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Topic 2: Production Externalities

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.

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Topic 2: Production Externalities

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

  2. Topic 2: Production Externalities $ MSC = MPC + MEC $ • Recall: MSC = MPC + MEC • So if MEC is constant in Q then • And if MEC is increasing Q then 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 = 1,200 - 100P (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 Supply: Q = 50P Demand: Q = 1200 - 100P c 12 • Solve for equilibrium price and quantity, assuming that firms aim to maximize profits (PS). MPC (S) 8 MB (D) Q (thousands kwh) 400 1,200 Maximize profits  Firms ignore EC Then equilibrium is where S = D:  50P = 1200 - 100P  P = 8 & Q = 400.

  7. Topic 2: Production Externalities c MSC = MPC + MEC CS = TB - (PQ) = $8,000 = area A. PS = (PQ) - VC = $16,000 = area B. 12 MEC • Calculating NB at the equilibrium: 1st approach: • NB = TB - TC = CS + PS - EC (sum of individual NB). A 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 TB = area under D curve = $40,000 TC = area under MSC curve = $28,000 c MSC = MPC + MEC 12 MEC • Calculating NB at the equilibrium: 2nd approach: • NB = TB - TC MPC (S) Y X 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 c At Q = 400, MSC > MB  Units of Q were produced that TC by more than they TB. MSC 12 MB • Is the equilibrium Q = 400 efficient? • could NB could be higher at a different Q? 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 TC = A+B+C TB = A+B  NB = C (note: C = Y in slide 7) c MSC 12 MB • As we Q from 400 to 300: 11 MPC C X 8 B A 3 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 TB = area under MB curve = A+B+C = $31,500 c MSC 12 MB If NB are $1,500 higher at Q = 300, then NB should = $13,500. NB = TB - TC = TB - PC - EC. MPC PC = area under MPC curve = C = $9,000 A 8 6 B 3 C Q (thousands kwh) 300 400 1,200 EC = area between MPC & MEC = B = $9,000 NB = TB - PC - EC = (A+B+C) - (C) - (B) = A NB = TB - PC - EC = $31,500 - $9,000 - $9,000 = $13,500

  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 - 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 • The effects of a per unit output tax = MEC in electricity ex. MPC (S)  New MPC = old MPC + t = MSC 9 8 t 6  S curve shifts inwards 3 MB Q (thousands kwh) 400 300 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 CS = area A = $4,500 Recall that without the tax CS = A+B+C = $8,000 c New MPC = MEC 12 • NB = CS + PS - EC + REV A MPC (S) 9 B C 8 6 3 MB Q (thousands kwh) 400 300 1,200 Consumer lose B+C = $3,500. Loss due to P and Q

  22. Topic 2: Production Externalities PS = areas G+H = $9,000 Recall that without the tax PS = D+E+F+G+H = $16,000 c New MPC = MSC 12 • NB = CS + PS - EC + REV MPC (S) 9 8 F D E 6 G H 3 MB Q (thousands kwh) 400 300 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 PS + CS = areas B+C+D+E+F = $7,000 + $3,500 = $10,500 New MPC = MSC 12 MPC (S) 9 B C 8 F D E 6 3 MB Q (thousands kwh) 400 300 1,200 Who gains from the tax? Those who bear the pollution costs: EC Government/taxpayers: REV

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