Endogenous Growth, Sustainability and Cumulative Pollutants

Transcription

1 Endogenous Growth, Sustainability and Cumulative Pollutants Laura Gariup University of Munich Munich Graduate School of Economics Ludvigstrasse 28 VG/33 Phone: May 8, 24 Abstract The aim of this paper is to endogenize the regenerative capacity of renewable resources in the endogenous growth model of Aghion and Howitt [2] in the analysis of sustainable development and environmental pollution. A new function is introduced to show the dependence of the regenerative capacity on the loss of environmental quality caused by the existence of cumulative pollutants. Also the change from noncumulative to cumulative pollutants due to the excess of emission compared to the regenerative capacity is emphasized. A sustainable balanced optimal-growth path is found, but without unbounded consumption. JEL Codes: O, O3, Q, G2, Q5 Keywords: sustainable development, endogenous growth, cumulative pollutants, regenerative capacity, renewable resources Introduction The United Nations Conference on Environment and Development (UNCED) held in Rio de Janeiro in 992, recognized the pressing environment and development problems of the world and, through adoption of Agenda 2, produced a global program of action for sustainable development into the 2st century. After a decade known as the rhetoric decade, the World Summit for Sustainable Development (WSSD), held in Johannesburg in August 22, made it clear that urgent formulation and elaboration of national strategies for sustainable development are necessary. The main result of the summit was, that one of the three pillars of sustainable development - the environment - is seriously damaged because of the distortions placed on it by the actions of human population. The collapse of the environmental pillar is a serious possibility if action is not taken

2 as a matter of urgency to address human impacts, which have left: increased pollutants in the atmosphere, vast areas of land resources degraded, depleted and degraded forests, biodiversity under threat, reduction of the fresh water resources, depleted marine resources. Sustainability does not mean that resources must remain untouched, rather it means the rates of use of their services must be chosen so as not to jeopardize future generations. Services both in the sense of inputs for the production and consumption system, and in the sense of dump for residuals. The focus of this paper is on the second type of environmental services: the regulation of the gaseous composition of the atmosphere; the regulation of the hydrological cycle and climate; the generation and conservation of fertile soils; the protection of coastal zones; the dispersal and breakdown of waste; the absorption of pollutants. The importance of these services can be indirectly found in what is called regenerative capacity. But because the regenerative capacity is depending on living organisms (bacteria, fungi, algae, plants, animals; in one word: the biodiversity) as in the case of the nitrogen cycle responsible for the generation and conservation of fertile soils, it cannot be independent from the condition in which this living organisms are acting. As Dasgupta and Maeler [9] suggest, "... the speed of regeneration depends, among other things, upon:. the current state of the resource; 2. the rate at which pollutants are deposited; 3. the nature of the pollutants." These considerations are exactly what I want to capture in trying to endogenize the regenerative capacity and so to eliminate the limitation coming from its constancy. The importance of the nonconstancy of the regenerative capacity becomes clear when we consider the fact that the most serious problem our societies face is the highly complex environmental issue correlated with the increasing prevalence of cumulative pollutants. This increase exists not only due to an increase of production of strictly cumulative pollutants but also due to the change of per de nition noncumulative pollutants into cumulative pollutants. The change is caused by a to high rate of emission of them in comparison to the normal maximal rate of regeneration of the resources a ected. CO 2 is a noncumulative pollutant but now we are in a situation where its emissions are in fact accumulating over time. 2

