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Static Efficiency, Dynamic Efficiency and Sustainability

Static Efficiency, Dynamic Efficiency and Sustainability. Wednesday, January 25. $. Demand. Demand. Quantity. Represent the demand for a resource as: P = 8 – 0.4 q. Demand = marginal willingness to pay = Marginal Benefit (MB). P = 8 - 0.4q. $. Demand. Demand. Quantity.

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Static Efficiency, Dynamic Efficiency and Sustainability

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  1. Static Efficiency, Dynamic Efficiency and Sustainability Wednesday, January 25

  2. $ Demand Demand Quantity Represent the demand for a resource as: P = 8 – 0.4 q Demand = marginal willingness to pay = Marginal Benefit (MB)

  3. P = 8 - 0.4q

  4. $ Demand Demand Quantity Represent the demand for a resource as: P = 8 – 0.4 q (5,6) (15,2)

  5. Assume a constant marginal cost of extraction = $2.00 (Marginal cost = supply) $ MB Demand MC Quantity Efficient allocation occurs where MB = MC, q = 15 units

  6. Static Efficiency • MB = MC • Criteria for allocation in a given time period, with no consideration of future time periods • Efficiency: no one can be made better off without making someone else worse off

  7. $ MC MB>MC MC>MB MB Q MB=MC

  8. What are the net benefits of the efficient allocation? $ MB Demand MC Quantity Efficient allocation occurs where MB = MC, q = 15 units

  9. TC (area under MC curve) = (2x15) = 30 NB MB MC TB (area under MB curve)=½(6x15) + (2x15)=45+30=75 $ Quantity NB = TB – TC = ½(6x15) = 45

  10. This graph illustrates marginal net benefits: MB-MC = (8-0.4q)-2 = 6-0.4q = MNB $ MNB Quantity Total NB (area under MNB curve) = ½(6x15) = 45

  11. Dynamic Efficiency • When the concern is efficient allocation of a nonrenewable resource over multiple time periods • MNB0 = PV MNB1 = PV MNB2 = … = PV MNBt • t represents time period

  12. With only 20 units of the resource available, what is the present value of total net benefits if effective demand is met in the first period, with no consideration of the second period? • Only two time periods in this example • For present value calculations, r=.10

  13. Period t0 $ MB MC Quantity

  14. Period t0 $ MB MC Quantity NB = Area = ½(6x15) = 45

  15. Period t1 $ MB MC Quantity

  16. Period t1 $ MB MC Quantity NB = Area = ½(2x5) + (4x5) = 25

  17. Present Value of NB for t1 = 25/(1+r) = 25/1.1 = $22.73 PV Total net benefit for two periods = $45 + $22.73 = $67.73 NB for t0 = $45

  18. With only 20 units of the resource available, what is the present value of total net benefits if the resource is allocated equally across two time periods? (q0 = q1)

  19. Period t0 $ MB MC Quantity

  20. Period t0 $ MB MC Quantity NB = Area = ½(4x10) + (2x10) = 40

  21. Period t1 $ MB MC Quantity NB = Area = ½(4x10) + (2x10) = 40

  22. Present Value of NB for t1 = 40/(1+r) = 40/1.1 = $36.36 PV Total net benefit for two periods = = $40 + $36.36 = $76.36 NB for t0 = $40

  23. Find the efficient allocation of the resource over the two periods (dynamic efficiency). Find the dynamically efficient quantities for q0 and q1. Recall, for dynamic efficiency (to maximize PV of total net benefits), MNB0 = PV MNB1

  24. MNB0 = PV MNB1 • MNB = MB - MC • MB = 8 – 0.4q • MB – MC = (8 – 0.4q) – 2 = 6 – 0.4q • MNB = 6 – 0.4q

  25. MNB0 = PV MNB1 • 6 - .4q0 = (6 - .4q1)/1.1 • q0 + q1 = 20 • 6 - .4q0 = (6 - .4[20-q0])/1.1 • 1.1(6 - .4q0)= (6-8+.4q0) • 6.6-.44q0 = (-2 +.4q0) • 8.6=.84q0 • q0 = 10.238 • q1 = 9.762

  26. This graph illustrates marginal net benefits: MB-MC=MNB $ MNB Quantity

  27. Period t0 $ MNB0 Quantity MNB = MB – MC = 6 – 0.4q

  28. $ 5.45 PV MNB1 Quantity Period t1 Present value calculation: 6/1.1 = 5.45

  29. $ 7 6 5.45 5 MNB0 MNB1 4 3 2 1 t0 0 5 10 15 t1 5 15 10 0 q0=10.238 Quantity q1=9.762

  30. MNB0 = 6 – 0.4(10.238) = 1.9048 • MNB1 = [6 – 0.4(9.762)]/1.1 = 2.9052/1.1 = 1.9048

  31. $ 7 6 5.45 5 MNB0 MNB1 4 3 MNB=1.9048 2 1 t0 0 5 10 15 t1 5 15 10 0 q0 Quantity q1

  32. To calculate total benefits, total costs, and net benefits: P0 = 8 - .4q0 P0 = 8 - .4(10.238) P0 = 3.905 P1 = 8 - .4q1 P1 = 8 - .4(9.762) P1 = 4.095

  33. Period t0 $ MB 3.905 MC Quantity 10.238 NB = ½(4.095x10.238) + (1.905x10.238) = 40.46

  34. Period t1 $ 4.095 MB MC 9.762 Quantity NB = ½(3.905x9.762) + (2.095x9.762) = 39.51

  35. Present Value of NB for t1 = 39.51/(1+r) = 39.51/1.1 = $35.92 Total net benefit for two periods = $40.46+35.92 = $76.38 NB for t0 = $40.46

  36. Comparing allocations: • Maximize NB to period 0 • TNB = $67.73 • q0 = q1 • TNB = $76.36 • Dynamically efficient allocation • TNB = $76.38

  37. Sustainability • Environmental sustainability • Do not reduce total stock of natural capital • Strong sustainability • Do not reduce productivity (value) of natural capital stock • One type of natural capital may substitute for another • Weak sustainability • Do not reduce productivity of capital • May substitute manufactured capital for natural capital

  38. With equal distribution • NB0 = $40 • NB1 = $40 • With efficient distribution • NB0 = $40.46 • NB1 = $39.51 • With sharing, keep NB0 = $40, invest $.46 @ 10%, send to t1 • .46(1.1) = .506 • NB1 = $39.51 + .51 = $40.02

  39. Marginal User Cost • MNB0 = 6 – 0.4(10.238) = 1.905 • MNB1 = [6 – 0.4(9.762)]/1.1 = 2.0952/1.1 = 1.905 • The value of the last unit extracted in t0 • Foregone benefit for t1 • Opportunity cost of choosing to extract the last unit used in t0

  40. User Cost and Natural Resource Rent • P = MEC + MUC • $3.905 = $2.00 + 1.905 Period t0 $ Rent MB 3.905 User Cost MC Wages, etc. Quantity 10.238

  41. Period t1 $ Rent 4.095 MB User Cost MC 9.762 Quantity • P = MEC + MUC • $4.095 = $2.00 + 2.095 • MUC increases at the rate of discount • 2.095 = 1.1(1.905)

  42. Reading for Wed. Feb. 2: Hartwick and Olewiler, on ANGEL and Field, Ch. 6

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