Existence of optimal strategies in linear multisector models

Abstract

In this paper we give a sufficient and almost necessary condition for the existence of optimal strategies in linear multisector models when time is continuous, consumption is limited to one commodity, the instantaneous utility is of the CES type, and available technology allows a positive growth rate.

Existence of optimal strategies in linear multisector models with several consumption goods

“…From the technical point of view the results obtained in this paper can be seen as generalizations of those obtained elsewhere [7]. Indeed, while some preliminary Lemmas (see e.g.…”

“…However Magill used an assumption on "regularity" ( [12], Assumption T.2, p. 703) justified on the basis of the Gale [9] indecomposability assumption implying that the upper bound of the uniform over time rates of reproduction of any commodity equals the maximum rate of growth. In a more recent paper, Freni et alii [7] analyzed in greater depth the existence of optimal strategies in linear multisector models when time is continuous and proved, on the assumption that only one commodity is consumed, that if…”

“…Indeed, while some preliminary Lemmas (see e.g. Lemma 4.1) are straightforward extensions of results contained in [7], the technical core of the present paper needs new ideas and techniques to be dealt with. The main reason is the fact that as we want to find "sharp" results (i.e.…”

“…existence when (1) holds and nonexistence when (2) holds), we have to understand precisely the role of the function ν in the existence of optimal trajectories. It would be very easy to extend the result of the paper [7] and find only rough sufficient conditions for the existence (e.g. substituting Γ ν with the maximum of the Γ i 's) and for the non-existence (e.g.…”

Generically distributed investments on flexible projects and endogenous growth

“…We could prove this result directly [see, e.g., Freni et al (2006)], but for sake of brevity we omit the proof here. The result will be proved a posteriori on a suitable subset of H ++ .…”