On the uniform limit condition for discrete-time infinite horizon problems

Jan Brinkhuis

No EI2015-40, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: In this note, a simplified version of the four main results for discrete-time infinite horizon problems, theorems 4.2-4.5 from Stokey, Lucas and Prescott (1989) [SLP], is presented. A novel assumption on these problems is proposed—the uniform limit condition, which is formulated in terms of the data of the problem. It can be used for example before one has started to look for the optimal value function and for an optimal plan or if one cannot find them analytically: one verifies the uniform limit condition and then one disposes of criteria for optimality of the value function and a plan in terms of the functional equation and the boundedness condition. A comparison to [SLP] is made. The version in [SLP] requires one to verify whether a candidate optimal value function satisfies the boundedness condition; it is easier to check the uniform limit condition instead, as is demonstrated by examples. There is essentially no loss of strength or generality compared to [SLP]. The necessary and sufficient conditions for optimality coincide in the present paper but not in [SLP]. The proofs in the present paper are shorter than in [SLP]. An earlier attempt to simplify, in Acemoglu (2009) --here the limit condition is used rather than the uniform limit condition-- is not correct.

Keywords: Dynamic optimization; Discrete time; Infinite horizon; Bellman equation; Total discounted return; Counterexample (search for similar items in EconPapers)
JEL-codes: E00 O1 (search for similar items in EconPapers)
Pages: 11
Date: 2015-12-03
New Economics Papers: this item is included in nep-mac
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://repub.eur.nl/pub/79541/EI2015-40.pdf (application/pdf)

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:ems:eureir:79541

Access Statistics for this paper

More papers in Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute Contact information at EDIRC.
Bibliographic data for series maintained by RePub ( this e-mail address is bad, please contact ).