IEAS Working Paper. An Ecological-Economic Integrated General. Equilibrium Model. Amy R. Hwang. IEAS Working Paper No. 05-A011.

Transcription

1 論 EAS Woking Pape An Ecological-Economic ntegated Geneal Equilibium Model Amy R. Hwang EAS Woking Pape No. 05-A0 Decembe, 005 nstitute of Economics Academia Sinica Taipei 5, TAWAN NSTTUTE OF ECONOMCS, ACADEMA SNCA TAWAN copyight 005 (Amy R. Hwang)

2 An Ecological-Economic ntegated Geneal Equilibium Model Amy R. Hwang The nstitute of Economics Academia Sinica Nankang, Taipei, Taiwan 59 Phone: (0) 7879#0 Fax: (0) Decembe 7, 005 Abstact A thoough analysis of sustainable development equies a bette undestanding of how economic and ecological systems inteact ove the long un. This pape povides an integated model to analyze inteactions between economic and ecological systems. The linkages between these two systems ae geneated by a utility function contains both economic outputs and ecological sevices in the demand side and by intoducing land as the common input in poduction of economic outputs and ecological sevices in the supply side. The optimal allocation of land between these two systems thus detemines the tade-off between economic outputs and ecological sevices of an ecosystem. Keywods: sustainable development, ecosystem, geneal equilibium, the specific-facto model of tade. 0

3 . The Natue of the Envionmental Cisis and Sustainable Development: Thee has been a maked gowth of inteest in the past thity yeas in the quality of the envionment, the disuption of the eath s natual ecosystems and the depletion of esouces due to the ising intensity and fequency of envionmental elated poblems all ove the wold. Some poblems, like geenhouse effect and climate change, ozone depletion, species extinction, depletion of fossil fuels and vaious mineals, ae of global magnitude. Othes, like acidification, toxic contamination, defoestation, land degadation, fishey and maine destuction, wate depletion, and landscape loss, ae of national o local magnitude. These envionmental poblems have esulted in mounting cleanup costs of toxic waste sites; in educed poductivity of coplands, foests, gasslands and fisheies; in ising health cae costs fo cance, bith defects, allegies, emphysema, asthma and othe espiatoy diseases; and in the spead of hunge. (Bown et al. 993). These poblems, if not deal with popely in time, may poduce ievesible damages to the eath s capacity to sustain life. Moe and moe evidence have shown that the common cause of ecent envionmental poblems is human activities, especially population gowth and inceased mateial aspects of pe capita consumption of goods and esouces bought about by economic gowth (The Bluepint fo Suvival, Ecologist, 97). Two of the wold s most pestigious scientific institutions, National Academy of Science (NAS) and Royal Science (RS) issue a joint statement in 99 which states that

4 n the Eath Summit at Rio in 99, the United Nations Confeence on Envionment and Development (UNCED) fimly identified the need to integate the envionment into all levels of economic decision-making. Fo this to be conceivable, a bette undestanding of how economic and ecological systems inteact ove the long un is equied. n this pape, we setup a geneal equilibium model that contains both economic system and ecological system. The supply side setup of the economic system follows that of the specific-facto model of tade. What s new in this pape is that we fist intoduce the concept of poduction into ecological system and teat the physical and biological chaacteistics of ecosystem as inputs of an ecological poduction function. The economic system and ecological system shae a common input, land. And both systems poduce outputs that consumed by human society. The linkages between economic and ecological systems ae thus geneated in the demand side though a society s utility function and in the supply side though the shaed input land. Such an integated model thus povides a platfom that allows us to analyze the inteactions between economic activities and envionmental changes. n the next section of the pape, we fist eview the economic liteatue on Unestained esouce consumption fo enegy poduction and othe uses could lead to catastophic outcomes fo the global envionment. Some of the envionmental changes may poduce ievesible damage to the eath s capacity to sustain life.. The futue of ou planet is in the balance. The PCC s (ntegovenmental Panel on Climate Change) epot in Decembe 995 also pointed out that the majo cause of the incease in tempeatue is not natual factos but the emission of geen house gases, including CO and CFC, due to human activities.

