An Optimal Greenhouse Tax in an Optimal Growth Model

The Bertalanffy-Pütter growth model describes mass m at age t by means of the differential equation dm/dt = p⋅ma−q⋅mb. The special case using the Bertalanffy exponent-pair a=2/3 and b=1 is most common (it corresponds to the von Bertalanffy growth function VBGF for length in fishery literature). For data fitting using general exponents, five model parameters need to be optimized, the pair a<b of non-negative exponents, the non-negative constants p and q, and a positive initial value m0 for the differential equation. For the case b=1 it is known that for most fish data any exponent a<1 could be used to model growth without affecting the fit to the data significantly (when the other parameters p, q, m0 were optimized). Thereby, data fitting used the method of least squares, minimizing the sum of squared errors (SSE). It was conjectured that the optimization of both exponents would result in a significantly better fit of the optimal growth function to the data and thereby reduce SSE. This conjecture was tested for a data set for the mass-growth of Walleye (Sander vitreus), a fish from Lake Erie, USA. Compared to the Bertalanffy exponent-pair the optimal exponent-pair achieved a reduction of SSE by 10%. However, when the optimization of additional parameters was penalized, using the Akaike information criterion (AIC), then the optimal exponent-pair model had a higher (worse) AIC, when compared to the Bertalanffy exponent-pair. Thereby SSE and AIC are different ways to compare models. SSE is used, when predictive power is needed alone, and AIC is used, when simplicity of the model and explanatory power are needed.

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DON’T FEED THE BEARS! ENVIRONMENTAL DEFENSIVE EXPENDITURES AND SPECIES-TYPICAL BEHAVIOR IN AN OPTIMAL GROWTH MODEL

Macroeconomic Dynamics ◽

10.1017/s1365100519000397 ◽

2019 ◽

pp. 1-20 ◽

Cited By ~ 1

Author(s):

Angelo Antoci ◽

Simone Borghesi ◽

Paolo Russu

Keyword(s):

Growth Model ◽

Growth Process ◽

Anthropogenic Activities ◽

Optimal Growth ◽

Single Species ◽

Social Planner ◽

Species Survival ◽

The Social ◽

And Behavior ◽

Number Of Individuals

Many studies have stressed that human activities may cause the extinction of single species. Anthropogenic activities, however, may affect not only the number of individuals of single species, but also their behavior. To investigate this issue, we propose a growth model in which agents may care not only for the species’ survival but also for the typicality of their behavior. We assume that the environmental defensive expenditures can protect the species avoiding their extinction, but can induce the species to modify their behavior. Results emerging from the model suggest that if the social planner cares for typicality of species behavior, then an infinite growth process may no longer be optimal. Numerical simulations, moreover, show the possible existence of a trade-off between number and behavior of the species, leading the system to a high number of species’ members that behave in an atypical way or to few members behaving very typically.

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Nonbalanced Growth in a Neoclassical Two-Sector Optimal Growth Model

Studies in Economic Theory - Sunspots and Non-Linear Dynamics ◽

10.1007/978-3-319-44076-7_14 ◽

2016 ◽

pp. 339-359

Author(s):

Harutaka Takahashi

Keyword(s):

Growth Model ◽

Optimal Growth

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