1. Topic 3.b: Emissions taxes
Recall the questions of interest:
When is it desirable (from the viewpoint of efficiency) to make R&D expenditures that will shift MAC curve down?
Does a given pollution control policy (in this case, an E tax) create the correct (efficient) incentive for the firm to make R&D expenditures?
Recall it is efficient to invest in R&D whenever the present value of the increase in maximized net benefits exceeds the cost of R&D.
That is, efficient if (b+e)/r > K.
We want to think about whether emissions taxes induce the firm to make R&D expenditures when it is efficient to do so.

2. Topic 3.b: Emissions taxes
Reminder: We are looking at the Q of when it is efficient to invest in R&D. $ MD
MAC1
If we invest $K in R&D NOW, we can permanently
shift annual MAC from MAC1 to MAC2.
MAC2 a t1 t2 e b E2 E1
Emax
If MAC1 it is efficient to set t = t1.
 NB = TB - TC = a
permanent annual increase in NB = b+e. 
If MAC2 it is efficient to set t = t2
 NB = TB - TC = a+b+e
It is efficient to invest in R&D if (b+e)/r > K
PV of b+e each year forever = (b+e)/r

3. Topic 3.b: Emissions taxes
When will the firm want to adopt the new technology?
Depends on the regulatory environment.
Three possibilities we will consider with respect to E taxes:
Emissions tax at t1, (efficient level given MAC1) and will remain there even if new technology is adopted.
Emissions tax at t1, but will be lowered to t2 (efficient level given MAC2) if new technology is adopted.
Emissions tax at t2 and will remain there if new technology is adopted.
These are analogous to the three situations we looked at for E standards.

4. Topic 3.b: Emissions taxes
If MAC1 and t=t1, then firm chooses E1.
Compliance cost
= (t1E1) + TAC
= (j+k+l+g+h+i+d+e+f)
+ (b+c)
If MAC2 and t=t1, then firm chooses E3.
= (t1E3) + TAC
= (j+k+l) + (c+f+g+h+i)
1. Emissions charge is fixed at t1. $ MD
MAC1
MAC2 a t1 j g d t2 e h b k f i l c E3 E2 E1
Emax
Annual compliance cost is lower by b+e+d under MAC2.
So firm will want to adopt the new technology if (b+e+d)/r > K
Recall that we want the firm to adopt the new technology if (b+e)/r > K.
 Firm faces too large an incentive to adopt.
If (b+e)/r < K < (b+e+d)/r, then firm will adopt, even though its not efficient to do so.

5. Topic 3.b: Emissions taxes
2. Emissions charge is t1 if MAC1 but drops to t2 if MAC2.
If MAC1 and t=t1, then firm chooses E1.
Compliance cost
= (t1E1) + TAC
= (j+k+l+g+h+i+d+e+f)
+ (b+c)
If MAC2 and t= t2, then firm chooses E2.
= (t2E2) + TAC
= (k+h+l+i) + (c+f) $ MD
MAC1
MAC2 a t1 j g d t2 e h b k f i l c E3 E2 E1
Emax
Annual compliance cost is lower by b+e+d+g+j under MAC2.
So firm will want to adopt the new technology if (b+e+d+g+j)/r > K
Recall that we want the firm to adopt the new technology if (b+e)/r > K.
 Firm faces too large an incentive to adopt (larger than last case).
If (b+e)/r < K < (b+e+d+g+j)/r, then firm will adopt, even though its not efficient to do so.

6. Topic 3.b: Emissions taxes
3. Emissions charge is t2 no matter which MAC. $ MD
MAC1
We will work through this case in class.
MAC2 a t1 j g d e t2 h k b f i l c E3 E2 E1 E4
Emax
Starting point: you need to recognize that if firms faces t2 under MAC1 it will choose E4.
So we’ll need to label some new areas to work through this exercise.

7. Topic 3.b: Emissions taxes
Summary: E charges don’t create the right incentive for firms to invest in abatement.
This was also true with E standards.
Difference between E standard and charges? E charges are more likely to ensure adoption of new technology than E standards.

8. Topic 3.b: Emissions taxes
A combination of emissions charges and technology standards could, however result in efficient adoption.
Combination of emissions and technology standards:
If (b+e)/r > K, regulator mandates adoption of new technology and set emissions charge at t2.
If (b+e)/r < K, regulator doesn’t require adoption of new technology and set emissions charge at t1.

9. Topic 3.b: Emissions taxes
Now we want to answer the question on whether the policy create the right incentive for firms to remain operating within an industry?
Decision rule for whether we want a firm to stay in business:
Is the firm able to generate positive NB?
If yes, then we don’t want environmental regulation to drive such firms into bankruptcy.