5 natual esouce management to explain the need to take ecosystem into consideation in economic decision-making in the ea that sustainable development is an inevitable common goal of evey society. t is followed by a step-by-step constuction of a geneal equilibium model. And, the last section contains the conclusion and discussion of futue wok.. Economic Liteatue on Natual Resouce Management Economists attention on issues associated with scacity of exhaustible natual esouce stats in 930s due to the oil shotage. Most of economic studies focus on the intetempoal allocation efficiency (Hotelling, 93; Ramsey, 98 ), on integeneational justice (Hatwick, 977), and on utility maximization ove time (Solow, 976, 986; and Dixit et al. 980) of exhaustible natual esouce like oil and mineal. The objects of analysis in the above liteatues ae natual esouces with maket values so that the optimal extaction ates can be analyzed as a dynamic optimization poblem that choosing a consumption path to maximize pesent value of these esouces. Howeve, as Heal (998) pointed out while the esult deived fom Hotelling-Hatwick ule is fascinating and supising, it is also slightly suspect fom an envionmental pespective: imagine all tees eplaced by buildings of equivalent value. Some may claim that supply and demand would take cae of this poblem since as we appoach such a situation, the pice of tees might ise, and that of 3

6 dwellings fall, to a point whee it is impossible to eplace tees by dwellings of equal maket value. The key diffeence between economic goods and ecological goods is they ae not substitutable in tems of the ecological function povided by the latte. Fo exhaustible natual esouces like oil and othe mineals, which do not play much ole in maintaining ecological stability, it may be appopiate to allow fo the substitution of natual by poduced capital of equal maket value. Howeve, some natual esouces, like foest, land, ai, wate, teestial and aquatic biomass etc., ae citical elements in maintaining the integity and stability of ecological envionment. Altenatively, Babie and Makandya (993) establish the tadeoff between economic gowth and envionmental degading by incopoating the inteactions of consumption and envionmental quality into a model of social welfae optimization. They develop a dynamic optimization model to maximize the net benefits of economic development, subject to maintaining the sevices and quality of natual esouces ove time. An impotant implication deived fom thei model is that both the initial level of envionmental quality as well as the ate of social discount ae significant factos in detemining the optimal choice between sustainable and unsustainable gowth. This implication easonably explains the cuent status of envionments in the developing counties: an economy with a low initial level of envionmental quality tends to choose envionmentally unsustainable economic 4

7 gowth because the benefits of inceased consumption occu in the pesent wheeas envionmental degadation and collapse is a futue poblem. n othe wods, a low initial level of envionmental quality foces esouce uses today to discount the futue heavily. One poblem still emains. The discounting method taditionally used in dynamic optimization poblems is not appopiate appoach in poblems associated with sustainable development. The eason is that the full ecological effects of human activities, even if tactable, often ae not seen fo a vey long time because of the time it takes fo a given action to popagate though components of the whole ecosystem. Moeove, utility-discounting was ethically inappopiate by giving ealie geneations systematically geate weight than late ones simply by eason of position in time. Thee ae two conclusions can be deived fom the above liteatue eview. Fist, in the issues associated with sustainable development, the object of analysis should be boaden to include ecological goods. Second, discounting method taditionally used in dynamic optimization poblems is inappopiate in dealing with sustainable development elated issues both technically and ethically. Theefoe, in this pape, we povide an integated geneal equilibium model that contains both economic and ecological goods. The economic and ecological systems ae 5

8 connected though the social utility function and the poduction functions of the two systems by a natual esouce (land) constaint. The optimal allocation of natual esouce that maintains sustainable ecosystem can be deived by setting an appopiate objective functions so that vaious issues associated with sustainable development can be analyzed without using discounting method. n the next section, the model is biefly descibed.. An Ecological-Economic ntegated Geneal Equilibium Model The basic needs that human beings must have to suvive and maintain good health ae clean ai, clean wate, enough food, clothing, and shelte. n today s society, most of these basic needs, fo example, food, clothing, and shelte, ae economic goods and sevices that povide and tade in makets. Even so, most of the aw mateials of economic goods and sevices ae outputs of ecosystems. Let alone some othe basic needs of human beings, fo example, clean ai and wate, ae ecological goods and sevices that maket alone can not povide. Theefoe, both economic goods and sevices and ecological goods and sevices ae essential to human welfae. The utility function of a society thus should contain consumptions of economic goods and sevices, C, and that of ecological goods and sevices, N. That is, U = U ( C, N). 6

