Hendrik Wolff
Regulation under Unknown Control Cost (Chapter 15 of Kolstad)
Structure of Lecture
1. Motivation
2. Asymmetry of Regulator versus Industry
Objective Function of Regulator
Objective Function of Firm
3. Truth telling about Marginal Control Cost Function possible?
Pigouvian Fee (Pig Fee)
Cap and Trade (C&T)
4. Comparison of C&T with Pig Fee under unknown Control Cost
Weitzman Proposition
Implications for Climate Change
5. Mechanism Design
Solution 1 with "dynamic emission fee"
Solution 2 with subsidy incentive for truth telling
Solution 3 via "Hybrid Price/Quantity Regulation
3a) via Flip a coin of Prices or Quantities
3b) via Subsidy coupled with Emission Fee
3c) via Subsidy coupled with a C&T Regulation
Motivation
Everyday newspaper stories:
EPA considers stricter pollution regulation, but industry lobbies against it, claiming regulation is
too costly.
Shut down firms
Export Jobs
Problem: Regulator does not observer firm's Control Cost Function C(e) of emissions (e)
C(e) is Confidential/proprietary information by firm!
In EE, two big questions arise from this setting.
(a) What is better C&T or Pig Fee, under unknown C(e)?
(b) Mechanism Design (Construct Policies that enhance truth telling about firms MS)
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Notation
Notation with an example of an emission fee
r = emission fee
e = quantity of emissions
C(e) = Control Cost of emission
MC = Marginal Cost of emissions
MS = -MC = Marginal Savings of emissions.
D = Damage function of e
MD = Marginal damage function of e
Objective of Firm
Objective of Firm is to Minimize Private Cost of (e):
Min {C(e) + re}
FOC
-MC(e) = r
MS(e) = r
Note this is exactly equivalent of Max {S(e) –r*e}
Objective Regulator
Objective Regulator is to minimize Social Cost of (e) = {Min C(e) + D(e)}
FOC - MC(c) = MD(e)
MS(e) = MD(e)
Note this is exactly equivalent of Max {S(e) –D(e)}
Assumption 1: Firm knows MD &MS
Assumption 2: Regulator knows MD, but does not know MS!
If MS were known, no asymmetric information problem. Optimal solution would be at
MD(e*) = MS(e*)
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Problem under Assumption 1 & 2 MS not known to regulator  (Control Cost (CC) are
unknown to regulator)
Assumption 3: 50%/50% that CC is high or CC is low (Bernoulli Distribution with probability
Prob =0.5)
Q: For a Pigouvian fee: What is social loss if firm is of type High CC?
A:
Q: What is social loss if it is a “low” CC firm?
A:
Objective of Regulator: Miminize both triangels!
Objective of Regulator is not anymore to set r where MD(e) = E[MS(e)]
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Example of non-linear damage function:
Problem: no single fee can eliminate triangles.
Is Truth telling possible, or do firms have the incentive to lie?
Question (Q): If regulator announces a C&T on pollution what do firms tell the regulator?
Answer: (A): Both firms claim to be …..
Q: If regulator announces a Pig Fee?
Answer: (A): Both firms claim to be …..
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Weitzman: Prices versus Quantities
If MS were known to regulator Pig Fee and C&T with auction leads exactly to same results.
Q: What is social loss for C&T?
A:
Q: What is social loss for Pig Fee?
A:
Proposition, see p. 313 & 9 of p. 322
Under assumption that marginal savings and marginal damages are linear and that uncertainty is
in the intercept of these linear marginal savings functions only:
With uncertainty over marginal costs of emissions, quantity regulations are preferred if marginal
damages are more steeply sloped than marginal savings from emissions. Emission fees are
preferred if marginal savings are more steeply sloped than marginal damages.
Trick: Steering Wheel approach and follow the triangles!
Application to Climate Change:
C&T is preferred if MD is kinked due to irreversebilities (i.e. in chemical composition of
atmosphere/positive self-enforcing GHG emission cycles, i.e. melting of the permafrost releases
additional methan resources):
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Question: Are we left or right of the ‘kink’?
Answer: It depends on the functional form of the Social Welfare Function:
Ralw’sian Social Welfare Function: one Pacific island gets extinct  aggregate marginal
damagesteep
Benthamtite: Industrial “North” (Europe/USA) likely not to be damaged (compared to more
vulnerable “South” (Developing Countries).
