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?MotivationGroup Project on Newport Bay TMDLWhat 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 problemMany 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 ReceptorsSources 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,…,pJConnection: pj=fj(e1,e2,…,eI)“Transfer function”—from Arturo“Transfer coefficients”Typically f is linear (makes life simple)pj = aijei + BjWhere B is the background level of pollutionaij 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 dispersionHigher transfer coefficient = higher impact of source on receptorExample: concrete-lined channelDoes this increase or decrease transfer coefficient?Add some economics:Simple case of one receptorEmission control costs depend on abatement:Ai = Ei – ei whereEi = 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 ≤ SIn words: minimize abatement cost such that total pollution at Carpinteria Salt Marsh ≤ S.Solution (mathematical)Set up LagrangianL = 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 iSolution: find ei such thatMarginal abatement cost normalized by transfer coefficient is equal for all sources (interpretation?)Resulting pollution level is just equal to standardSpatial equi-marginal principleInstead 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?RollbackStandard engineering solution.Desired pollution level x% of current level reduce all sources by x%Marketable permits – no spatial differentiationPolluters with big transfer coefficients would not control enoughPolluters with small transfer coefficients would control too much.Constant fee to all pollutersSame problem as permitsSpatial Version of Marketable PermitsIssue 10 permits to degrade Salt MarshAllowed emissions for source i, holding x permits: ei=xi/ai.What is total pollution at receptor? aiei = ai(xi/ai) = xi = 10Does 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 aiFor each source, marginal cost divided by ai = πTherefore, Equimarginal Principle HoldsIdea: Trade or value damages not emissions.Constructing a Policy Analysis ModelCarpinteria Salt Marsh ExampleVariables of interesti=1,…,I sourcesei, emissions by source iAi, pollution abatement by source iData neededCi(Ai), pollution control cost function for source iEi, uncontrolled emissions by source iai, transfer coefficient for source iS, upper limit on pollution at single receptorModel ConstructionGoal is to minimize cost of meeting pollution concentration objectiveObjective function (minimize): Σi ci(Ai) = Σi [i + i(Ai) + i(Ai)2] orΣi ci(Ei-ei) = Σi [i + i(Ei-ei) + i(Ei-ei)2]Constraintsi aiei ≤ Sei ≥ 0 (non-negativity constraint)Solve using Excel or other optimization softwarePolicy Experiments with ModelWhat is the least cost way of meeting S?Always start with this baselineCan be achieved through spatially differentiated permitsConsider a variety of different policiesRollbackSimple (non-spatially differentiated) emission permitsPolicy Experiments with Model: RollbackHow much would it cost to achieve S using rollback?Calculate pollution from current emissions, EiCalculate percent rollback and then emissionsCompute costs of this emission levelPolicy Experiments with ModelEmission permitsWhy?Simpler than spatially differentiated emission permitsHow much would it cost to use emission permits (non-spatially differentiated)?Eliminate constraint on pollution
View Full Document