Application Deadline: March 5

1. Preparing Resource and Environmental Managers with International Understandings and Merits (PREMIUM) A Summer Research Experience for Undergraduates Program in China May 16 - July 8, 2005 Application Deadline: March 5 http://forestry.msu.edu/China/Premium.htm

2. Static Efficiency, Dynamic Efficiency and Sustainability Wednesday, January 26

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

4. P = 8 - 0.4q

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

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

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

10. This graph illustrates marginal net benefits: MB-MC $ MNB Quantity Total NB = 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 Quantity q1

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