9 Assume that the economy poduces two goods, good and good. Then C denotes the consumption index of the economy defined as C = C k C k. Ego (00) suggests a flexible ways of expessing the complementaity that combined with some substitutability at the magin between economic outputs and ecological sevices as following: U = C + N. 0 is the elasticity of substitution between C and N. Maket equilibium implies that C = y. C = y. Theefoe, the utility function of a society can be ewitten as U = ( y k k y ) + N. () The Economic System The economic system is epesented by a modified Ricado-Vine model. Thee ae two sectos, agicultue ( Y ) and manufactuing ( Y ), and thee inputs, X is the The value of can be anywhee between 0 and ; the lage the, the geate the substitutability between C and N. The limiting case of = 0 = is whee C and N must be consumed in a fixed popotion as complements to each othe. The othe limiting case, with, is whee C and N ae pefect substitutes fo each othe. 7

10 facto specific to the poduction of good, and X specific to good. The thid facto, land, is the mobile facto that used in the poduction of goods and. Land is also an essential input in the poduction of ecological goods and sevice. Let the land employed in sectos,, and N be denoted as,, and N, espectively. The poduction functions of the economic system can be witten as y = f x, ). () ( y = g x, ). (3) ( The income poduced by the economic system is y = y + py. (4) n ode to focus on the inteaction between economic and ecological systems, assume that demands fo both goods in a simplified fom that a fixed popotion k of income is spent on good and the est on good. 3 p y = ( k) y. (5) The maket stuctues fo goods and facto inputs ae pefect competitive. Use the pice of good as numeaie so that the pice of good is p. The competitive maket equilibium conditions equie that the pice of each good equal to its unit poduction cost. That is, 3 k Define a consumption index C k C = C. This demand function is deived fom consume optimization poblem. See appendix B. 8

11 w a x a. (6) + z = w ax + az = p. (7) The land esouce constaint is + + N =. (8) The Ecosystem An ecosystem is a community of living (the oganic o biotic component like plants, animals including man, and mico-oganisms) and nonliving things (the inoganic o abiotic component like soil and ock, wate, and ai) that depend on one anothe. All of the eath s ecosystems togethe make up the biosphee. Within the biosphee the oganic components and the inoganic envionmental components ae intimately connected though a seies of lage-scale cyclic mechanisms which involve the tansfe of enegy, wate, chemical elements and sediment thoughout the biosphee. The ecosystem sevices povided by this complex set of systems include climate contol, ai esouces and puification, wate esouces and puification, soil fomation and enewal, waste emoval and detoxification (dilution, decomposition, ecycling), natual pest and disease contol, biodivesity and gene pool (fo adaptation to changing conditions), potentially enewable matte esouces (foests, gasslands, wildlife, soil, wate, food) nonenewable mineal esouces (coppe, aluminum, ion, 9

12 uanium), nonenewable enegy esouces (oil, coal, natual gas) enewable enegy esouces (sun, wind, flowing wate, geothemal heat, plant matte, biomass), ecycling vital chemicals (cabon, oxygen, nitogen, wate, phosphous, sulfu). (Mille (00), p. 99) These ecological sevices suppot and sustain all life and all economies on the eath. n tems of economic concept, the ecological sevices ae joint outputs of the oganic components and the inoganic envionmental components of inte-locking ecosystems. Theefoe, we teat the whole mechanism of ecosystem functions as an ecological poduction function. Howeve, how exactly each of the systems (fo example, cabon cycle) woks and how these diffeent systems ae elated to each othe ae beyond the state of knowledge today, theefoe, we simplify the ecological poduction function by teating the non-living envionment as a composite input, A (fo abiotic) and the living components as a composite input B (fo biotic). The thid input in the poduction of ecological goods and sevices is land. This is because accoding to Aldo Leopold s philosophy of land ethics, That land is a community is the basic concept of ecology, but that land is to be loved and espected is an extension of ethics. The land ethic simply enlages the boundaies of the community to include soils, wates, plants, and animals, o collectively the land. Aldo Leopold ( ), A Sand County Almanac Ecological goods and sevice thus is a composite output jointly poduced by land and the abiotic (A) and biotic (B) envionments upon it. Theefoe, the Ecological 0