Mechanism Design
Solution 1: "dynamic emission fee":
Obvious technical solution
fee= MD(e_observed)
So if industry claimed to be low cost, but then emits e_tildeH, then fee adjusts from fee_0 to
fee_1.
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Problem with Solution 1: Uncertainty over planning!
1. Government: no good planning possible if government budget changes constantly due to
altering revenues from pollution fees.
2. Firm: no good planning possible if firm cost rt*et changes at every period t
Remark 1: Temporal Uncertainty of Industry often cited as most single factor why firms do not
commit to invest in industry.
Remark 2: Changing the fee is very involved legally.
Solution 2 Design a subsidy incentive for truth telling
Here: example for quantity restriction:
We know CH does not lie! Hence subsidy reward for high type RH=0
How much should we subsidize low cost firm, such that it tells the truth?
(from P. 307)
The first attribute of the regulation is that if a firm is high cost, it should be cheaper for the firm
to tell the truth than to claim to be low cost!
CH(eH)<CH(eL)-RL
and similarly for a low cost firm,
CL(eL)-RL<CL(eH)
Putting these together we obtain
CL(eL)-CL(eH) < RL < CH(eL) - CH(eH)
In Words:
CL(eL)-CL(eH) =Gains of lying for CL
CH(eL) - CH(eH) = Gains of truth telling for CH
These Gains can be displayed in our familiar Figure, displaying the MS functions:
Figure:
Finding optimal reward (RL) for truth telling
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Hence, optimal Reward RL should be >
,but smaller than
Solution 3 via "Hybrid Price/Quantity Regulation
3a) via Flip a coin:
Step 1: ask firm about MS
Step 2: Flip coin whether to impose C&T or Pig Fee for truth telling
Good approach (not perfect, depending on shape of MS &MD)
Below Case 1 & Case 2 demonstrate that it depends on shape of MS and MD, but overall, it
leads to higher probability of truth telling compared to announced Pig fee or C&T.
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Case 1:
If industry is CL, gains from lying is
minus
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Case 2: If industry is CH, but lies:
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3b via Subsidy coupled with Fee Regulation
Assumption 4: Regulator knows distribution of MS, (but not outcome location of MS)
If Bernoulli: hybrid leads to Zero DWL!!! (Subject to disclaimer of Ch. 12 why subsidies are
inefficient!)
Of course, for more complicated distributions: regulators objective is again to minimize the
triangles.
Excursion: One sided regulation: C&T with Emission Fee: Example carbon safety valve, p. 317.
Firms like carbon valve emission fee as it guarantees that the pollution certificate price is upper
bounded!
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3c via Subsidy coupled with C&T Regulation
Important feature: In order to receive subsidy, firm MUST hold the permit.
Again, we assume the Bernoulli distribution over MS.
Does it lead to truth telling?
Figure: p. 319
Suppose the polluters lied when telling the regulator their costs.
Case 1: Firms understated MS (while the true is MS_high). With only L* permits available,
competition drives Market Price of pollution certificate to PH, the value of MSH(L*). Because the
subsidy is lower than PH: none of the firms will choose to receive a subsidy.
Implications:
1. If firms had told the truth, the subsidy rate would be higher (SH**).
2. The number of permits would be larger.
3. The Market Price of pollution certificates would be lower.
Case 2: Firms overstated MS (while the true MS is MS_low.
Implications
1. The market price initially drops to PL but yields S* as firms can reduce emissions. As long as
S* > PL there will be access demand for permits (remember firm MUST hold permit in order to
receive subsidy).
2. Hence permit price increases via S*.
If firms had told the truth, the subsidy rate would be at SL**, which would result in a lower
permit price than S*.
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Thus by lying, the polluters have increased the price of permits in the market. This is
undesirable. Hence subsidy and C&T regulation enhances truth telling.
Summary of Chapter 15:
1. Regulation problems involving asymmetric information typically are associated with the
regulator having less information than the polluter.
2. When Regulators must make a decision under uncertainty of the MS, the relative slopes of the
MS and MD determine whether C&T or Pig Fee is more desirable. Remember the Weitzman
principle!!
3. C&T with subsidy for polluting less than the cap and a fee if polluting more than the cap can
perform better than either an emission fee alone or a C&T alone, when MS is uncertain to the
regulator.
4a. Announcing an emission fee will cause the polluter to understate MS.
4b. A C&T will cause polluters to overstate MS.
4c. A C&T coupled with Subsidy will induce telling the truth about the firms MS.
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