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UCSB ESM 204 - SPATIAL DIMENSIONS

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Spatial Dimensions of Environmental RegulationsMotivationExample: Carpinteria marsh problemCarpinteria Salt MarshSlide 5The Carpinteria Marsh problemSources and Receptors“Transfer coefficients”Example: concrete-lined channel Does this increase or decrease transfer coefficient?Add some economics: Simple case of one receptorHow much abatement?Solution (mathematical)Spatial equi-marginal principleEffect of higher “a”What kind of regulations would achieve desired level of pollution?Spatial Version of Marketable PermitsConstructing a Policy Analysis Model Carpinteria Salt Marsh ExampleModel ConstructionPolicy Experiments with ModelPolicy Experiments with Model: RollbackPolicy Experiments with Model Emission permitsWhat might the results look like?Spatial Dimensions of Environmental RegulationsWhat happens to simple regulations when space matters? Hotspots?Locational differences?MotivationGroup Project on Newport Bay TMDLWhat rules on maximum emissions from different industries will assure acceptable level of water quality in Newport Bay?Reference: http://www.bren.ucsb.edu/research/2002Group_Projects/Newport/newport_final.pdfExample: Carpinteria marsh problemMany creeks flow into Carpinteria salt marsh; pollution sources throughout.Pollution mostly in form of excess nutrients (e.g. Nitrogen & Phosphorous)How should pollution be controlled at each upstream source to achieve an ambient standard downstream?Carpinteria Salt MarshSalt MarshThe Carpinteria Marsh problemMarshoWhere we care about pollution: receptor (o)Where pollution originates: sources (x)xxxxxxxxSources and ReceptorsSources are where the pollutants are generated – index by i. [“emissions”]Receptors are where the pollution ends up and where we care about pollution levels – index by j. [“pollution”]Emissions: e1, e2, …, eI (for I sources)Pollution concentrations: p1, p2,…,pJConnection: pj=fj(e1,e2,…,eI)“Transfer function”—from Arturo“Transfer coefficients”Typically f is linear (makes life simple)pj =  aijei + BjWhere B is the background level of pollutionaij is “transfer coefficient”dfj/dei = aij = transfer coefficient (if linear)Interpretation of aij: if emissions increase in a greenhouse on Franklin Creek, how much does concentration change in salt marsh?What causes the aij to vary?Distance, natural attenuation and dispersionHigher transfer coefficient = higher impact of source on receptorExample: concrete-lined channelDoes this increase or decrease transfer coefficient?Add some economics:Simple case of one receptorEmission control costs depend on abatement:Ai = Ei – ei whereEi = uncontrolled emissions level (given)ei = controlled level of emissions (a variable)E.g. ci(Ai) = i + i(Ai) + i(Ai)2 Control costs (by industry) often available from EPA, other sources (e.g. Midterm)What is marginal cost of abatement?MCi(Ai) = βi +2 i AiHow much abatement?To achieve ambient standard, S, which sources should abate and how much?Problem of finding least cost way of achieving SMine i ci(Ei-ei) s.t. i aiei ≤ SIn words: minimize abatement cost such that total pollution at Carpinteria Salt Marsh ≤ S.Solution (mathematical)Set up LagrangianL = Σi ci(Ei-ei) + µ ( aiei - S)Differentiate with respect to ei, µ∂L/∂ei = -MCi(Ei-ei) + µ ai = 0 for all i equalize MCi/ai = µ for all iSolution: find ei such thatMarginal abatement cost normalized by transfer coefficient is equal for all sources (interpretation?)Resulting pollution level is just equal to standardSpatial equi-marginal principleInstead of equating marginal costs of all polluters, need to adjust for different contributions to the receptor.All sources are controlled so that marginal cost of emissions control, adjusted for impact on the ambient, is equalized across all sources.MCi / ai equal for all sources.Sources with big “a”’s controlled more tightlyEffect of higher “a”AbatementMCAMCBMCA(a high)MCA(a low)What kind of regulations would achieve desired level of pollution?RollbackStandard engineering solution.Desired pollution level x% of current level  reduce all sources by x%Marketable permits – no spatial differentiationPolluters with big transfer coefficients would not control enoughPolluters with small transfer coefficients would control too much.Constant fee to all pollutersSame problem as permitsSpatial Version of Marketable PermitsIssue 10 permits to degrade Salt MarshAllowed emissions for source i, holding x permits: ei=xi/ai.What is total pollution at receptor? aiei =  ai(xi/ai) =  xi = 10Does the equimarginal principle hold?Price of permit = π (cost for i: π xi)Price per unit emissions = π xi/ ei= π xi /(xi/ai) = π aiFor each source, marginal cost divided by ai = πTherefore, Equimarginal Principle HoldsIdea: Trade or value damages not emissions.Constructing a Policy Analysis ModelCarpinteria Salt Marsh ExampleVariables of interesti=1,…,I sourcesei, emissions by source iAi, pollution abatement by source iData neededCi(Ai), pollution control cost function for source iEi, uncontrolled emissions by source iai, transfer coefficient for source iS, upper limit on pollution at single receptorModel ConstructionGoal is to minimize cost of meeting pollution concentration objectiveObjective function (minimize): Σi ci(Ai) = Σi [i + i(Ai) + i(Ai)2] orΣi ci(Ei-ei) = Σi [i + i(Ei-ei) + i(Ei-ei)2]Constraintsi aiei ≤ Sei ≥ 0 (non-negativity constraint)Solve using Excel or other optimization softwarePolicy Experiments with ModelWhat is the least cost way of meeting S?Always start with this baselineCan be achieved through spatially differentiated permitsConsider a variety of different policiesRollbackSimple (non-spatially differentiated) emission permitsPolicy Experiments with Model: RollbackHow much would it cost to achieve S using rollback?Calculate pollution from current emissions, EiCalculate percent rollback and then emissionsCompute costs of this emission levelPolicy Experiments with ModelEmission permitsWhy?Simpler than spatially differentiated emission permitsHow much would it cost to use emission permits (non-spatially differentiated)?Eliminate constraint on pollution


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