Time Scale Externalities and the Management of Renewable Resources

Vardas, Giannis; Xepapadeas, Anastasios

doi:10.2139/ssrn.2596609

Cited by 2 publications

(4 citation statements)

References 18 publications

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“…In this paper, we contribute to the discussion of optimal resource management under time scale separation by analyzing externalities emerging because of time scale separation and potential inefficiencies of regulation related to harvesting rules, in the context of interacting populations. This extends earlier results of Vardas and Xepapadeas [] to a multispecies renewable resource harvesting model. In particular, we study, by applying the singular perturbation reduction methods (Fenichel []), optimal regulation when emissions cause environmental damages and at the same time cause a slowly varying carrying capacity of the interacting populations, as our first case (case i).…”

Section: Introductionsupporting

confidence: 87%

“…The model can be extended to M interacting populations with biomasses

x_{m}

m = 1, 2, . ., M

. Denoting the interaction coefficients between the μth, νth populations with

a_{μ ν}

and the intrinsic growth rates

m = 1, . ., μ, ν, . . . M

with

ρ_{m}

, population dynamics can be written in the general case as:

\begin{matrix} true \\ right d x & = & left (Ξ - H) d t \\ right d x & = & left ([], \begin{matrix} d x_{1} \\ . . \\ d x_{M} \end{matrix}), H = ([], \begin{matrix} h_{1} \\ . . . \\ h_{M} \end{matrix}), h_{m} = \sum_{j = 1}^{J} h_{m j}, m = 1, . ., M \\ right Ξ & = & left ([], \begin{matrix} ξ_{1} \\ . . ξ_{m} . . \\ ξ_{M} \end{matrix}), ξ_{m} = ρ_{m} x_{m} (() 1 - \sum_{μ = 1}^{M} a_{m μ} \frac{x_{μ}}{K_{m} (S)}), \\ right a_{italicmm} & = & left 1, \sum_{μ = 1, m \neq μ}^{M} a_{m μ} < 1 . \end{matrix}

At this point, we introduce a link between emissions and the evolution of carrying capacity following Vardas and Xepapadeas [] by assuming that the nonfishing sector of the economy generates emissions through production processes. Emissions are generated by a finite number of homogeneous agents

i = 1, . . I,

and generate benefits according to a strictly concave benefit function …”

Section: Optimal Regulation When Emissions Cause a Slowly Varying Carmentioning

confidence: 99%

“…Working in this section with alternative (i) and replacing into and the following parameter setting (see Da Rocha et al. [], Vardas and Xepapadeas []):

\begin{matrix} true \\ right β & = & left α = 1 / 2, J = 2, p_{1} = p_{2} = 10, w_{1} = w_{2} = 5, q_{1} = 0, 048, q_{2} = 0, 042, \\ right ρ_{1} & = & left 0.45, ρ_{2} = 0.35, r = 0, 05, a_{12} = a_{12} = 0.3, \end{matrix}

we obtain, using , the following solutions:

\begin{matrix} true \\ right s o l_{1} & = & left {(x_{1,} x_{2}, λ_{1}, λ_{2})}_{1} = (0.315786 K, 0.707977 K, - 367.664, 94.785) \\ right s o l_{2} & = & left {(x_{1,} x_{2}, λ_{1}, λ_{2})}_{2} = (0.33198 K, 0.309629 K, - 249.870, 40.6759) \\ right s o l_{3} & = & left {(x_{1,} x_{2}, λ_{1}, λ_{2})}_{3} = (0.75375 K, 0.755806 K, 0.05816, 0.0447838) \\ right s o l_{4} & = & left {(x_{1,} x_{2}, λ_{1}, λ_{2})}_{4} = (0.697341 K, 0.278107 K, 75.49248, - 522.37705) . \end{matrix}

…”

Section: Optimal Regulation When Emissions Cause a Slowly Varying Carmentioning

confidence: 99%

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Managing Interacting Populations Under Time Scale Separation

Vardas

Xepapadeas

2015

Natural Resource Modeling

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Renewable resource modeling is usually characterized by different time scales where some state variables such as biomass may evolve relatively faster than other state variables such as carrying capacity. A strong form of time scale separation (STSS) means that a slowly changing variable is treated as constant over time. Management rules that assume STSS do not account for a time scale externality and this may induce inefficiencies in resource management. In the current work, we study multispecies resource management under time scale separation by adopting the framework of singular perturbation reduction methods. By extending recent work by Vardas and Xepapadeas [2015] to interacting populations, we study regulation with full internalization of the time scale externality. We further study regulation and noncooperative outcomes under STSS and identify deviations in harvesting and biomass paths among these cases. Deviations indicate the inefficiencies associated with adopting STSS.

