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Copyrighted Material VII.9 Ecological : Principles of Design for Anastasios Xepapadeas

OUTLINE . An externality is present when the well- being () of an individual or the 1. Introduction possibilities of a firm are directly affected by the 2. Ecological modeling and dynamics actions of another agent in the . 3. Economic modeling for ecosystem management internalization of an externality. A situation in which 4. Instruments of economic policy and policy the agent who generates the externality bears the design cost that the externality imposes on other agents. failure. A exists when competi- studies the interactions and coevo- tive markets fail to attain Pareto optimum. lution in time and space between and Pareto optimum. A situation in which it is not possible . The rate at which exploit or harvest to make someone better off without making some- ecosystems services exceeds what might be regarded as a one else worse off. desirable level from society’s point of view. The conse- production function. A real-valued function that shows quences of this are well known (e.g., cli- the maximum amount of that can be pro- mate change, loss and extinction of species, duced for any given combination of inputs. collapse of fisheries, overexploitation of ). . A for which use of one unit of The objective of designing economic policy is to develop a the good by one agent does not preclude its use by system of regulatory instruments so that the state of the other agents. regulated ecosystems will converge toward the socially state variable. A variable that characterizes the state desirable outcome. The purpose of this chapter is to present of a system at any point in time and space. an approach describing how economic policies might be utility function. A real-valued function that shows that designed to achieve this objective. if a prefers the bundle of x to the bundle of goods y, then the utility of x is greater than the utility of y. GLOSSARY control variable. A variable whose values can be chosen 1. INTRODUCTION by a decision maker in order to affect the path of the state variables. Ecological economics studies the interactions and co- ecological economics. The study of the interactions and in time and space between ecosystems and in time and space between ecosystems human economies. Human economies in the process of and human economies. their operation and development use the flows of ser- economic policy. The intervention by a regulator vices generated by ecosystems. In using these services, through policy instruments in private markets so humans make decisions about the size and the time that a desired market outcome is attained. profile of the harvested flows of ecosystems services as Copyrighted Material

Ecological Economics 741 well as about the growth rates of different types of Ecosystems Assessment (2005) classification, these natural that are embedded in the ecosystems services may include provisioning services (e.g., , and that generate the flows of desirable services. Long water, fiber, fuel), regulating services (e.g., climate series of empirical observations have established that, regulation, disease), cultural services (e.g., spiritual, given the institutional structure of the economies (e.g., aesthetic, education), or supporting services (e.g., pri- markets, allocation of rights, regulatory au- mary production, formation). It should be noted thorities, international agreements), the rate at which that some of the above services, mainly the provision- economic agents exploit (or harvest) ecosystems ser- ing, can be used after harvesting the resources stock vices exceeds what might be regarded as a desirable (e.g., fishing, water pumping), whereas others, mainly level from society’s point of view. The consequences of regulating and cultural services, are associated with this overexploitation are well known and include se- the existing stock of the resource (e.g., aesthetic ser- rious interrelated environmental problems such as cli- vices and preservation of a ). Let F(x(t)) be a mate change, and extinction of spe- function describing the growth of the resource cies, collapse of fisheries, and overexploitation of water stock. This growth function embodies factors such as resources. To put this point differently, the market birth, death, migration in case of biological resources outcome, or the outcome stemming from individual (e.g., fisheries), natural inflows, and seepage in case of actions, regarding the harvesting of ecosystem services renewable resources ( or accumulation and the time paths of the stocks of (or of pollutants), whereas in the case of exhaustible re- natural resources) is different from an outcome (or a sources with no discoveries, FðxðtÞÞ 0. If we denote state) that is socially desirable. by h(t) the harvesting of the resource, so that provi- The challenge of designing economic policy in sioning services are used, then the