Thresholds in concave renewable resource models

I am getting tired: Effort and fatigue in intertemporal decision-making

“…This result has been observed, inter alia, byWirl (2004). 9 This is equivalent to assume that the firm can observe the condition of fatigue.…”

“…This is equivalent to assume that there exists a maximum sustainable effort e MS > 0 such that _ sðtÞ ¼ gðs MS Þ À e MS ¼ 0 and that higher levels of effort are not sustainable over an infinite time horizon because they would exhaust the worker. This set of assumptions is consistent with the literature that studies (over)training and recovery in soldiers and athletes, and it has been widely used to study the optimal use of renewable resources (see, for example, Wirl, 2004, where the logistic function is used as a special case of the class of recovery functions under examination). To guarantee the existence of at least one internal steady state, I also require gð0Þ ¼ 0 and @gð0Þ=@s > q, where q > 0 is the intertemporal discount rate of the worker.…”

Sustainable use of renewable resources: an identity approach

“…The first one regards final consumption as the only source of satisfaction (Dasgupta andHeal 1974, 1979;Stiglitz 1974, Solow 1974Grossman and Helpman 1991;Aghion and Howitt 1992). The second one, taken from a wider viewpoint, considers an intrinsic valuation of natural resources as an additional element for personal well-being (Krautkraemer 1985;Beltratti et al 1993Beltratti et al , 1995Beltratti et al , 1998Chichilnisky 1997;Heal 1998Heal , 2001Lafforgue 2005;Wirl 1999Wirl , 2004. Despite the theoretical advances offered by this inclusion of the intrinsic evaluation of natural resources as a source for personal satisfaction, the framework defined by the authors in this field is insufficient to analyze how certain non-economic factors, such as the existence of identities promoting cooperative attitudes regarding the environment, can bear an influence on the behavior of agents.…”

Fishing in a Shallow Lake: Exploring a Classic Fishery Model in a Habitat with Shallow Lake Dynamics

“…Echoing previous work, she finds that the interesting results follow from considering multiple states, but that this means there are few general statements that can be made. In a discussion of the possibility of multiple equilibria in well behaved systems, Wirl (2004) also comments on the difficulty of identifying thresholds in more complex systems.…”