3 An easy example to show the latter idea clearer: if we imagine the regenerative capacity as a long-distance runner transporting the total pollution into a rucksack on his back from A to B, the higher the amount of pollution is, the higher is the handicap for the runner and he needs more time to reach his destination or maybe, in the worst case, the destination cannot be reached at all, because the runner breaks down caused by exhaustion. And so the pollution cumulates. The paper is organized as follows. In section 2, I will shortly present the model of Aghion and Howitt [2] on the analysis of sustainable development in the case of environmental pollution, which gave me the intuition for the improvement. In section 3, the constancy of the regenerative capacity will be eliminated and the result of the modi ed model will be presented, followed by the conclusions in section 4. 2 The Schumpeterian Approach to Pollution The model developed by Aghion and Howitt is not a pure endogenous model with technological progress, but it combines two alternative visions of the growth process:. capital accumulation as in Solow [8]; 2. innovation as in Aghion and Howitt []. That is the reason why in the optimization problem there are one law of motion for the tangible capital K _K (t) = Y (t) and another for the intellectual capital B c (t) _B (t) = n (t) B (t) B is nothing else than the quality of the technology incorporated in the intermediate goods, needed for the production of the nal output. It is called Schumpeterian approach because the stochastic research activities produce technological innovation not in the sense of an increase of the number of intermediate goods as in Romer but in the sense of an increase of their quality. So, vertical instead of horizontal innovation produces obsolescence of the old technologies or the so-called Schumpeterian "creative destruction" feature. As Aghion and Howitt write, indicates the rate at which the ow of innovations pushes out the economy s technological frontier; is a positive parameter of the research technology indicating the Poisson arrival rate of innovation to a single research worker; n is the number of researchers. Five new steps are then considered necessary from the authors to take the costs of environmental pollution into account: 3

4 . the insertion of the lost of environmental quality E into the utility function of the representative agent: u (c (t) ; E (t)) ; 2. the formulation of a law of motion for this loss: _E (t) = P (t) (Y (t) ; z (t)) E (t) where P is the ow of pollution and as a positive parameter, represents the maximal potential rate of regeneration. E is de ned as the di erence between the actual environmental quality (A.Q.) and the maximal environmental quality (M.Q.) (the latter could only be reached if all productions would cease inde nitely); 3. E is subjected to an ecological threshold of the form E min E (t) because the authors want to take into account that a lower limit exists, below which environmental quality cannot fall without starting in motion an irreversible deterioration process; 4. the formalization of the production of the ow of pollution taken from Stokey [2] P (t) = Y (t) (z (t)) where > and z 2 [; ] is a measure of the "dirtiness" of the existing technique; 5. adaptation of the production function to the Stokey model where < <. Y (t) = K (t) (B (t) ( n (t))) z (t) Following, the social planner s problem is described, where for concision I omit the temporal notation: max c;z;n Z e t u (c; E) dt s:t: _K = Y c = K (B ( n)) z c _B = nb _E = P E 4

5 K () = K B () = B E () = E K (t) B (t) E min E (t) 8t Aghion and Howitt show that assuming E 2 (E min ; ) is su cient to construct constant growth paths for E; K; B; Y; c; n; z; ; ; with a positive growth rate for capital, consumption and output if three conditions hold. (" +!) g K = g c = g y = ( ) " + ( +!) C ( ) A This is positive only if the rst condition ( ) > is respected. The second " < is indispensable for the satisfaction of the ecological threshold on E and comes from: where g E must be negative. And the third condition (" ) ( ) < g E = "! g K comes from the need of K greater than zero: " ( +!) + " +! ( ) + ( + "g K ) ( + "g K) g K K = ( E ) ( + g E ) " C A " The model shows that a balanced optimal-growth path with unbounded consumption can be sustainable if the three conditions hold and E 2 (E min ; ). 5

6 3 Endogenous Regenerative Capacity For trying to show the connection between the regenerative capacity and the damage caused by the pollution, I suggest a function: (t) = + ae (t) to respect the de nition of E the authors give: E = A:Q: M:Q: and the ecological threshold E min E (t). In the case of an idyllic maximal quality situation when E is equal to, the actual quality is equal to the maximal quality. This implies that also the regenerative capacity is equal to its maximum. When the actual quality starts to decrease, caused by an increased stock of pollution, E becomes more and more negative until the assumed E min. This means also a min ensuring not to fall into irreversibility, with (t) 2 [ min ; ]. The parameter a is positive. The introduction of this new equation changes the Hamiltonian as following: h i H = u (c; E)+ K (B ( n)) z c +Bn h i K (B ( n)) z + + ( + ae) E This implies a new Euler equation for E: _ = ( E)! + ( + 2aE) instead of the original Euler equation: _ = ( E)! + Solving the model, assuming that E 2 (E min ; ) as before and the condition that = + ae >, leads to the existence of a pair of positive hypothetical initial values for K and B such that a balanced optimal-growth path can be reached immediately. In fact, the new K is positive and that implies that the new B is also positive. The ecological threshold condition is also satis ed at all times because it holds at time by assumption and because the new g E =. Now the balanced path is sustainable with bounded consumptions because the growth rates are: g Y = g K = g c = g n = g z = g B = g E = g = g = g = The new initial values are: = ( E )! + + ae = c " = ( ) Y + B 6

