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Habitat loss and harvesting of non-timber forest products (NTFPs) significantly affect the population dynamics. In this paper, we propose a general mathematical modelling approach incorporating the impact of habitat size reduction and non-lethal harvesting of NTFP on population dynamics. The model framework integrates experimental data of Pentadesma butyracea in Benin. This framework allows us to determine the rational non-lethal harvesting level and habitat size to ensure the stability of the plant ecosystem, and to study the impacts of distinct levels of humidity. We suggest non-lethal harvesting policies that maximize the economic benefit for local populations. [ABSTRACT FROM AUTHOR]

Optimal asset replacement is analysed under non-exponential technological improvement, whereby the asset capital cost and the operational cost reduce for newer assets, and the relative rate of this decrease varies with time. We establish that the optimal lifetime of sequentially replaced assets increases if the relative rate of technological change decreases, and converse. Next, the two-cycle replacement algorithm is employed to take the unequal asset lifetime into account. The algorithm is adjusted to the case of several discrete estimates of changing asset costs and demonstrates good performance in various scenarios of improving technology. [ABSTRACT FROM AUTHOR]

A hierarchical economic-environmental model is formulated to analyze the sustainable management of farming production in a landlord-tenant system. The problem under study is interdisciplinary and combines various agricultural, economic, social, and environmental factors. To maximize profit, the landlord chooses a rental payment and the duration of a lease contract. Tenants invest into farmyard fertilizer in order to improve future crop growth and maximize their profit. It is shown that the qualitative behavior of optimal trajectories in the landlord-tenant problem is mostly affected by environmental conditions rather than by the end-of-horizon and delay effects. A range of model parameters is identified, where the optimal trajectory coincides with the first-best environmentally and socially efficient solution. [ABSTRACT FROM AUTHOR]

In operations research, the equipment replacement process is usually modeled in discrete time. An alternative approach is represented by continuous-time vintage capital models that explicitly involve the equipment lifetime and are described by nonlinear integral equations. The paper introduces and analyzes a model that unites both these approaches. The structure of optimal replacement, transition, and long-term dynamics, and clustering and splitting of replaced machines are discussed and illustrated with numeric examples. Equipment splitting is demonstrated when the optimal equipment lifetime increases. [ABSTRACT FROM AUTHOR]

Optimization problems with nonlinear utility and endogenous capital lifetime are investigated in one- and two-sector modifications of the Solow vintage capital model. Both models have the same balanced growth path in the case of exponential technological change and labour. Turnpike theorems in normal form are proved for the optimal capital lifetime in both models. The differences between the cases of the linear and nonlinear utility are highlighted. [ABSTRACT FROM AUTHOR]

Abstract: The paper analyzes the structure of optimal trajectories in the one-sector vintage capital model that optimizes the endogenous lifetime of age-structured capital under technological change. A new repetition pattern (anticipation echoes) is demonstrated in both optimal investment and optimal capital lifetime in the case of finite-horizon optimization. The anticipation echoes are caused by expectation of the future “no-investment” policy at the end of the planning horizon. It is shown that the anticipation echoes represent a general structural property of dynamic systems with endogenous delay. Mathematically, the problem under study is the optimal control of non-linear integral equations with unknowns in the integration limits. [Copyright &y& Elsevier]

The nonlinear optimal control problem investigated in this paper is governed by Volterra integral equations with an unknown function in the limit of integration. Problems of such type arise in vintage capital models of mathematical economics and reveal new non-linear phenomena in economic-technological development. The main result of the paper is the explicit solution of the problem in important special cases. To construct these solutions, necessary and sufficient conditions for an extremum are derived. The exact solutions show the behavior of a capital replacement process under technological change. [ABSTRACT FROM AUTHOR]