ECON 4910 Spring 2007 Environmental Economics Lecture 11, Chapter 10 Kolstad

1. ECON 4910 Spring 2007 Environmental Economics Lecture 11, Chapter 10 Kolstad Lecturer: Finn R. Førsund Unknown control cost

2. Designing contracts when purification cost is unknown to the regulator • Two types, high-cost, H, and low-cost, L • Emissions measurable ex post • Contracts state permitted emission and a tax • The objectives of the contracts • Ensure participation of the firm, i.e. the gross profit must be non-negative • Give incentive to tell the truth about the cost type, i.e. tax according to type must induce truth-telling Unknown control cost

3. Designing incentives • The problem is that type L has an incentive to choose an H contract if L is not given pure profit telling the truth. If L chooses an H contract: • UL(H) = π –TH - cL(eH) = π –TH - cL(eH) + (cH(eH) - cH(eH)) = (π –TH - cH(eH)) + cH(eH) - cL(eH) = UH + cH(eH) - cL(eH) >0 • Type L must be given the incentive • UL≥ UL(H) = UH + cH(eH) - cL(eH) Unknown control cost

4. If type H chooses an L contract: • UH(L) = π –TL - cH(eL) = π –TL - cH(eL) + [cL(eL) - cL(eL)] = π – TL - cL(eL) - cH(eL) + cL(eL) = UL- cH(eL) + cL(eL) If minimum for UL is inserted we get UH(L) = UH + cH(eH) - cL(eH) – (cH(eL) - cL(eL)) < UH • Since type H will always choose an H contract the tax can be designed so that pure profit is zero. Type H has an incentive to tell the truth anyway. Unknown control cost

5. The regulator’s objective function • The objective function must reflect a conflict between the two parties: • The general consumer experiencing the environmental damage D(e) • The firm enjoying pure profit, Uj, j=L,H • The benefit of taxes must also be included, i.e. assuming that tax benefit the consumer • W = T- D(e) + αU= π - c(e) – U - D(e) + αU = π - c(e) - D(e) - (1- α)U , 0 ≤ α<1 • The regulator must evaluate pure profit less than environmental damage Unknown control cost

6. Determining emission- and tax quantities of the contracts • Maximising the expected value of the objective function • E{W} = p(π – cL(eL) – D(eL) - (1-α)(cH(eH) - cL(eH) ) + (1-p)(π – cH(eH) – D(eH) ) (setting UH = 0 ) Differentiating: Unknown control cost

7. Illustration of giving an incentive to the high-cost firm to tell the truth -c’,D’ D’(e) -cH’ D’ >-cH’ Efficiency loss -cL’ -cH’ Savings in pure profit -cL’=D’ Pure profit L e eL* eH* eH Unknown control cost

8. Emission tax or quantity regulation • Direct regulation more in use than economic incentives, why? • Simplifying: • Single firm that can be high-cost, H, or low-cost, L • Emissions not measured ex post • Finding tax t* and quantity regulation e* by equating (-)expected marginal cost to marginal damage Unknown control cost

9. Illustration Social loss using e* if L and if H -E{c’(e)} D’(e) Social loss if H using t* t* -cH’ Social loss if L using t* -cL’ e eL e* eH eL(t*) eH(t*) Unknown control cost

10. Pivoting the marginal damage function Social loss using e* if L and if H -E{c’(e)} D’(e) Social loss if H using t* t* -cH’ Social loss if L using t* -cL’ e eL e* eL(t*) eH eH(t*) Unknown control cost

11. Pivoting the marginal cost functions Social loss using e* if L and if H -E{c’(e)} D’(e) Social loss if H using t* t* -cH’ Social loss if L using t* -cL’ e eL e* eH eL(t*) eH(t*) Unknown control cost

12. Weitzman rule • With uncertain purification costs • Use emission tax if marginal purification cost curve (absolute value) is relatively steeper than the marginal damage curve • Use direct regulation if marginal damage curve is relatively steeper than marginal cost curves (absolute value) Unknown control cost

13. Hybrid price/quantity regulation • Type of purification cost function for a single firm unknown, but the regulator knows the two types and can form expectations • Regulators quantity benchmark • The contract stipulates that if ej> e*, then the firm has to pay a tax t per unit emitted, if ej > e*, then the firm gets a subsidy s per unit emitted Unknown control cost

14. Hybrid price/quantity regulation, cont. • Calculation of tax/subsidy scheme • Tax • Subsidy Unknown control cost

15. Illustration of hybrid contract -E{c’(e)} D’(e) t -cH’ s -cL’ e eL e* eH Unknown control cost

16. Regulation with unobserved emissionKolstad Chapter 11 • Regulator cannot (or too expensive) observe firm emissions, but can observe total amount of pollutants deposited in the environmental receptor • Regulator knows the purification cost functions of each firm and the unit transport coefficients (may be 1), and the damage function • Then the regulator can work out the optimal deposition Unknown control cost

17. Regulation with unobserved emission, cont. • Optimal total deposition Unknown control cost

18. The tax scheme • The tax/subsidy on (unobserved) firm emission is equal for all firms and proportional to total exceedence in the environmental receptor • Firm adaptation Unknown control cost

19. Calibration of the common tax rate • From the social solution • From the private solution • The optimal tax rate Unknown control cost

20. Auditing an emission standard • The total cost of the firm concerning emissions • π probability of an audit • f fine per unit of emission above the regulation • D lump-sum fine Unknown control cost

21. The firm’s decision problem • Assuming that violating the standard is considered Unknown control cost

22. Illustration auditing an emission standard Corner solution for e -c’ Regulators choice of πf (πf)’ πf e e* Unknown control cost