Abstract
In our analysis thus far, we have studied environmental allocation in a static context. However, environmental systems are used not only by one generation, but by a number of generations. Today’s use of the environment may affect the role of the environment in the future. Consequently, the environmental-allocation problem also has to be interpreted over time.
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Notes
In equation 13.2 the case can obviously arise that, because of the exogenously given assimilative capacity Sa, more pollutants are assimilated than the stock of pollutants plus net emissions. This case must be excluded. This can be done by assuming that a constant part of the stock of pollutants is reduced. For simplicity, we assume equation 13.2. It should be noted that equation 13.2 in this chapter replaces equation 3.4. New pollutants do not disappear automatically at the end of a period; rather, they expire at the rate Sa.
The economic argument suggests that EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqr % pepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs % 0-yqaqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaai % aabeqaamaabaabauaakeaacaWGKbGaam4vaiaac+cacaWGKbGaam4u % aiaacIcacaWG0bGaaiykaiabg2da9maaCeaaleqabaGaaGimaaaaki % abeY7aTjaacIcacaWG0bGaaiykaiabgYda8iaaicdaaaa!4D68! ]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$dW/dS(t) = {}^0\mu (t) < 0$$ and there-fore EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqr % pepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs % 0-yqaqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaai % aabeqaamaabaabauaakeGabaaUfiabeY7aTjaacIcacaWG0bGaaiyk % aiabgsMiJkaaicdaaaa!4656!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\mu (t) \leqslant 0$$, for EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqr % pepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs % 0-yqaqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaai % aabeqaamaabaabauaakeGabaaUfmaaCeaaleqabaGaaGimaaaakiab % eY7aTjaacIcacaWG0bWaaSbaaSqaaiaaicdaaeqaaOGaaiykaaaa!45C9!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$${}^0\mu ({t_0})$$ states how a unit of pollution, put into the system at time t0, affects the present value of the welfare function. From 13B.4e it follows thatEquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqr % pepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs % 0-yqaqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaai % aabeqaamaabaabauaakeaacqGHsislcqaH8oqBcqGH9aqpcqaH7oaB % daWgaaWcbaGaam4uaaqabaGcdaWgaaWcbaWaaSbaaWqaaiaadMgaae % qaaaWcbeaakiaadchacqGHIaYTcaWGtbGaamyAaiaad6gacaWGJbGa % amyzaiabeU7aSnaaBaaaleaacaWGtbWaa0baaWqaaiaadMgaaeaaca % WGWbaaaaWcbeaakiabgwMiZkaaicdacaGGSaGaeqiVd0MaeyizImQa % aGimaaaa!5A1E!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$ - \mu = {\lambda _S}_{_i}p \bullet Since{\lambda _{S_i^p}} \geqslant 0,\mu \leqslant 0$$ (that is, μ is not Positive).
Noté that the capital value can be determined by the interest rate and interest revenue. For an interest rate of 6 percent and an interest revenue of $12 per period, the capital value amounts of $200 at the beginning of the period.
Note that the minus sign on the right hand side of equation 13.3 ensures that we measure the marginal prevented damage.
If the assimilative capacity is sufficiently large, the S = 0 curve would coincide with the horizontal axis and a penalty on pollution would not be necessary.
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© 1992 Springer-Verlag Berlin Heidelberg
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Siebert, H. (1992). Long-Term Aspects of Environmental Quality. In: Economics of the Environment. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02842-1_13
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DOI: https://doi.org/10.1007/978-3-662-02842-1_13
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