10. Topic 3.b: Emissions taxes
Example: Suppose that an unregulated firm generates annual profits of $35,000. MAC = (2/5)E, MD = (3/5)E.
If we regulate this firm using an E charge, then set t = $120.
If t = 120, then compliance costs
= (t  E) + TAC
= $24,000 + $18,000
= $42,000. $ MD
200
MAC
120
$24,000
Firm’s profits net of compliance costs incurred = -$7,000 < 0
 firm goes out of business.
$18,000
$12,000 E
200
500
Is this the right choice? Recall in this example we want firms to stay in business as long as profits > TAC + TD.
That is, if profits are greater than $30,000.
So here we are driving a firms out of business that we would like to remain in business.

11. Topic 3.b: Emissions taxes
The reason for this is that we make the firm pay (in compliance costs) an amount that exceeds the true costs of their actions.
Compliance costs = (t  E) + TAC
Costs (environmental-related) = TD + TAC
Because (t  E) > TD, we overcharge the firm, and as a consequence, sometimes we drive firms into bankruptcy that in fact generate positive NB.
Exactly the opposite of the case of E standards, where sometimes we didn’t drive firms into bankruptcy when we should have, from the viewpoint of economic efficiency.

12. Topic 3.b: Emissions taxes
That is, under:
An E standard we charge the firm nothing for emissions, when emissions result in costs = TD.
A linear E charge we charge the firm for emissions, but we charge them more than TD.

13. Topic 3.b: Emissions taxes
Is there a way in which we can charge the firm the “right” amount for their emissions?
What if we don’t charge same t on all units emitted?
Example: Could charge t1 < t* for E < E* and then t2 = t* for E > E*, such that total revenue raised just equals TD from E.
MAC MD
i.e., pick t1 such that revenue ( t1  E*) = (a + c) = TD from emissions (b + c)
t2= t* b t1 a
If we do this, we are only going to drive firms out of business if revenue is insufficient to cover TD. c E*
Which is OK: just means we are driving firms out of business that are unable to cover the true costs of being in business.
This type of E charge is referred to as a non-linear emissions charge.

14. Topic 3.b: Emissions taxes
Back to previous ex, where t=120 drove firm out of business.
Suppose instead we impose the following non-linear E:
If E < 200, then t = $60
If E > 200, then t = $120 $ MD
200
MAC
Firm will choose E = 200 and face compliance costs
= (t  E) + TAC
= (60  200) + $18,000
= $12,000 + $18,000
= TD + TAC
120 60
$18,000
$12,000 E
200
500
Because we have picked ts such that (t  E) = TD at firm’s choice of E, firm will now make the right choice as to whether to stay in business.

15. Topic 3.b: Emissions taxes
Linear t = 120 drives firm out of business, even though firm’s revenue was sufficient to cover abatement costs and damages from emissions at the efficient level of abatement.
Non-linear emissions charge that kept the firm in business:
t = $60/unit of E for all E < 200
t = $120/unit of E for all E > 200

16. Topic 3.b: Emissions taxes
No reason that there only had to be two possibilities for t.
Could have had three (or more) “steps” in emissions charges
For instance, the following set of emissions charges work in our example:
t = $15/unit of E for E ≤ 50
t = $45/unit of E for 50 < E ≤ 100
t = $75/unit of E for 100 < E ≤ 150
t = $105/unit of E for 150 < E ≤ 200
t = $120/unit of E for E > 200

17. Topic 3.b: Emissions taxes$
200
120
105 75 45 15
Firm will choose E=200 (efficient E)
Compliance costs
= $12,000 + $18,000
= $30,000 MD t
MAC E
Again, we are picking different ts here such that the total tax paid by the firm equals TD, so the firm has the right incentive to stay in business.
Note that as we increase the number of “steps” in the t function, we are get a closer and closer approximation of the MD curve.

18. Topic 3.b: Emissions taxes$
200
120
105 75 45 15
So why not face the firm with a continuously varying tax per unit of E, such that t always = MD?
MAC MD
= t t
TAC = $18,000
Tax paid
= $12,000 E
That is, we could make the tax schedule exactly coincide with the MD function.
Tax paid by firm = area under the MD curve (which is also the “tax curve”) up to the level of E chosen by the firm.

19. Topic 3.b: Emissions taxes
This is the most extreme version of a non-linear E charge
Every unit of E is charged a different tax rate.
We have seen that this gets the incentive right for the firm to stay in business/go out of business
The tax paid always equals the TD from emissions.
It also gets the firm’s incentives right to abate efficiently
We just need set t = MD and the firm will minimize its compliance costs by choosing E such that t = MAC.
 we end up with E such that MAC = MD.
Nice feature: this doesn’t require any information for the regulator, except the knowledge of MD.

20. Topic 3.b: Emissions taxes
Exercise: Does setting non-linear t = MD give the firm the right incentive to invest in new abatement technology?
You should discover that the answer is yes.
Seems like a perfect policy instrument.
But, never really used in practice. Why not?
Suppose we have more than one polluting firm.
How can we identify what the MD function is for each firm?
TD is a function of E1 + E2.
Can’t figure out what the marginal damages are for each firm independently of the other.