evolution of the re- this context is to develop a system of regulatory in- source can be described by an ordinary differential struments or incentive schemes that will affect the equation (ODE), which can be written, for some initial behavior of economic agents (individuals, firms, na- stock, x0, as: tions) regarding the harvesting of ecosystem services in such a way that harvesting rates and time paths of the dx(t) x_ (t) ¼ F(x(t)) h(t), x(0) ¼ x > 0: (1) stock of natural capital under the economic policy dt 0 will converge toward the socially desirable outcome. The purpose of this chapter is to present an ap- The most common specification of the growth func- proach describing how these economic policies might tion F(x(t)) is the , FðxÞ¼rx(1 x=K), be designed. where r is a positive constant called intrinsic growth rate, and K is the of the environ- ment, which depends on factors such as resource 2. ECOLOGICAL MODELING AND RESOURCE availability or environmental . If h(t) ¼ DYNAMICS F(x(t)), then the population remains constant because The building of meaningful ecological–economic harvesting is the same as the population’s net growth. models capable of helping in the design of policies for This harvesting rate corresponds to . ecosystem management requires the development of Harvesting rate is usually modeled as population two interacting modules: an ecological module de- dependent or h ¼ qEx where q is a positive constant, scribing the evolution of the state of the ecosystem and referred to as a catchability coefficient in fishery the ways that the interventions of the economic agents models, and E is harvesting effort. The activities of influence this evolution; and an economic module de- economic agents can affect the resource stock, in ad- scribing, in broad terms, the net benefits accruing to dition to harvesting, by affecting parameters such economic agents from the use of the ecosystem’s flow as the intrinsic growth rates or the carrying capacity. of services. Assume, for example, that the intrinsic rate of growth The traditional resource models presented, for ex- and the carrying capacity of the environment for ample, by Clark (1990) or Dasgupta and Heal (1979) the resource described by equation 1 are affected by describe the evolution of the population (or the stock of environmental pollution that accumulatesP n or stock) of a biological, a renewable, or an exhaust- on the ecosystem (e.g., a lake). Let S(t) ¼ i ¼ 1 si(t) ible resource when exploitation (harvesting) by eco- denote the sum of emissions generated by i ¼ 1, ..., n nomic agents takes place. Let x(t) denote the stock of sources at time t, and let P(t) be the stock of the pol- a resource at time t, which generates a flow of valuable lutant accumulated in the ecosystem (e.g., phosphorus services to economic agents. Following the Millennium accumulation from agricultural ). Then the Copyrighted Material

742 Managing the evolution of the pollutant stock can also be described limiting resource. Then a mechanistic resource-based by an ODE: model with a single limiting factor in a given area can be described by the following equations: _ P(t) ¼ S(t) bP(t), P(0) ¼ P0 > 0 (2) x_ j(t) ¼ gj(R(t)) dj, xj(0) ¼ xj0, j ¼ 1, ..., J, where b > 0 is a constant reflecting the environment’s xj(t) self-cleaning capacity. The negative impact of the pol- XJ lutant’s stock on the intrinsic growth rate and the en- _ R(t) ¼ S(t) aR(t) wjxj(t)gj(R(t)), vironment’s carrying capacity can be captured by j ¼ 1 functions r(P), r0(P) < 0 and K(P), K0(P) < 0. Then the R(0) ¼ R (5) evolution of the resource is described by: 0 x(t) where gj(R) is resource-related growth for species j, dj x_(t) ¼ r(P(t))x(t)1 h(t): (3) is the species’ natural death rate, S(t) is the amount of K(P(t)) resource supplied, a is the removal The ODE system (equations 2 and 3) is an example rate (leaching rate), and wj is the specific resource of a simple in which economic agents by species j. affect the resource stock in two ways, through har- Another important characteristic of ecosystems, in vesting and through emissions generated by their eco- addition to the temporal variation captured by the nomic activities. The agents that harvest the resource models described above, is that of spatial variation. and the agents that generate emissions are, in the major- Biological resources tend to disperse in space under ity of the cases, not the same, and it is hard to coor- forces promoting ‘‘spreading’’ or ‘‘concentrating.’’ dinate their decisions. Furthermore, the pollutant can These processes, along with intra- and interspecies in- generate additional environmental damages to individ- teractions, induce the formation of spatial patterns for uals, which can be summarized in a damage function. species in a given spatial domain. A central concept in The simple model of resource dynamics described modeling the dispersal of biological resources is that by equation 1 can be generalized in many ways (see, of diffusion. Biological diffusion when coupled with e.g., Murray, 2003). Generalizations may include age- population growth equations leads to general reaction– structured populations, multispecies populations and diffusion systems (e.g., Okubo and Levin, 2001; Mur- Lotka-Volterra predator–prey models, mechanistic re- ray, 2003). When only one species is examined, the source-based models of species , models coupling of classical diffusion with a logistic growth with spatial variation including mod- function leads to the so-called Fisher-Kolmogorov els, and models with resource diffusion over space. equation, which can be written as A general multispecies model with J prey popula- @x(z, t) @2x(z, t) tions denoted by xj(t) and J predator populations de- ¼ F(x(z, t)) þ Dx 2 , (6) noted by yjðtÞ can be written, for j ¼ 1, ..., J, as: @t @z "# XJ where x(z, t) denotes the concentration of the biomass x_ j(t) ¼ xj(t) aj bjkyk(t) , xj(0) ¼ xj0, at spatial point z at time t. The biomass grows ac- cording to a standard growth function F(x) but also "#k ¼ 1 XJ disperses in space with a constant diffusion coefficient y_j(t) ¼ yj(t) gjkxk(t) dj , yj(0) ¼ yj0, (4) Dx. In general, a diffusion process in an ecosystem k ¼ 1 tends to produce a uniform population density, that is, spatial homogeneity. However, under certain condi- where all parameters are positive constants. tions reaction–diffusion systems can generate spatially In the mechanistic resource-based models of species heterogeneous patterns. This is the so-called Turing competition emerging from the of Tilman (e.g., mechanism for generating diffusion instability. Tillman, 1982), species compete for limiting resources. Spatial variations in ecological systems can also be In these models, the growth of a species depends on the analyzed in terms of metapopulation models. A meta- limiting resource, and interactions among species take population is a set of local populations occupying place through the species’ effects on the limiting re- isolated patches, which are connected by migrating source. Let x(t) ¼ (x1(t), ..., xj(t)) be the vector of individuals. Metapopulation dynamics can be devel- species , and R(t) the amount of the available oped for single or many species. For the single species Copyrighted Material

Ecological Economics 743 8 9 8 9 occupying a spatial domain consisting of s ¼ 1, ..., S < x ‡ y = < U(x) U(y) = patches, the dynamics becomes if: x y ; then : U(x) > U(y) ;: x y U(x) ¼ U(y) x_ (t) XS s ¼ F(x (t)) þ d x (t), s ¼ 1, ..., S, (7) x (t) s sk k s k ¼ 1 A central paradigm of modern economic theory (e.g., Mass Colell et al., 1995) is that, for exogenously where xsðtÞ is the species population in patch s, and dsk determined and income, consumers choose the is the rate of movement from patch k to patch s, combinations of goods they consume by maximizing ðs 6¼ kÞ. Thus, dynamics is local with the exception of their utility function subject to a budget constraint, movements from one patch to the other. whereas competitive firms, for exogenously determined If harvesting is introduced into the ecological models prices of inputs and outputs, maximize profits subject of equations 4–7, and growth functions depend on to the constraints imposed by , which are pollutants generated by economic activities, then the usually summarized by a production function. ecological model is extended to include economic var- iables whose time paths are chosen by economic agents. Pareto Efficiency 3. ECONOMIC MODELING FOR ECOSYSTEM MANAGEMENT Economic Allocation Consider an economy consisting of i ¼ 1, ... , I con- Choosing time paths for harvesting or other variables sumers, j ¼ 1, ... , J firms, and l ¼ 1, ... , L goods. The that might affect the state of the ecosystem, which are consumption for individual i is given by the vector called control variables, implies management of the xi ¼ (x1i, ... , xLi), and production by firm j is given by ecosystem. In economics, the most common type of the vector yi ¼ (y1j, ... , xLj). Consumers maximize management is the optimal management, which means profits subject to their budget constraint, whereas firms that the control variables are chosen so that an objec- maximize profits subject to technology. tive function is optimized (maximized or minimized). An economic allocation (x1, ... , xI, y1, ..., yJ)isa Of course, other types of management rules can be specification of a consumption vector for each con- applied such as adaptive rules or imitation rules, but sumer and a production vector for each firm. The al- the focus of the present article is on optimal rules. To location is feasible if provide a meaningful presentation of the optimal rules, some fundamental economic concepts are useful. Xl XJ xil yjl, l ¼ 1, ..., L: Some Fundamental Economic Concepts i ¼ 1 j ¼ 1

Preferences, Utility, Profits Pareto Optimality Individuals have preferences summarized by the pref- A feasible allocation (x1, ..., xI, y1, ..., yJ) is Pareto erence relationship , which means ‘‘at least as good as.’’ optimal or Pareto efficient, if there is no other alloca- 0 0 0 0 0 Let n goods be indexed by i 1, ..., n, and the com- tion (x1, ..., xI, y1, ..., yJ) such that u(xi) u(xi), ¼ 0 binations of different quantities from these goods 8i ¼ 1, ..., I and u(xi) > u(xi) for some i. To put it differently, a feasible allocation (x1, ..., xI, y , ..., y ) x ¼ (x1, ..., xn), y ¼ (y1, ..., yn). Then a consumer’s 1 J preferences regarding the two combinations or bundles is Pareto optimal or Pareto efficient if society’s re- of goods could be described as: sources and technological possibilities have been used in such a way that there is no alternative way to orga- x ‡ y means that combination x is at least as good nize production and that makes some as combination y. consumers better off without making someone worse x y means that combination x is better than (is off. preferred to) combination y. x * y means that the consumer is indifferent be- Competitive Equilibrium tween x and y. An allocation (x1*, ... , xI*, y1*, ... , yJ*) and a A utility function is a real-valued function of the vector p* ¼ (p1*, ... , pL*) comprise a competitive or combinations of goods, such as: Walrasian equilibrium if Copyrighted Material

744 Managing the Biosphere

Firms maximize profits by taking equilibrium Economic Policy prices p* as given. The above results imply that competitive markets fail Consumers maximize utility subject to their to produce a Pareto optimal outcome or a socially op- budget constraint determined by their given timal outcome in the presence of environmental ex- income w, taking equilibrium prices p* ternalities and open-access resources. When competitive as given. markets fail to produce the Pareto optimal allocation, Markets clear, or demandP equals supply,P at the I J there is a need for market intervention and prices p*, or i ¼ 1 xil ¼ j ¼ 1 yjl, policy to achieve the Pareto optimal allocation. Be- l ¼ 1, ..., L. cause environmental and open-access characteristics are predominant in ecosystems, compet- First Theorem itive (and of course imperfectly competitive) markets If the price vector p* and the allocation fail to attain the socially optimal ecosystem state. Thus, * (x1*, ..., xI*, y1*, ..., yJ ) constitute a competitive there is a need for economic policy for ecosystem equilibrium, then this allocation is Pareto optimal. management.

Second Welfare Theorem Optimal Ecosystem Management Suppose that (x1*, ..., xI*, y1*, ..., yJ*) is a Pareto efficient allocation, then there is a price vector p*, such The economic concepts defined above can help formu- that (x1*, ..., xI*, y1*, ..., yJ*) and p* constitute a late optimal ecosystem management and methods for competitive equilibrium. designing economic policy to achieve a socially optimal state for ecosystems. The approach is to define an ob- Welfare Efficiency jective function for the economic agent(s), that will be A Pareto efficient allocation maximizesP a linear social optimized subject to the constraints imposed by the I welfare function of the formW ¼ i ¼ 1 aiui(xi): ecological model of the ecosystem, which will be along the lines of models described in section 2. In principle the objective function will include profits associated Externalities with harvesting or utility associated with the ecosys- Environmental and resource economics have long been tem services. The way in which the objective function associated with the concepts of externalities and market is set up, the ecological constraints that are taken into failure. An externality is present when the well-being account, determine the solution of the ecological– (utility) of an individual or the production possibilities . By solution we mean the paths for the of a firm are directly affected by the actions of another control variables and the stock of ecosystems resources, agent in the economy. When externalities are present, which are the state variables, and the equilibrium state the competitive equilibrium is not Pareto optimal. of the ecosystem under a specific management rule. Two types of solution are distinguished in general, a socially optimal solution and a privately optimal solution. Public Goods (Bads) A public good is a commodity for which use of The Socially Optimal Solution one unit of the good by one agent does not pre- clude its use by other agents. Public goods (bads) The socially optimal solution corresponds to a solution are not depletable. Environmental externalities (air in which social welfare is maximized. This means that pollution, ) are nondepletable public the objective function includes utility accruing from bads and are mainly associated with missing mar- harvesting (which is sometimes called consumptive kets or missing property rights. Competitive markets utility and is mainly associated with provisioning eco- have the following characteristics in the presence of system services) and utility associated with the other externalities: services such as regulation, cultural or supporting ser- vices, existence values, or benefits associated with pro- Competitive markets cannot obtain the ductivity or gains (which is sometimes called Pareto optimal levels of public goods or public nonconsumptive utility). The objective function for the bads. social welfare maximization problem also includes Competitive markets cannot obtain the Pareto damages from environmental degradation, which are optimal levels of harvesting for open-access or environmental externalities (nondepletable public bads), common-pool natural resources. as well as stock effects that negatively affect production Copyrighted Material

