Spatial Dimensions of Environmental Regulations What 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 2002Gro up Projects Newport newport final pdf Example 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 Marsh Salt Marsh The Carpinteria Marsh problem x x x x x x x Where we care about pollution receptor o Where pollution originates sources x x Marsh o Sources 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 aijei Bj Where B is the background level of pollution p j 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 receptor Example concrete lined channel Does 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 i 2 i Ai How much abatement To achieve ambient standard S which sources should abate and how much Problem of finding least cost way of achieving S Mine 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 i ci Ei ei aiei S Differentiate with respect to ei L ei MCi Ei ei ai 0 for all i equalize MCi ai 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 standard Spatial 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 tightly Effect of higher a MCA a low MCA MCA a high Abatement MCB 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 permits Spatial 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 cost for i xi Price per unit emissions xi ei xi xi ai ai For each source marginal cost divided by ai Therefore Equimarginal Principle Holds Idea Trade or value damages not emissions Constructing a Policy Analysis Model Carpinteria 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 receptor Model Construction Goal is to minimize cost of meeting pollution concentration objective Objective function minimize ci Ai i i i Ai i Ai 2 or i ci Ei ei i i i Ei ei i Ei ei 2 i Constraints i aiei S ei 0 non negativity constraint Solve using Excel or other optimization software Policy 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 permits non spatially differentiated emission Policy Experiments with Model Rollback How much would it cost to achieve S using rollback Calculate Calculate pollution from current emissions E i percent rollback and then emissions Compute costs of this emission level Policy Experiments with Model Emission permits Why Simpler than spatially differentiated emission permits How much would it cost to use emission permits non spatially differentiated Eliminate constraint on pollution and substitute i ei E where E is number of permits issued This simulates how a market for E emission permits would operate Calculate resulting pollution levels i aiei S How do you think the cost of achieving S with emission permits will compare to the least cost way of achieving S Vary E until S exactly equals S Bingo You know the amount of emission permits to issue What might the results look like Rollback Approach Total Pollution Control Costs Emission Permits Least Cost Uncontrolled pollution levels at Marsh 0 Pollution at Salt Marsh Note order of costs need not be as shown