topic 2: production externalities

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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

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• 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.

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• 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)

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• 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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• 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


• 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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• 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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• 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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• 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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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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• 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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• 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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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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• 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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• 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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• 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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• 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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• 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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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:

topic 2: production externalities

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