Characterizing Optimality in Dynamic Settings: A Monotonicity-based Approach

Zhuokai Huang, Demian Pouzo and Andres Rodriguez-Clare

No 34224, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: We develop a novel analytical method for studying optimal paths in dynamic optimization problems under general monotonicity conditions. The method centers on a locator function—a simple object constructed directly from the model’s primitives—whose roots identify interior steady states and whose slope determines their local stability. Under strict concavity of the payoff function, the locator function also characterizes basins of attraction, yielding a complete description of qualitative dynamics. Without concavity, it can still deliver sharp results: if the function is single crossing from above, its root identifies a globally stable steady state; if the locator function is inverted-U-shaped with two interior roots (a typical case), only the higher root can be a locally stable interior steady state. The locator function further enables comparative statics of steady states with respect to parameters through direct analysis of its derivatives. These results are obtained without solving the full dynamic program. We illustrate the approach using a generalized neoclassical growth model, a rational (un)fitness model, and a learning-by-doing economy.

JEL-codes: C02 C61 O40 (search for similar items in EconPapers)
Date: 2025-09
Note: EFG ITI
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.nber.org/papers/w34224.pdf (application/pdf)
Access to the full text is generally limited to series subscribers, however if the top level domain of the client browser is in a developing country or transition economy free access is provided. More information about subscriptions and free access is available at http://www.nber.org/wwphelp.html. Free access is also available to older working papers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberwo:34224

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/w34224
The price is Paper copy available by mail.

Access Statistics for this paper

More papers in NBER Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().