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Section: Introductionsupporting

confidence: 87%

“…The model can be extended to M interacting populations with biomasses

x_{m}

m = 1, 2, . ., M

. Denoting the interaction coefficients between the μth, νth populations with

a_{μ ν}

and the intrinsic growth rates

m = 1, . ., μ, ν, . . . M

with

ρ_{m}

, population dynamics can be written in the general case as:

\begin{matrix} true \\ right d x & = & left (Ξ - H) d t \\ right d x & = & left ([], \begin{matrix} d x_{1} \\ . . \\ d x_{M} \end{matrix}), H = ([], \begin{matrix} h_{1} \\ . . . \\ h_{M} \end{matrix}), h_{m} = \sum_{j = 1}^{J} h_{m j}, m = 1, . ., M \\ right Ξ & = & left ([], \begin{matrix} ξ_{1} \\ . . ξ_{m} . . \\ ξ_{M} \end{matrix}), ξ_{m} = ρ_{m} x_{m} (() 1 - \sum_{μ = 1}^{M} a_{m μ} \frac{x_{μ}}{K_{m} (S)}), \\ right a_{italicmm} & = & left 1, \sum_{μ = 1, m \neq μ}^{M} a_{m μ} < 1 . \end{matrix}

i = 1, . . I,

and generate benefits according to a strictly concave benefit function …”

Section: Optimal Regulation When Emissions Cause a Slowly Varying Carmentioning

confidence: 99%

“…Working in this section with alternative (i) and replacing into and the following parameter setting (see Da Rocha et al. [], Vardas and Xepapadeas []):

\begin{matrix} true \\ right β & = & left α = 1 / 2, J = 2, p_{1} = p_{2} = 10, w_{1} = w_{2} = 5, q_{1} = 0, 048, q_{2} = 0, 042, \\ right ρ_{1} & = & left 0.45, ρ_{2} = 0.35, r = 0, 05, a_{12} = a_{12} = 0.3, \end{matrix}

we obtain, using , the following solutions:

\begin{matrix} true \\ right s o l_{1} & = & left {(x_{1,} x_{2}, λ_{1}, λ_{2})}_{1} = (0.315786 K, 0.707977 K, - 367.664, 94.785) \\ right s o l_{2} & = & left {(x_{1,} x_{2}, λ_{1}, λ_{2})}_{2} = (0.33198 K, 0.309629 K, - 249.870, 40.6759) \\ right s o l_{3} & = & left {(x_{1,} x_{2}, λ_{1}, λ_{2})}_{3} = (0.75375 K, 0.755806 K, 0.05816, 0.0447838) \\ right s o l_{4} & = & left {(x_{1,} x_{2}, λ_{1}, λ_{2})}_{4} = (0.697341 K, 0.278107 K, 75.49248, - 522.37705) . \end{matrix}

…”

Section: Optimal Regulation When Emissions Cause a Slowly Varying Carmentioning

confidence: 99%

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Managing Interacting Populations Under Time Scale Separation

Vardas

Xepapadeas

2015

Natural Resource Modeling

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show abstract

“…In this section we apply numerical simulations due to the nonlinearity of the hamiltonian system. The following parameterization will be used, following Da-Rocha et al 2014and Vardas & Xepapadeas (2015): a = b = 1 2 , n = 3 or n = 4, p = 10, w = 5, q = 0:045, g = 0:45, K = 7000, r = 0:02. 10 The subjective probability of audition is given by p (x) = 1 (1 x ) , with ( ; ) = (2; 5).…”

Section: Numerical Approximationmentioning

confidence: 99%

Resource harvesting regulation and enforcement: An evolutionary approach

Petrohilos-Andrianos

Xepapadeas

2017

Research in Economics

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We study the evolution of compliance and regulation in a common pool resource setup with myopic appropriators whose decision on whether to comply or not with the harvesting rule is a result of imitation as described by a proportional rule. The regulator …rst sets the optimal quota and then harvesters can choose between compliance and violation. We investigate myopic regulation and optimal regulation regimes with both proportional and non-proportional …ne formulation and and an endogenized probability of audition. The equilibria are then characterized in terms of their stability properties.

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Time Scale Externalities and the Management of Renewable Resources

Cited by 2 publications

References 18 publications

Managing Interacting Populations Under Time Scale Separation

Managing Interacting Populations Under Time Scale Separation

Resource harvesting regulation and enforcement: An evolutionary approach

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