Ecological Economics 745 functions in the case of management of open access re- resource has open-access characteristics, each harvester sources. The socially optimal solution is sometimes re- enters in competition to catch the fish first before ferred to as the so-called problem of the social planner, someone else does. As a result, in the open-access or where a fictitious social planner maximizes social wel- bionomic equilibrium, the stock of fish is smaller rel- fare by taking into account all the externalities not ac- ative to the social optimum, which internalizes ‘‘stock counted for by competitive markets. effects.’’ Overfishing and stock collapse can be attrib- Let Uc(h(t)) denote consumptive utility at time t uted to this type of externality, also known as the associated with harvesting h ¼ (h1, ... , hn) species, tragedy of the . In the case of pollution con- and Unc(x(t)) denote nonconsumptive utility associated trol, emissions are generated by a group of agents (e.g., with ecosystem services generated by species biomasses an industry), but the damages affect another group of existing in the ecosystem and not removed by har- agents (e.g., inhabitants of a certain area). Because the vesting. The total flow of utility at time t can be written cost of emissions is not internalized by the emitters, in as Uc(h(t)) þ Unc(x(t)). Because the objective in the the absence of regulation, emissions exceed the socially dynamic context is, in the majority of cases, to maxi- desirable level, which is determined by internalizing mize the present of the utility flow over an infinite environmental damages. In other cases harvesters do time horizon, the objective can then be written as: not take into account nonconsumptive utility associ- Z ated with the stock of the harvested resource (e.g., 1 existence values), which increases even more the devi- max e rt½Uc(h(t)) þ Unc(x(t)) dt, (8) {h(t)} 0 ation between the social and the private optimum that results from open access. There are also situations in where r 0 is a utility discount rate, subject to the which the harvester does not take into account the fact constraints imposed by the structure of the ecosystem. that harvesting the specific resource might harm the A solution to this problem will produce the socially stock of other resources (e.g., by-catch in fishing), optimal paths for the controls and the states (h*(t), which is an additional externality. Another type of x*(t)) and a long-run equilibrium state (h*, x*) as externality can be associated with strategic behavior in t !1, provided that the solution satisfies appropriate resource harvesting if more than one economic agent stability . It should be noted that, in princi- harvests the resource. If many small harvesters are ple, benefits associated with consumptive can present, then the privately optimal solution can be be approximated using market data from concepts obtained as an open loop or feedback Nash equilib- such as consumer and producer surplus, whereas ben- rium, which also deviates from the social optimum. efits associated with nonconsumptive utility and envi- The fact that general ‘‘stock effects’’ are not taken ronmental externalities are hard to estimate because into account at the private optimum implies that markets for the larger part of the spectrum of ecosys- Unc(x(t)) ¼ 0 in equation 8. As a result, the privately tem services and environmental pollution are missing. optimal solution will deviate from the socially optimal solution. Furthermore, because all the ecological con- straints are operating in the real ecosystem, there will The Privately Optimal Solution be discrepancies between the perceived evolution of The privately optimal solution is distinguished from ecosystems under management that ignores certain the socially optimal one by the fact that only con- constraints and the actual evolution of the ecosystem. sumptive utilities or profits enter the objective func- These discrepancies might be a cause for surprises in tion. In particular, when the market outcome regarding ecosystem management. the ecosystem’s state is analyzed, the basic assumption is that management is carried out by a ‘‘small’’ profit- maximizing private agent that in general ignores ‘‘stock 