Unknown control cost1 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:  U L (H) = π –T H - c L (e H ) = π –T H - c L (e H ) + (c H (e H ) - c H (e H )) = (π –T H - c H (e H )) + c H (e H ) - c L (e H ) = U H + c H (e H ) - c L (e H ) >0 Type L must be given the incentive  U L ≥ U L (H) = U H + c H (e H ) - c L (e H )

Unknown control cost 4 If type H chooses an L contract:  U H (L) = π –T L - c H (e L ) = π –T L - c H (e L ) + [c L (e L ) - c L (e L )] = π – T L - c L (e L ) - c H (e L ) + c L (e L ) = U L - c H (e L ) + c L (e L ) If minimum for U L is inserted we get U H (L) = U H + c H (e H ) - c L (e H ) – (c H (e L ) - c L (e L )) < U H 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, U j, 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 – c L (e L ) – D(e L ) - (1-α)(c H (e H ) - c L (e H ) ) + (1-p)(π – c H (e H ) – D(e H ) ) (setting U H = 0 ) Differentiating:

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

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 e D’(e) -E{c’(e)} e* t* -c H ’ -c L ’ e H (t*) eHeH eLeL e L (t*) Social loss if H using t* Social loss if L using t* Social loss using e* if L and if H

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

Unknown control cost 11 Pivoting the marginal cost functions e D’(e) -E{c’(e)} e* t* -c H ’ -c L ’ e H (t*) eHeH eLeL e L (t*) Social loss if H using t* Social loss if L using t* Social loss using e* if L and if H

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 e j > e*, then the firm has to pay a tax t per unit emitted, if e j > 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 D’(e) -E{c’(e)} e* -c H ’ -c L ’ s t eHeH eLeL

Unknown control cost 16 Regulation with unobserved emission Kolstad 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 e* -c’ πfπf Regulators choice of πf (πf)’ e Corner solution for e