7 z = ( + ) c = n = + K Y = K B c B = K z z " + K = B ( E ) ( + ae ) A " With the new burden, which is the indirect e ect of cumulative pollutants on the environmental quality through the damaged regenerative capacity, the result of the original model changes signi cantly. The intuition for such a result can be found in the fact that the intellectual capital B doesn t grow enough to o set the fall in z. In the original model z, which Stokey also interprets as the emission standard, must fall to compensate for the environmental costs coming from the ow of pollution. But now, in the modi ed model, z must fall quicker than before because it must compensate also for the environmental costs coming from the negative e ect of the accumulation of some pollutants on the regenerative capacity. Even I am conscious that the regenerative capacity is an extremely complex phenomenon di erent for each resource and probably non-linear, I have developed such a function for to capture the crucial idea that the accumulation of pollutants has an exact dangerous e ect on the fundamental service of renewable resources: the regenerative capacity. I have also used the powerful de nition of E given by Aghion and Howitt: di erence between actual environmental quality and maximal environmental quality. In one term, it is possible to control indirectly for the current state of the resources (actual quality) and directly for the loss of environmental quality (the di erence). And as main point, this loss can be explain, thanks to the law of motion for E, directly by the emission of pollution, as general term for the sum of noncumulative and cumulative pollutants ( ow of pollution), and indirectly by the accumulation of those pollutants that are strictly cumulative or have become cumulative (stock of pollution). 7

8 4 Conclusion This was the rst attempt to formally introduce in an endogenous growth framework the power of the non-constancy of the regenerative capacity. The stimulation for this improvement was the interest to capture the critical management of cumulative pollutants and therefore to better describe some of the actual environmental problems, as for example the climate changes and the loss of fertility or fresh water. The result of the modi ed model is driven by the speci c functional form I have developed for being as coherent as possible with the powerful de nition of E. But the result can be seen plausible and possible if the di culty of the elimination of pollution already accumulated is considered. Di erent from the case of noncumulative pollutants, which can be managed just by acting on the emission ow, in the case of cumulative pollutants the management of the stock and because of this the damage correlated with it, can be not only extremely costly but also in the near future technically impossible. I think that a rst insight on the importance of a non-constant regenerative capacity for searching a sustainable balanced optimal-growth path is given. References [] P. Aghion and P. Howitt, A Model of Growth through Creative Destruction, Econometrica 6, (992). [2] P. Aghion and P. Howitt, "Endogenous Growth Theory", MIT Press, Cambridge, MA (998). [3] G. B. Asheim, W. Buchholz and B. Tungodden, Justifying Sustainability, J. Environmental Economics and Management 4, (2). [4] R. J. Barro and X. Sala-i-Martin, "Economic growth", McGraw-Hill, New York (995). [5] A. Beltratti, "Models of Economic Growth with Environmental Assets", Kluwer Academic Publishers, Dordrecht, (996). [6] G. Chichilnisky, What Is Sustainable Development?, Land Economics 73, (997). [7] P. Dasgupta, "Human Well-Being and the Natural Environment", Oxford University Press, Oxford, UK (2). [8] P. Dasgupta and G. Heal, The Optimal Depletion of Exhaustible Resources, Rev. Economic Studies 4, 3-28 (974). [9] P. Dasgupta and K. G. Maeler, Poverty, Institutions, and the Environmental-Resource Base, World Bank Environment Paper 9, Washington, D.C. (994). 8

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