikaido, H., Convex structures and economic theory. Academic Press, 1968.

Takayama, A., Mathematical economics (2nd edition). Cambridge University Press, 1985.

Venditti, A., Strong concavity properties of indirect utility functions in multisector optimal growth models, “Journal of Economic Theory” 74, pp. 349-367, 1997.

Vial, J.-P., Strong and weak convexity of sets and functions, “Mathematics of Operations Research” 8, pp. 231-259, 1983.



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