1. Topic 2: Production Externalities
Suppose (E/Q) is constant in Q, but MD is increasing in E
True if TD as E, but at an increasing rate.
TD ($)
 an additional unit of E causes more damage if E is already high. TD
 given E, TD2 > TD1.
TD2
so MD is upward sloping.
 MEC will be increasing in Q
TD1
(even if E/Q is constant in Q) E E E
MD ($)
MEC ($) MD
MEC  E Q

2. Topic 2: Production Externalities
Recall: MSC = MPC + MEC
So if MEC is constant in Q then
And if MEC is increasing Q then $ $
MSC = MPC + MEC
MPC
MEC
MEC 
MEC Q Q $ $
MSC = MPC + MEC
MEC
MEC
MPC
MEC Q Q

3. Topic 2: Production Externalities
For now, keep things simple: back to SO2 ex. of constant MEC.
MEC = $0.03.
Suppose there are 100 coal-fired power plants, each with:
MPC = 2Q, where Q is measured in thousands of kwh
 Each power plant’s supply curve is given by:
Q = (1/2)P.

4. Topic 2: Production Externalities
Aggregate supply of electricity is:
Q = (1/2)P + (1/2)P + … + (1/2)P (adding over all 100 firms)
= 100  (1/2)P (as the firms have identical S curves)
= 50P.
Also suppose that
Firms’ FC = 0; and
Aggregate demand for electricity is given by:
Q = 1, P (again, Q is thousands of kwh)

5. Topic 2: Production Externalities
Given this info, we want to know:
How much electricity will be produced in equilibrium?
What do net benefits equal at the equilibrium?
Is this efficient?
That is, are net benefits maximized?
If inefficient, what policies could correct the market failure?
We will see that there is more that one policy that will allow us to achieve the efficient outcome.
Policies will differ in terms of the:
distribution of net benefits
information required for implementation

6. Topic 2: Production Externalities
Solve for equilibrium price and quantity, assuming that firms aim to maximize profits (PS). c
Supply:
Q = 50P
Demand:
Q = P 12
MPC (S) 8
MB (D) Q
(thousands kwh)
400
1,200
Maximize profits  Firms ignore EC
Then equilibrium is where S = D:
 50P = P
 P = 8 & Q = 400.

7. Topic 2: Production Externalities
Calculating NB at the equilibrium: 1st approach:
NB = TB - TC = CS + PS - EC (sum of individual NB). c
MSC = MPC + MEC
CS = TB - (PQ)
= $8,000
= area A.
PS = (PQ) - VC
= $16,000
= area B. 12 A
MEC
MPC (S) 8 C B
MB (D) 3 Q
(thousands kwh)
400
1,200
Every unit of Q  EC of 3 cents:
 EC = $0.03  400 = $12,000
= area C.
Note: MSC = 3 + (1/50)Q = MPC + MEC
NB = $ 8,000 (CS)
+ $16,000 (PS)
- $12,000 (EC)
= $12,000

8. Topic 2: Production Externalities
Calculating NB at the equilibrium: 2nd approach:
NB = TB - TC
TB = area under
D curve
= $40,000
TC = area under
MSC curve
= $28,000 c
MSC = MPC + MEC 12
MEC
MPC (S) X Y 8
MB (D) 3 Q
(thousands kwh)
400
1,200
 NB = $40,000 - $28,000
= $12,000
= X - Y.
Note: both approaches to calculating NB give us the same answer (which should make sense)

9. Topic 2: Production Externalities
Is the equilibrium Q = 400 efficient?
could NB could be higher at a different Q? c
At Q = 400, MSC > MB
 Units of Q were produced that TC by more than they TB.
MSC 12 MB
MPC 8 3 Q
(thousands kwh)
300
400
1,200
 NB could be higher at lower Q.
NB maximized if we produce Q such that MSC = MB:
 3 + (1/50)Q = 12 - (1/100)Q
 Q = 300.
i.e., Q = 300 is efficient.

