topic 2: production externalities
DESCRIPTION
Topic 2: Production Externalities. TD ($). an additional unit of E causes more damage if E is already high. TD. Suppose (E/Q) is constant in Q, but MD is increasing in E True if TD as E, but at an increasing rate. given E, TD 2 > TD 1. TD 2. - PowerPoint PPT PresentationTRANSCRIPT
1
Topic 2: Production Externalities
• Suppose (E/Q) is constant in Q, but MD is increasing in E
• True if TD as E, but at an increasing rate.TD ($)
E
an additional unit of E causes more damage if E is already high.
E E
TD2
TD1
given E, TD2 > TD1.
TD
E
MD ($)
so MD is upward sloping.
MD
MEC will be increasing in Q
MEC ($)
Q
MEC
(even if E/Q is constant in Q)
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Topic 2: Production Externalities• Recall: MSC = MPC + MEC• So if MEC is constant in Q then
• And if MEC is increasing Q then
$
Q
MEC
Q
$
MEC
$
Q
MPC
MEC
MEC
$
MPC
MSC = MPC + MEC
Q
MSC = MPC + MEC
MEC
MEC
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
1. Firms’ FC = 0; and
2. Aggregate demand for electricity is given by:
Q = 1,200 - 100P (again, Q is thousands of kwh)
5
Topic 2: Production Externalities
• Given this info, we want to know:
1. How much electricity will be produced in equilibrium?
2. What do net benefits equal at the equilibrium?3. Is this efficient?
– That is, are net benefits maximized? 4. 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:1. distribution of net benefits 2. information required for implementation
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Topic 2: Production Externalities
• Solve for equilibrium price and quantity, assuming that firms aim to maximize profits (PS).
MPC (S)
MB (D)
400
8
12
c
1,200
Maximize profits Firms ignore ECThen equilibrium is where S = D:
50P = 1200 - 100P P = 8 & Q = 400.
Supply: Q = 50P
Demand: Q = 1200 - 100P
Q (thousands kwh)
7
A
Topic 2: Production Externalities
• Calculating NB at the equilibrium: 1st approach:– NB = TB - TC = CS + PS - EC (sum of individual NB).
MPC (S)
MSC = MPC + MEC
MB (D)
MEC
400
8
12
c
1,200
3
Every unit of Q EC of 3 cents: EC = $0.03 400 = $12,000
= area C.
Note: MSC = 3 + (1/50)Q = MPC + MEC
CS = TB - (PQ) = $8,000 = area A.
PS = (PQ) - VC = $16,000 = area B.
B
Q (thousands kwh)
C
NB = $ 8,000 (CS) + $16,000 (PS) - $12,000 (EC) = $12,000
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Topic 2: Production Externalities
• Calculating NB at the equilibrium: 2nd approach:
– NB = TB - TC
MPC (S)
MSC = MPC + MEC
MB (D)
MEC
400
8
12
c
1,200
3
NB = $40,000 - $28,000 = $12,000 = X - Y.
TB = area under D curve = $40,000
TC = area under MSC curve = $28,000
Q (thousands kwh)
Note: both approaches to calculating NB give us the same answer (which should make sense)
X Y
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Topic 2: Production Externalities
• Is the equilibrium Q = 400 efficient?– could NB could be higher at a different Q?
MPC
MSC MB
400
8
12
c
1,200
3
NB maximized if we produce Q such that MSC = MB:
3 + (1/50)Q = 12 - (1/100)Q Q = 300.
At Q = 400, MSC > MB
Units of Q were produced that TC by more than they TB.
Q (thousands kwh)300
NB could be higher at lower Q.
i.e., Q = 300 is efficient.
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Topic 2: Production Externalities
• As we Q from 400 to 300:
MPC
MSC MB
400
8
12
c
1,200
3
At equilibrium Q = 400, NB = X - CAt efficient Q = 300, NB = X
Q (thousands kwh)
TC = A+B+C
TB = A+B
NB = C (note: C = Y in slide 7)
300
DWL at equilibrium = C
A
B
C11
area C = $1,500Tells us NB are $1,500 higher at Q = 300 than at Q = 400.
X
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Topic 2: Production Externalities
If NB are $1,500 higher at Q = 300, then NB should = $13,500. NB = TB - TC = TB - PC - EC.
MPC
MSC MB
400
8
12
c
1,200
3
Q (thousands kwh)
TB = area under MB curve = A+B+C = $31,500
300
NB = TB - PC - EC = $31,500 - $9,000 - $9,000 = $13,500
C
A
B
PC = area under MPC curve = C = $9,000
EC = area between MPC & MEC = B = $9,000
NB = TB - PC - EC = (A+B+C) - (C) - (B) = A
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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.
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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.
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Topic 2: Production Externalities
1. 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.
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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).
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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).
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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.
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Topic 2: Production Externalities• The effects of a per unit output tax = MEC in electricity ex.
MPC (S)
MB
400
8
12
c
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.
- Recall, equilibrium was P = 8 & Q = 400
Q (thousands kwh)
If firms face t = MEC, MPC by t.t = $0.03/kwh in ex.
New MPC = old MPC + t = MSC
300
9
6
3
New MPC = MSC
S curve shifts inwards
t
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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?
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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.
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Topic 2: Production Externalities• NB = CS + PS - EC + REV
MPC (S)
MB
400
8
12
c
1,200
Consumer lose B+C = $3,500.
Loss due to P and Q
Q (thousands kwh)
CS = area A = $4,500
Recall that without the tax CS = A+B+C = $8,000
300
9
6
3
New MPC = MEC
A
CB
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Topic 2: Production Externalities• NB = CS + PS - EC + REV
MPC (S)
MB
400
8
12
c
1,200
Producers lose D+E +F = $7,000.
Loss due to P and Q
Q (thousands kwh)
PS = areas G+H = $9,000
Recall that without the tax PS = D+E+F+G+H = $16,000
300
9
6
3
New MPC = MSC
D FE
HG
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Topic 2: Production Externalities
MPC (S)
MB
400
8
12
c
1,200
Who gains from the tax?
Those who bear the pollution costs: EC Government/taxpayers: REV
Q (thousands kwh)
PS + CS = areas B+C+D+E+F = $7,000 + $3,500 = $10,500
300
9
6
3
New MPC = MSC
D FE
B C
Combined losses of producers and consumers: