NATURAL RESOURCE EXTRACTION WITH REVERSIBLE STOCK POLLUTION

Transcription

1 NATURAL RESOURCE EXTRACTION WITH REVERSIBLE STOCK POLLUTION Speaker: Peifang Yang China University of Petroleum (Beijing) Co-author: Graham A. Davis Colorado School of Mines 5 th IAEE Asian Conference Feb 15,

2 2 Outline 1. Motivation 2. Contribution 3. Methodology 4. Results 5. Numerical simulation 6. Conclusions

3 3 1. Motivation On the mainland of China, 19.4% of the farmland, about 57.5 million acres, has been polluted by heavy metals. Annually, over 12 million tons of grains contaminated by heavy metals are produced.

4 4 1. Motivation The strategy, pollute first, clean up later, which means polluting and suffering damages during a period of economic development and then remediating the polluted land in the future when there is plenty of wealth, is often believed to be an optimal strategy for developing countries. Do we pollute too much now? Do we clean up too late?

5 5 1. Motivation To answer these questions we have to consider not only the strategy to control the pollution flow, but also when and how to eliminate the remaining pollution stock in the future. The pollution stock can be reduced by human capital investment: heavy metal pollution in soil For reversible stock pollution, how should efforts be allocated between control of the pollution flow versus cleanup of the pollution stock, and how does this affect extraction decisions?

6 6 2. Contribution Keeler et al. (1971) find the optimal control of pollution based on the assumption that pollution stock decays at a constant exponential rate. Forster (1975) introduces a non-constant exponential decay rate and an irreversible stock level. Farzin (1996) assumes once the pollution stock is created, there is no way to clean up. Cheve (2000) also adopts the feature that pollution stock can reduce the natural decay rate to zero. What s missing in the literature? The pollution stock can be reversed through the application of capital

7 7 2. Contribution In many real situations, the application of capital dominates the natural decay process in terms of remediating stock pollutants. The recovery of polluted land and water Carbon capture and sequestration

8 8 2. Contribution First natural resource extraction model that includes capital investment as the only method for stock pollution remediation. Key findings: The current regulation that only requires the mining firm to reclaim the disturbed land after an operation shuts down fails when interest rates are positive. A policy that requires the firm to pay both the ongoing pollution damage and the land recovery cost can work well in reasonable circumstances.

9 9 3 Methodology Two industries Mining Agriculture Two control variables Mining extraction q(t) Pollution area a(t) Two policy regimes The current regulation that internalizes the recovery cost only Regulations that require mining firms to recover the disturbed land only after an operation shuts down. Policy that internalizes both the ongoing damage and the recovery cost

10 10 3 Methodology Under the current regulation, the mining firm will: Maximize q(t),a(t) T C subject to R = q(t) A = a(t) 0 [ pq c 1 (q) c 2 (q, a)] e rt dt c 3 A(T C )e rt ' R(0) = R 0 and A(0) = 0 given, where T ' T C Proposition 1. If the mining firm is only required to clean up after an operation shuts down, the firm will put off the reclamation as long as possible to let the recovery cost be discounted away. Proof. The firm will minimize c 3 A(T C )e rt ' Clearly, as T è, the cleanup cost is minimized to be zero.

11 11 3 Methodology A real world example: <A Fight in Colorado Over Uranium Mines> By DAN FROSCH APRIL 16, 2013 Despite bursts of activity from 2003 through 2008, most uranium mines scattered across Colorado have largely been out of production for decades, a testament to fluctuating mineral prices....the mines had since switched to intermittent status, allowing them to stay open with minimal activity We feel these mines are doing everything they can not to reclaim, Since the mines are staying open while doing essentially nothing, the law that requires cleanup after closing fails.

12 12 3 Methodology Since the recovery cost can be discounted away, the firm will have no incentive to invest in any pollution control during operations. Thus, the pollution control cost c 2 = 0. Then the firm s problem will be to: Maximize q(t),a(t) T C [ pq c 1 (q)] e rt dt c 3 A(T C )e rt ' The current value Hamiltonian equation is: 0 H = pq c 1 (q) λ 1 ( q(t)) The firm will extract the reserve as if there were no environmental regulations until the mine is depleted.

13 13 3 Methodology If the mining firm is required to pay a pollution damage D during each period of stock pollution, then: Maximize q(t),a(t) T C subject to R = q(t) where T ' T C A = a(t) [ pq c 1 (q) c 2 (q, a) D(A(t))] e rt dt DA(T C )e rs ds c 3 A(T C )e rt ' 0 R(0) = R 0 and A(0) = 0 given, T ' T C

14 14 3 Methodology The firm begins the reclamation at time T and will minimize the total damage plus the recovery cost: or Minimize T ' T C DA(T C )e rt dt + c 3 A(T c )e rt ' Minimize C = D r (e rt C e rt ' )+ c 3 e rt ' Proposition 2. The firm will begin the reclamation immediately after the mine is depleted when the damage D > rc 3 and will defer cleanup indefinitely when D < rc 3.

15 15 4. Results Policy of internalizing the recovery cost only Strategy on reclamation Put off the reclamation as long as possible to let the recovery cost be discounted away Strategy on pollution flow control No investment if planning to put off the reclamation Apply an increasing marginal cost over time (results in a decreasing pollution path) if obeying the current regulation Policy of internalizing the damage only Strategy on pollution flow control Pollution control cost vs. Accumulating damage Apply a declining cost over time Pollute more at the end period of extraction

16 16 4. Results Policy of internalizing both the damage and recovery cost Strategy on reclamation Damage vs. Recovery cost Clean up immediately if D > rc 3 Defer cleanup indefinitely when D < rc 3 Strategy on pollution flow control Pollution control cost vs. Accumulating damage and recovery cost Apply a declining cost over time (increasing pollution path), if D > rc 3 /(1-r) Apply an increasing cost over time(declining pollution path), if D < rc 3 /(1-r) When firms signal shirking? A sharply increasing pollution path (setting the recovery cost c 3 =0)

17 5. Numerical Simulation 17

18 5. Numerical Simulation 18

19 19 6. Conclusions The stock pollution is reversible with capital investment. The typical regulation that requires the mining firm to recover the disturbed land only after an operation shuts down fails because of the crucial role of the discounting given positive interest rates. A policy that requires the firm to pay both the ongoing pollution damage and the recovery cost is optimal. Apply to other reversible stock pollution situations The CO 2 stock in the atmosphere can at any time be reduced by capital investment

20 Thank you! 20