On two classical turnpike results for the Robinson–Solow–Srinivasan model

The Concavity Assumption on Felicities and Asymptotic Dynamics in the RSS Model

“…3. ξ σ = 1. By (16) we immediately get that x σ (t) = x σ (0) for all t =2 and x σ (t) = 1/a σ − x σ (0) for all t =2 and then to assure that b σ x σ (t) ∈ S w , it is enough to know that b σ x σ (0) ∈ S w and b σ (1/a σ − x σ (0)) ∈ S w . These two conditions can be equivalently expressed as…”

On the Mitra–Wan forestry model: A unified analysis

“…For a reader wanting only a brief and basic introductory outline, Brock [2] remains the relevant reference. 19 In the setting of a finite-dimensional Euclidean space, Brock defined maximal and optimal programs of an infinite period optimization problem, and under a uniqueness assumption of the solution of a static version of this problem, showed the existence of maximal programs. 20 Through an example, he also showed the non-existence of an optimal program.…”

“…18 As will emerge in the sequel, we do not use assumptions A.1, A.2, A.4 and A.7 in [32] at all. 19 See, for example, the reference to Brock's 1970 paper in [28,Section 7]. 20 Footnotes 11 and 12 above are relevant here.…”

“…Following [2], this property has subsequently referred to in the literature as the "average turnpike property;" see, for example, [32] and [16] and also Lemma 6.2 and Footnote 32 below. Other than in this sentence, and in keeping with the discussion in [19], we avoid the term turnpike or average turnpike in this paper.…”

“…We already know from [31], [10] and [40] the difficulties of delineating optimal transition dynamics in the discounted setting, and whereas a full understanding of the model can hardly be had without a resolution of these difficulties, substantial analysis of the undiscounted case that is feasible remains to be done. More importantly, and given the recent emphasis on numerical computation, 38 the proximity of finite horizon optimal programs to their infinite-horizon counterparts (as is investigated in [19] for the RSS model and [18] for the Mitra-Wan model), and questions of their sensitivity to initial and terminal stocks (as investigated in [3] and [26]), remain to be investigated in the setting considered in this paper. We leave such investigations for future work.…”