13 poduction function is specified as following: N AB N B A E N N = = ] ),, ( [, (9) whee A is the abiotic chaactes of the ecosystem that epesented by local climatic, hydologic, edaphic, and geomophologic (landscape, etc.) factos. B is the biotic featue of an ecosystem which in geneal can be epesented by the measue of biodivesity that contains the numbe, composition, and distibution of species. The ecological poduction function specification in equation (9) is definitely ovesimplified, but since ou pupose at this stage is to study the inteactions between economic system and ecosystem. The linea fom ecological function seves the pupose. The utility-maximization conditions of the above model ae 0 = = z k z k g f f k C U L λ. (0) 0 ) ( = = z z k k g g f k C U L λ. () 0 = = z N AB N U L λ. () 0 = = N N L λ. (3) Land demand in ecosystem: The optimal allocation of land in ecosystem and in economic system deived

14 fom equations (0)-(3) ae Y = ( ). (4) N AB The above ecosystem land demand function is invesely elated with the land ental ate. t is illustated in the following Figue. Figue Ecosystem Land Demand Function N AB = ( ) Y N Land allocation in economic system: The optimal allocation of land within the economic system is solved accoding to equations (0) and (). t is the same as that of allocation of mobile facto in the specific-facto model of tade, which is summaized as following: 4 The land demand function in secto of the economic system is ) = φ ( x. (5) 4 See Caves and Jones (984), Chapte 6.

15 t is illustated in Figue by the cuve with the oigin O. Figue Land Maket Equilibium in Economic System z d = φ ) ( x ( x p z d = δ ) p E Y Y O z O z z Y 005//04 z Y Define the land demand elasticity in secto as γ z ( = d ) x. Then the land ˆ demand function in secto can be witten in gowth fom as ˆ = x. (5a) ˆ γ z Similaly, the demand fo land in secto is = δ ( x. (6) p ) t is illustated in Figue by the cuve with the oigin O. Define the demand elasticity of mobile facto in secto as 3

16 z d( ) x z x d( ) p p γ z = =, ^ ^ z ( x ) ( ) p The land demand function in secto can also be witten in gowth fom as ˆ = xˆ γ ( ˆ z ˆ). (6a) p Fo any given size of land allocated to economic system, the intesection of and, point E Y in Figue, detemines the equilibium land ental ate, Y. Y of land is allocated to the poduction of good and Y to that of good. Land allocation equilibium: The equilibium allocation of land among goods, and ecosystem sevices is illustated in Figue 3. n Figue 3, the land demand functions of goods and ae added hoizontal to obtain the aggegate land demand function of economic system + and the ecological land demand function in Figue is flipped ightwad. The intesection of aggegate land demand cuve, +, and ecosystem land demand cuve, N, detemines the integated equilibium point E, whee the supescipt denoted fo integated equilibium. The integated equilibium land ental ate is. The land allocated to goods,, and ecosystem ae,, and N, espectively. 4

17 Figue 3 The ntegated Land Allocation Equilibium + p N Y E E O z O z N O zn No-ecosystem equilibium Due to the confusion of economic goods and sevices with ecological goods and sevices, and due to inapplicable of maket mechanism to ecosystem goods and sevices, the ole of ecosystem is ignoed in taditional economic analysis. The following Figue 4 illustates the distotion of land allocation when ecosystem is ignoed. The no-ecosystem equilibium is epesented by point Y E with land ental ate Y lowe than. The land allocated to goods,, and ecosystem ae >, Y >, and = 0, espectively. Compaed the no-ecosystem Y N equilibium with the integated equilibium, land is unde-piced so that too much of it is allocated to economic poduction. The no-ecosystem equilibium in the taditional economic analysis is not the welfae maximization equilibium. 5

