Topic 2: Production Externalities

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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 Presentation


  • Topic 2: Production ExternalitiesSuppose (E/Q) is constant in Q, but MD is increasing in E

    True if TD as E, but at an increasing rate.

    TD ($)E an additional unit of E causes more damage if E is already high.EETD2TD1 given E, TD2 > TD1.TD EMD ($)so MD is upward sloping.MD

    MEC will be increasing in Q MEC ($)QMEC (even if E/Q is constant in Q)

  • Topic 2: Production ExternalitiesRecall: MSC = MPC + MECSo if MEC is constant in Q then

    And if MEC is increasing Q then$QMEC Q$MEC $QMPC MEC MEC $MPC MSC = MPC + MECQMSC = MPC + MECMEC MEC

  • Topic 2: Production ExternalitiesFor 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 plants supply curve is given by:Q = (1/2)P.

  • 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; andAggregate demand for electricity is given by:Q = 1,200 - 100P (again, Q is thousands of kwh)

  • Topic 2: Production ExternalitiesGiven 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

  • Topic 2: Production ExternalitiesSolve for equilibrium price and quantity, assuming that firms aim to maximize profits (PS).MPC (S)MB (D)400812c1,200Maximize 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)

  • Topic 2: Production ExternalitiesCalculating NB at the equilibrium: 1st approach:NB = TB - TC = CS + PS - EC (sum of individual NB).AMPC (S)MSC = MPC + MECMB (D)MEC400812c1,2003 Every unit of Q EC of 3 cents: EC = $0.03 400 = $12,000 = area C.

    Note: MSC = 3 + (1/50)Q = MPC + MECCS = TB - (PQ) = $8,000 = area A.

    PS = (PQ) - VC = $16,000 = area B.B Q (thousands kwh)CNB = $ 8,000 (CS) + $16,000 (PS) - $12,000 (EC) = $12,000

  • Topic 2: Production ExternalitiesCalculating NB at the equilibrium: 2nd approach:

    NB = TB - TCMPC (S)MSC = MPC + MECMB (D)MEC400812c1,2003

    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)XY

  • Topic 2: Production ExternalitiesIs the equilibrium Q = 400 efficient?could NB could be higher at a different Q?MPCMSC MB400812c1,2003NB 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.

  • Topic 2: Production Externalities

    As we Q from 400 to 300:MPCMSC MB400812c1,2003At 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 = CABC11area C = $1,500Tells us NB are $1,500 higher at Q = 300 than at Q = 400.X

  • Topic 2: Production ExternalitiesIf NB are $1,500 higher at Q = 300, then NB should = $13,500. NB = TB - TC = TB - PC - EC.MPCMSC MB400812c1,2003 Q (thousands kwh)TB = area under MB curve = A+B+C = $31,500

    300NB = TB - PC - EC = $31,500 - $9,000 - $9,000 = $13,500CABPC = area under MPC curve = C = $9,000EC = area between MPC & MEC = B = $9,000NB = TB - PC - EC = (A+B+C) - (C) - (B) = A6

  • Topic 2: Production ExternalitiesThe 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 outputPer unit subsidy on output reduction.

  • 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.

  • Topic 2: Production ExternalitiesPer 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.

  • 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).

  • Topic 2: Production ExternalitiesHow 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).

  • 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 doesnt make the EC go away altogether.

    Just makes the firm pay attention to them.

  • Topic 2: Production ExternalitiesThe effects of a per unit output tax = MEC in electricity ex.MPC (S)MB400812c1,200New 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 300963New MPC = MSC S curve shifts inwardst

  • Topic 2: Production ExternalitiesWe 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?

  • 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.

  • Topic 2: Production ExternalitiesNB = CS + PS - EC + REVMPC (S)MB400812c1,200Consumer 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 = $8,000300963New MPC = MECACB

  • Topic 2: Production ExternalitiesNB = CS + PS - EC + REVMPC (S)MB400812c1,200Producers 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 = $16,000300963New MPC = MSCDFEHG

  • Topic 2: Production ExternalitiesMPC (S)MB400812c1,200Who 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 = $10,500300963New MPC = MSCDFEBCCombined losses of producers and consumers: