econ 4910 spring 2007 environmental economics lecture 11 chapter 10 kolstad l.
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ECON 4910 Spring 2007 Environmental Economics Lecture 11, Chapter 10 Kolstad. Lecturer : Finn R. Førsund. 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

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econ 4910 spring 2007 environmental economics lecture 11 chapter 10 kolstad

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

Lecturer: Finn R. Førsund

Unknown control cost

designing contracts when purification cost is unknown to the regulator
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

designing incentives
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

slide4
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

the regulator s objective function
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

determining emission and tax quantities of the contracts
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

illustration of giving an incentive to the high cost firm to tell the truth
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

emission tax or quantity regulation
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

illustration
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

pivoting the marginal damage function
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

pivoting the marginal cost functions
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

weitzman rule
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

hybrid price quantity regulation
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

hybrid price quantity regulation cont
Hybrid price/quantity regulation, cont.
  • Calculation of tax/subsidy scheme
    • Tax
    • Subsidy

Unknown control cost

illustration of hybrid contract
Illustration of hybrid contract

-E{c’(e)}

D’(e)

t

-cH’

s

-cL’

e

eL

e*

eH

Unknown control cost

regulation with unobserved emission kolstad chapter 11
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

regulation with unobserved emission cont
Regulation with unobserved emission, cont.
  • Optimal total deposition

Unknown control cost

the tax scheme
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

calibration of the common tax rate
Calibration of the common tax rate
  • From the social solution
  • From the private solution
  • The optimal tax rate

Unknown control cost

auditing an emission standard
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

the firm s decision problem
The firm’s decision problem
  • Assuming that violating the standard is considered

Unknown control cost

illustration auditing an emission standard
Illustration auditing an emission standard

Corner solution for e

-c’

Regulators choice of πf

(πf)’

πf

e

e*

Unknown control cost