18 Figue 4 No ecosystem case p + N E Y Y E O z O z N O zn 005//6 Y Y The above analysis shows that the land ental ate in the integated equilibium,, is detemined jointly by paametes in economic as well as those in ecological systems. The economic goods and sevices poduced in the integated equilibium expessed in the gowth fom is ˆ z z z z z + y = [ kθ + ( k) θ ] γ ˆ + k x + ( k) x + ( k)( θ γ ) pˆ, (4a) whee x w i i θ xi = and pyi i θ zi = ae the shae of specific facto and land in good i. pyi The ecological goods and sevices supplied can be expessed as Nˆ = ( Aˆ + Bˆ) kxˆ ( k) xˆ γ ˆ ( k) θ pˆ, (9a) N z γ which shows how economic paametes and vaiables affect the ecological goods and sevices povided in a society. Theefoe, conditions and vaiations in ecological 6

19 system, fo example, changes in abiotic o biotic conditions affect not only the outputs of ecological goods and sevices povided, they also affect the outputs of economic system, and vise vesa. V. Conclusions and Futue Woks This pape constucts a geneal famewok to integate economic and ecological systems into a model of social welfae optimization so that the inteactions of economic outputs and ecological goods and sevices can be analyzed. t allows us to have a bette undestanding of how economic and ecological systems inteact ove the long un so that envionmental concens can be integate into economic decision-making, and vise vesa. Howeve, this famewok is only a simple illustation of how economic and ecological systems can be integated. n ode to obtain a closed fom solution, we assume that the ecological poduction function is a line function of abiotic, biotic chaacteistics, and size of ecosystem land. n the eal wold, the ecological poduction function is a much moe complicated function of these and othe vaiables. The next step of eseach should apply the ecological pinciples of elevance into the ecological poduction function so that the above famewok can be actually applied to economic and envionmental management. 7

20 Refeences Babie, Edwad B. and Anil Makandya, (993) Envionmentally sustainable development: optimal economic conditions, in Economics and Ecology: New Fonties and Sustainable Development, edited by Edwad B. Babie, Chapman & Hall. Bown et al. State of the Wold Repots 993, the Wold Watch nstitute: 4-5. Caves, Richad E. and Ronald W. Jones (984), Wold Tade and Payments: An ntoduction, Fouth Edition, Chapte 6. Little Bown. Dixit, Avinash, Pete Hammond, and Michael Hoel, On Hatwick s ule fo egula maximin paths of capital accumulation and esouce depletion, Review of Economic Studies, Apil 980, 47(3): Ego, Kaev (00), Stocks, flows and complementaity: fomalizing a basic insight of ecological economics, Ecological Economics 43: Hatwick, John M., (977) ntegeneational Equity and the nvesting of Rents fom Exhaustible Resouces. AER, Decembe 977, VOL. 67 NO. 5: Heal, Geoffey, ntepeting Sustainability, in Sustainability: Dynamics and Uncetainty, edited by Gaciela Chichilnisky, Geoffey M. Heal and Alessando Vecelli. Kluwe Academic Publishes Hotelling, Haold, (93), The Economics of Exhaustible Resouces, Jounal of Political Economy, Apil, pages Mille, G. Tyle, J. Chapte 6, Living in the Envionment, 6 th edition. Wadswoth Publishing Company, 00. Ramsey, Fank (98), A Mathematical Theoy of Saving. Economic Jounal, 38: Solow, R. M. (976) ntegeneational Equity and Exhaustible Resouces, Review of Economic Studies 4, 9-45., (986) On the ntegeneational Allocation of Natual Resouces, Scandinavian Jounal of Economics 88(),