10. Topic 2: Production Externalities
As we Q from 400 to 300:
TC = A+B+C
TB = A+B
 NB = C
(note: C = Y in slide 7) c
MSC 12 MB 11
MPC C X 8 B 3 A Q
(thousands kwh)
300
400
1,200
At equilibrium Q = 400, NB = X - C
At efficient Q = 300, NB = X
area C = $1,500
Tells us NB are $1,500 higher at Q = 300 than at Q = 400.
 DWL at equilibrium = C

11. Topic 2: Production Externalities
If NB are $1,500 higher at Q = 300, then NB should = $13,500.
NB = TB - TC = TB - PC - EC.
TB = area under MB curve
= A+B+C
= $31,500 c
MSC 12 MB
MPC
PC = area under
MPC curve
= C
= $9,000 8 A 6 B 3 C Q
(thousands kwh)
300
400
1,200
EC = area between MPC & MEC
= B = $9,000
NB = TB - PC - EC
= $31,500 - $9,000 - $9,000
= $13,500
NB = TB - PC - EC
= (A+B+C) - (C) - (B)
= A

12. Topic 2: Production Externalities
The market fails to achieve efficiency in the face of a negative externality.
Example of a market failure.
Next Q: What policies might correct this market failure?
Keeping our focus on the output market, we will examine 3 policies:
Per unit tax on the production of output.
Quota on the production of output
Per unit subsidy on output reduction.

13. Topic 2: Production Externalities
Each of these policies can achieve the efficient outcome.
i.e., will result in the same level of NB.
Policies will however differ in terms of the distribution of NB.
Policies will also differ in the information needed by the regulator.
Output tax covered in detail in class. The details of the remaining two policies will be left as exercises.

14. Topic 2: Production Externalities
Per unit tax on the production of output.
Also known as Pigovian tax.
Producer must pay a constant $ tax per unit of Q produced.
Ex: tax per kwh of electricity generated in coal-fired plants.
Note that we are targeting output in order to reduce pollution.
Not directly targeting the source of the EC (pollution).
In our example, SO2 is the cause, not electricity.

15. Topic 2: Production Externalities
Example: in Canada, sales tax on automobiles is based on weight and fuel efficiency.
Less fuel efficient cars use more gasoline  more emissions of pollutants like carbon (contributes to global warming).
Not directly targeting the source of emissions (gasoline).

16. Topic 2: Production Externalities
How does output tax correct the market failure?
Recall: the source of the inefficiency is the failure of firms to account for the EC.
EC are real costs, just like other costs associated with electricity generation (coal, labor etc.), but
EC are being paid by others (ex asthma sufferers).

17. Topic 2: Production Externalities
If we set a per unit output tax t = MEC, then the firm pays a $ amount equivalent to the EC it generates.
Forcing firms to “internalize the externality.”
Note: this doesn’t make the EC go away altogether.
Just makes the firm pay attention to them.

18. Topic 2: Production Externalities
The effects of a per unit output tax = MEC in electricity ex.
- Recall, equilibrium was P = 8 & Q = 400
If firms face t = MEC, MPC by t.
t = $0.03/kwh in ex. c
New MPC
= MSC 12
MPC (S) 9
 New MPC
= old MPC + t = MSC 8 t 6
 S curve shifts
inwards 3 MB Q
(thousands kwh)
300
400
1,200
New equilibrium is where new S = D  Q = 300 and P = $0.09.
P = $0.09 is price that consumers pay to producers  PC.
Producer must then give $0.03 to the govt.
PP  price producers receive net of tax = $0.06.

19. Topic 2: Production Externalities
We know that this tax achieves the “right” Q.
Q = 300 is efficient.
And we know that aggregate NB at Q = 300 = $13,500.
What about distribution of NB?
NB = sum of individual NB
Which individuals?
What are their NB?

20. Topic 2: Production Externalities
Individuals/groups we need to account for:
Consumers: CS
Producers: PS
Those that bear the costs of pollution: EC
Government (taxpayers): tax revenue (REV) raised.

21. Topic 2: Production Externalities
NB = CS + PS - EC + REV c
CS = area A
= $4,500
Recall that without the tax CS = A+B+C
= $8,000
New MPC
= MEC 12 A
MPC (S) 9 B C 8 6 3 MB Q
(thousands kwh)
300
400
1,200
Consumer lose B+C = $3,500.
Loss due to P and Q

22. Topic 2: Production Externalities
NB = CS + PS - EC + REV c
PS = areas G+H
= $9,000
Recall that without the tax PS = D+E+F+G+H
= $16,000
New MPC
= MSC 12
MPC (S) 9 8 D F E 6 G H 3 MB Q
(thousands kwh)
300
400
1,200
Producers lose D+E +F = $7,000.
Loss due to P and Q

23. Topic 2: Production Externalities
Combined losses of producers and consumers: c
New MPC
= MSC
PS + CS = areas B+C+D+E+F
= $7,000 + $3,500
= $10,500 12
MPC (S) 9 B C 8 D F E 6 3 MB Q
(thousands kwh)
300
400
1,200
Who gains from the tax?
Those who bear the pollution costs: EC
Government/taxpayers: REV