4. INSTRUMENTS OF ECONOMIC effects,’’ the general nonconsumptive flows of ecosys- POLICY AND POLICY DESIGN tem services, or other externalities generated by the The inability of privately optimal solutions realized agent’s activities. Thus, the private agents do not take in the context of unregulated market economies to at- into account, or do not internalize, externalities asso- tain the socially optimal outcome regarding the state of ciated with their management. There are some very an ecosystem calls for (detailed well-known examples. analysis can be found in Baumol and Oates, 1988; In the case of an open-access commercial fishery, Xepapadeas, 1997), which is assumed to be designed usually each harvester takes the landing price as fixed and implemented by a regulator. The classic instru- but ignores the fact that his/her own harvesting reduces ments of environmental policy can be divided into two the stock of fish and thus increases costs. Because the broad categories. 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746 Managing the Biosphere

tional policy instruments, because they allow Economic Incentives or Market-Based Instruments economic agents greater flexibility in their pollu- tion or harvesting control strategies and also have Environmental taxes (‘‘’’ or ‘‘green the potential to reduce transaction and compli- taxes’’). These are taxes imposed on emissions, ance costs. VAs can be classified into three basic harvesting, and polluting inputs or outputs. In categories, based mainly on the degree of public particular environmental taxes include: intervention: – Emissions taxes (tax payments related to mea- – Negotiated agreements imply a bargaining sured or estimated emissions). process between the regulatory body and an – Landing fees (tax related to the amount of economic agent to jointly set the environmental harvested resource from an ecosystem). goal and the means of achieving it. – Product charges (consumption taxes, input – Unilateral agreements are environmental im- taxes, or production taxes, which are substi- provement programs prepared and voluntarily tutes for emission taxes when emissions are not adopted by economic agents themselves. directly measurable or estimable). – Public voluntary agreements are environmental – Tax differentiation (variation of existing indi- programs developed by a regulatory body, and rect taxes in favor of clean products or activities economic agents can only agree to adopt them that are environmentally and ecologically or not. friendly). – User charges (payments related to environ- In general, participation in a VA program exempts mental delivered). the economic agent from stricter regulation. – Tax reliefs (tax provisions to encourage envi- ronmentally or ecologically friendly behavior). Direct Regulation or Command and Control Subsidies for reduction of harvesting or emissions. These include subsidies for -set-aside pro- This type of regulation includes the use of limits on grams, or buffer zone programs in agriculture, inputs, outputs, or technology at the firm level. When which aim at reducing overproduction, protect the objective of direct regulation is the firm’s harvesting and expand ecosystems (e.g., wetlands), or reduce (e.g., harvesting rates, harvesting periods, ‘‘no-take’’ agricultural runoff, as well as subsidies for intro- reserve areas) or emissions, then the type of regulation ducing or resource- is called a performance standard. When the regulator . requires the use of a specific technology, then the reg- Tradable quotas or tradable emission permits. ulation is called a design standard. Performance stan- Under these systems resource users or emitters dards can be associated with a maximum allowed operate under an aggregate limit on resource use amount of emissions or harvesting, whereas design or emissions and trading is allowed on permits or standards can be associated with the use of best avail- quotas adding up to a specific limit. For example, able technologies. a cap-and-trade system in fisheries management The above classification is by no means exhaustive, includes a total allowable commercial catch limit and it should be noted that instruments can be used in and assigns individual transferable quotas (ITQ). combinations and that they can be characterized by ITQs are rights to harvest fish from a particular spatial and temporal variation. area and are distributed to each commercial fish- Optimal environmental policy can be designed by ing permit holder based on some rule (e.g., hold- using the following approach: er’s historic catch levels). This instrument essen- tially creates a market for the environmental Obtain the socially optimal solution as the solu- good, which was missing because of absence of tion of the social planner’s problem that inter- well-defined property rights. Similar markets can nalizes all externalities. The paths for the control be created for biodiversity preservation by as- and the state variable are determined. signing rights for . Obtain the privately optimal solution as the so- Voluntary agreements (VAs). Voluntary ap- lution of a representative profit-maximizing agent proaches to environmental regulation have more or as market equilibrium without internalization recently been regarded as alternative instruments of externalities. The paths for the control and the of environmental policy. They are expected to state variables are determined, and the deviations increase economic and environmental effective- from the corresponding socially optimal paths are ness as well as social welfare, relative to tradi- established. Copyrighted Material