21 Numbe Autho(s) Title Date 05-A0 Amy R. Hwang An Ecological-Economic ntegated Geneal Equilibium Model /05 05-A00 Juin-jen Chang A Manageial Tade Union and Economic Gowth /05 Ming-fu Shaw Ching-chong Lai 05-A009 Lin-Ti Tan Spatial Economic Theoy of Pollution Contol unde Stochastic 0/05 Emissions Kamhon KAN Entepeneuship and Risk Avesion 0/05 率 08/05 05-A006 Shin-Kun Peng, Economic ntegation and Agglomeation in a Middle 06/05 Jacques-Fancois Thisse Poduct Economy Ping Wang 05-A005 令 論 05/05 05-A004 Lin-Ti Tan Spatial Monopoly Picing in a Stochastic Envionment 05/05 Yan-Shu Lin 05-A003 Been-Lon Chen Congestible Public Goods and ndeteminacy in a 03/05 Shun-Fa Lee Two-secto Endogenous Gowth Model* 05-A00 C. Y. Cyus Chu The Optimal Decoupled Liabilities: A Geneal Analysis 0/05 Hung-Ken Chien 05-A00 Cyus C.Y. Chu Duable-Goods Monopolists, Netwok Effects and 0/05 Hung-Ken Chien Penetation Picing 04-A05 Been-Lon Chen Multiple Equilibia in a Gowth Model with Habit Pesistence /04 04-A04 C. Y. Cyus Chu A New Model fo Family Resouce Allocation Among 05/04 R. R. Yu Siblings: Competition, Fobeaance, and Suppot Ruey S. Tsay 04-A03 C. Y. Cyus Chu Tansmission of Sex Pefeences Acoss Geneations: 05/04 Ruey S. Tsay The Allocation of Educational Resouces Among Siblings Huoying Wu 04-A0 C. Y. Cyus Chu Childen as Refigeatos: When Would Backwad 05/04 Altuism Appea? 04-A0 Macus Beliant Welfae Analysis of Numbe and Locations of Local 05/04 Shin-Kun Peng Public Facilities Ping Wang

22 04-A00 Daigee Shaw Assessing Altenative Policies fo Reducing Household 03/04 Yue-Mi Tsai Waste in Taiwan 04-A009 Daigee Shaw A Pobabilistic Risk Analysis fo Taipei Seismic Hazads: 03/04 Chin-Hsiung Loh Chin-Hsun Yeh An Application of HA-Taiwan with its Pe-pocesso and Post-pocesso Wen-Yu Jean Yen-lien Kuo 04-A008 Yu-Lan Chien A Geneal Model of Stating Point Bias in Double-Bounded 03/04 Cliff J. Huang Dichotomous Contingent Valuation Suveys Daigee Shaw 04-A007 不 行 0/04 玲 量 亮 04-A006 Chun-chieh Huang Woking Hous Reduction and Endogenous Gowth 0/04 Ching-Chong Lai Juin-Jen Chang 04-A005 Juin-Jen Chang On the Public Economics of Casino Gambling 0/04 Ching-Chong Lai Ping Wang 04-A004 Ming-Fu Shaw nteest Rate Rules, Taget Policies, and Endogenous 0/04 Shu-Hua Chen Economic Gowth in an Open Economy Ching-Chong Lai Juin-Jen Chang 04-A003 Po-Hsuan Hsu Re-Examining the Pofitability of Technical Analysis 0/04 Chung-Ming Kuan with White s Reality Check 04-A00 Kamhon Kan Obesity and Risk Knowledge 0/04 Wei-De Tsai 04-A00 Chi-Chung Chen Climate Change and Cop Yield Distibution: Some 0/04 Ching-Cheng Chang New Evidence fom Panel Data Models 03-A009 Joseph Geenbeg Toweing ove Babel: Wolds Apat but Acting Togethe /03 Sudhee Gupta Xiao Luo 03-A008 Shin-Kun Peng Soting by Foot: Consumable Tavel fo Local /03 Ping Wang Public Good and Equilibium Statification 03-A007 Been-Lon Chen Economic Gowth With Optimal Public Spending /03 Compositional 03-A006 Been-Lon Chen Facto Taxation and Labo Supply n A Dynamic /03 One-Secto Gowth Model