1. Spatial Dimensions of Environmental Regulations What happens to simple regulations when space matters? Hotspots? Locational differences?

2. 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/2002Gr oup_Projects/Newport/newport_final.pdf http://www.bren.ucsb.edu/research/2002Gr oup_Projects/Newport/newport_final.pdf

3. 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?

4. Carpinteria Salt Marsh

5. Salt Marsh

6. The Carpinteria Marsh problem Marsh o Where we care about pollution: receptor (o) Where pollution originates: sources (x) x x x x x x x x

7. 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: e 1, e 2, …, e I (for I sources) Pollution concentrations: p 1, p 2,…,p J Connection: p j =f j (e 1,e 2,…,e I ) “Transfer function”—from Arturo

8. “Transfer coefficients” Typically f is linear (makes life simple) p j =  a ij e i + B j Where B is the background level of pollution a ij is “transfer coefficient” df j /de i = a ij = transfer coefficient (if linear) Interpretation of a ij : if emissions increase in a greenhouse on Franklin Creek, how much does concentration change in salt marsh? What causes the a ij to vary? Distance, natural attenuation and dispersion Higher transfer coefficient = higher impact of source on receptor

9. Example: concrete-lined channel Does this increase or decrease transfer coefficient?

10. Add some economics: Simple case of one receptor Emission control costs depend on abatement: A i = E i – e i where E i = uncontrolled emissions level (given) e i = controlled level of emissions (a variable) E.g. c i (A i ) =  i +  i (A i ) +  i (A i ) 2 Control costs (by industry) often available from EPA, other sources (e.g. Midterm) What is marginal cost of abatement? MC i (A i ) = β i +2  i A i

11. How much abatement? To achieve ambient standard, S, which sources should abate and how much? Problem of finding least cost way of achieving S Min e  i c i (E i -e i ) s.t.  i a i e i ≤ S In words: minimize abatement cost such that total pollution at Carpinteria Salt Marsh ≤ S.

12. Solution (mathematical) Set up Lagrangian L = Σ i c i (E i -e i ) + µ (  a i e i - S) Differentiate with respect to e i, µ ∂L/∂e i = -MC i (E i -e i ) + µ a i = 0 for all i  equalize MC i /a i = µ for all i Solution: find e i such that Marginal abatement cost normalized by transfer coefficient is equal for all sources (interpretation?) Resulting pollution level is just equal to standard

13. 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. MC i / a i equal for all sources. Sources with big “a”’s controlled more tightly

14. Effect of higher “a” Abatement MC A MC B MC A (a high) MC A (a low)

15. 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

16. Spatial Version of Marketable Permits Issue 10 permits to degrade Salt Marsh Allowed emissions for source i, holding x permits: e i =x i /a i. What is total pollution at receptor?  a i e i =  a i (x i /a i ) =  x i = 10 Does the equimarginal principle hold? Price of permit = π (cost for i: π x i ) Price per unit emissions = π x i / e i = π x i /(x i /a i ) = π a i For each source, marginal cost divided by a i = π Therefore, Equimarginal Principle Holds Idea: Trade or value damages not emissions.

17. Constructing a Policy Analysis Model Carpinteria Salt Marsh Example Variables of interest i=1,…,I sources e i, emissions by source i A i, pollution abatement by source i Data needed C i (A i ), pollution control cost function for source i E i, uncontrolled emissions by source i a i, transfer coefficient for source i S, upper limit on pollution at single receptor

18. Model Construction Goal is to minimize cost of meeting pollution concentration objective Objective function (minimize): Σ i c i (A i ) = Σ i [  i +  i (A i ) +  i (A i ) 2 ] or Σ i c i (E i -e i ) = Σ i [  i +  i (E i -e i ) +  i (E i -e i ) 2 ] Constraints  i a i e i ≤ S e i ≥ 0 (non-negativity constraint) Solve using Excel or other optimization software

19. 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 (non-spatially differentiated) emission permits

20. Policy Experiments with Model: Rollback How much would it cost to achieve S using rollback? Calculate pollution from current emissions, E i Calculate percent rollback and then emissions Compute costs of this emission level

21. 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 e i ≤ E + where E + is number of permits issued This simulates how a market for E+ emission permits would operate Calculate resulting pollution levels:  i a i e i = 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

22. What might the results look like? Total Pollution Control Costs ($) Pollution at Salt Marsh Rollback Approach Emission Permits Least Cost Uncontrolled pollution levels at Marsh 0 Note: order of costs need not be as shown.