Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach

Van, Cuong Le; Morhaim, Lisa

doi:10.1006/jeth.2001.2880

Cited by 56 publications

(7 citation statements)

References 7 publications

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“…As a simple consequence of Proposition 6.1, we obtain a result that can be viewed as an abstract version of the existence result shown in [12], Proposition 4.1; see [18], Theorem 1, for a similar result that requires stronger assumptions.…”

Section: An Application To Infinite-horizon Optimization In Discrete supporting

confidence: 53%

A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time

Kamihigashi

2017

J Inequal Appl

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Given a sequence of measurable functions on a σ-finite measure space such that the integral of each as well as that of exists in , we provide a sufficient condition for the following inequality to hold: Our condition is considerably weaker than sufficient conditions known in the literature such as uniform integrability (in the case of a finite measure) and equi-integrability. As an application, we obtain a new result on the existence of an optimal path for deterministic infinite-horizon optimization problems in discrete time.

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Section: An Application To Infinite-horizon Optimization In Discrete supporting

confidence: 53%

A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time

Kamihigashi

2017

J Inequal Appl

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“…Part ( i ) of Proposition 1 (as well as the continuity of V in part ( ii )) follows from Proposition 6 in Le Van and Morhaim (2002) 8 . The other parts of Proposition 1 can be proved in a fairly standard fashion; see, for example, Mitra (2000) (the fact that our production technology allows for unbounded growth is not relevant to the proof of these results).…”

Section: Preliminariesmentioning

confidence: 84%

On sustained economic growth with wealth effects

Roy

2010

Int J of Economic Theory

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In a discounted one-sector convex model of optimal economic growth where utility may depend on both consumption and capital stock, I derive necessary and sufficient conditions for sustained growth (unbounded expansion of capital and consumption). Conditions for bounded growth and extinction are also outlined. Optimal paths may be nonmonotone. Sustained growth may occur even though the asymptotic marginal productivity is less than the discount rate and may require the initial capital stock to be above a critical level. The behavior of the marginal rate of substitution between consumption and capital plays a crucial role in the conditions.

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“…Recently, Rincón‐Zapatero (2024) extended this method to a stochastic environment. Le Van and Morhaim (2002), Le Van and Vailakis (2005), Kamihigashi (2014), and Wiszniewska‐Matyszkiel and Singh (2021) proposed a more primitive transversality condition to identify an appropriate space of candidate value functions. Jaśkiewisz and Nowak (2011) and Matkowski and Nowak (2011) presented a systematic study of all these approaches under uncertainty.…”

Section: Related Literaturementioning

confidence: 99%

Do not Blame Bellman: It Is Koopmans' Fault

Bloise,

Le Van,

Vailakis

2024

ECTA

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We provide a unified approach to stochastic dynamic programming with recursive utility based on an elementary application of Tarski's fixed point theorem. We establish that the exclusive source of multiple values is the presence of multiple recursive utilities consistent with the given aggregator, each yielding a legitimate value of the recursive program. We also present sufficient conditions ensuring a unique value of the recursive program in some circumstances. Overall, acknowledging the unavoidable failure of uniqueness in general, we argue that the greatest fixed point of the Bellman operator should have a privileged position.

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Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach

Cited by 56 publications

References 7 publications

A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time

A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time

On sustained economic growth with wealth effects

Do not Blame Bellman: It Is Koopmans' Fault

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