ECON 4910 Spring 2007 Environmental Economics Lecture 8, The RAINS model Memorandum No 37/99

1. ECON 4910 Spring 2007 Environmental Economics Lecture 8,The RAINS modelMemorandum No 37/99 Lecturer: Finn R. Førsund RAINS

2. The cost function in RAINS • The emitting unit is a country, i • Purification costs for different sectors are agggregated in merit order • The emissions, eio, for a future year (2010) are based on projections of energy use and economic activities of key sectors • Costs change with projected emissions RAINS

3. Purification measures with constant average cost Marginal costs 3 2 1 Purification max r 1 RAINS

4. Merit order of purification measures Marginal costs 3 2 1 Emissions e o e min RAINS

5. The environmental block • Simplification to one pollutant, SO2 • Deposition of SO2 into a grid cell from all sources (countries) • bj = background deposition • Average Accumulated Exceedance RAINS

6. The optimisation problem • Minimise total purification costs subject to environmental targets for each grid cell and limits on emissions RAINS

7. The Lagrangian RAINS

8. First order conditions • The interpretation of the shadow price λj: • The increase in total cost if the environmental target AAE is made more ambitious, • a reduction of AAE* increases costs • an increase in AAE* decreases cost RAINS

9. First order conditions, cont. • The interpretation of the environmental term • The “value” of the marginal increase in average accumulated exceedances in all receptors affected by a unit increase in emissions from country i expressed by positive transport coefficients RAINS

10. First order conditions, cont. • Both the shadow price on the upper and on the lower constraint on emissions cannot be positive at the same time. • If the constraints are not binding both shadow prices μi,γi will be zero. This is the interior solution • Upper constraint on emission is binding: • Marginal purification costs is greater than the shadow ”value” of the environmental effect at maximal emission RAINS

11. First order conditions, cont. • Lower constraint on emission is binding: • Marginal purification cost is lower than the shadow ”value” of the environmental effect at minimal emission • Interior solution: • Marginal purification costs equal to total shadow-priced evaluation of contribution to accumulated exceedance RAINS

12. Illustration of optimal solution Marginal costs S(emin) γ c’ c’ c’* c’ μ S(eo) Emissions eo e* emin RAINS

13. Economic interpretations • Marginal purification costs differ between countries due to individual transfer coefficients • non-uniform reductions of pollutants • Shadow price for each receptor shows system marginal costs of deposition constraint • May have non-feasible solution due to fixed initial emissions and limited purification possibilities • maximal purification, reducing future projected emissions, or changing target loads RAINS

14. Ambient tradable permits • Permits issued for each receptor, sources have to acquire pollution permits for each receptor affected by source • Finding the total target load for each receptor • Total ambient pollution quota for each receptor RAINS

15. Ambient tradable permits, cont. • Pollution quotas can be grandfathered, calculation of quotas ensuring that environmental targets are reached complicated • Source problem given price tj for pollution permit (dropping emission constraints) RAINS

16. Ambient tradable permits, cont. • First-order condition for interior solution • Setting the price of pollution permits • The equilibrium price of pollutant permits in receptor j should reflect the shadow price on the receptor j specific constraint, multiplied with the marginal impact on AAEj RAINS