Ecological Economics 747

Introduce an instrument or a menu of economic max Bi(ei) tei policy instruments and derive the regulated pri- ei 0 vately optimal solution as a function of the policy with necessary and sufficient first-order conditions: instruments. Choose the policy instruments so that the pri- B0(e0) t 0, with equality if e0 > 0: (12) vately optimal solution converges to the socially i i i P optimal solution. 0 Because t ¼ D i ei* , it can be seen by compar- ing equation 11 to equation 12 that the emission tax The following example from the literature of de- leads to the socially optimal emissions for firm i, for termining optimal emission taxation can help clarify all i. this approach. We choose the emission problem instead In many cases the design and/or the implementa- of an ecosystem management problem because the tion of optimal policy might not be possible because of latter requires the use of more complicated optimal informational constraints, cost of implementation, control techniques. and so on. In this case, another approach is for the We start by considering a market of i ¼1, ..., n regulator to set a given standard, such as ambient firms that behave competitively. The firms produce a pollution standards, maximum harvesting rates, mini- homogeneous output qi and, during production, gen- mum safety margins for species populations, and then erate emissions ei. A derived profit or derived benefit choose the instrument or the menu of instruments function can be defined as: from those described above to achieve the standard at a minimum cost. The policy instruments can be revised Bi(ei) ¼ max pi ¼ max [pqi ci(qi, ei)], qi 0 qi 0 or updated as the state of the ecosystem changes or as more information is acquired about the responses of B00(e ) < 0, (9) i i the economic agents and the ecosystem to economic policy. This type of policy is not optimal, but if it is where p is the exogenously determined output price, combined with the general insights obtained by hav- and c (q , e ) is a convex cost function decreasing in e .A i i i i ing determined the structure of the optimal policy, it reduction in emissions will increase costs because this might be a useful approach to policy design and im- involves the use of resources for pollution abatement. plementation. Social welfare is defined as total benefits from pro- duction less social damages from emissions. Using the derived profit function (equation 9) and a social dam- FURTHER READING age function D(E) which is an increasing and convex function reflecting environmental damages caused by Baumol, W. J., and W. E. Oates. 1988. The Theory of En- vironmental Policy, 2nd ed. Cambridge, UK: Cambridge emissions, the social planner solves the problem: University Press. Xn Xn Clark, C. 1990. Mathematical : The Optimal Management of Renewable Resources, 2nd ed. New York: max Bi(ei) D(E), E ¼ ei: (10) (e , ... , e ) 0 Wiley. 1 n i ¼ 1 i ¼ 1 Dasgupta, P. S., and G. M. Heal. 1979. Economic Theory and The necessary and sufficient first-order conditions for Exhaustible Resources. Oxford: James Nisbet and Co. and the socially optimal emissions e * generated by the ith Cambridge University Press. i Mas-Colell, A., M. D. Whinston, and G. R. Green. 1995. firm are: Microeconomic Theory. New York: Oxford University 0 0 Press. Bi(ei*) D (E*) 0, with equality if ei* > 0: (11) Millennium Ecosystem Assessment. 2005. Ecosystems and Human Well-Being: Synthesis. Washington, DC: Island Thus, when positive emissions are generated, mar- Press. ginal benefits equal marginal social damages. The pol- Murray, J. D. 2003. Mathematical . Berlin: Springer- luting firms fully internalize external social damages if Verlag. they are confronted with an emission tax per unit of Okubo, A., and S. Levin, eds. 2001. Diffusion and Ecological released in the ambient environment equal to Problems: Modern Perspectives, 2nd ed. Berlin: Springer. marginal social damages. This price incentive for emis- Tilman, D. 1982. Resource Competition and sion control is the well-known ‘‘Pigouvian tax’’ or Structure. Princeton, NJ: Princeton University Press. emission tax. Xepapadeas, A. 1997. Advanced Principles in Environmental Policy. Aldershot: Edward Elgar. LetP the emission tax t be defined as 0 n t ¼ D i ¼ 1 ei* . The firm solves the problem