Lecture 10

1. Lecture 10 The efficient and optimal use of renewable resources

2. What are renewable resources? • Examples: • Renewable stock resources: fishery, forestry, water, wildlife, arable land, grazing land, soil, anti-biotic and pesticide resistance • Renewable flow resources: solar, wave, wind, and geothermal energy • We consider only renewable stock resources

3. Biological growth processes for renewable resources • Change of population over time: • Stock level at any point in time:

4. Integration of the growth process

5. Integration of the growth process

6. Growth Function

7. Where is the maximum growth rate?

8. Logistic biological growth function G(S) S S 0 S MSY MAX

9. Logistic biological growth function with threshold level

10. Logistic biological growth function with depensation

11. Logistic biological growth function with critical depensation

12. Steady-State Harvesting

13. Figure 17.2 Steady-state harvests (Perman et al.: page 560) G = H MSY MSY G = H 1 1 0 S S 1L 1U MAX MSY S S

14. Open access resource: fishery as a case

15. Static analysis of a renewable resource harvesting

16. Costs and benefits of harvesting

17. Bio-economic equilibrium

18. Open-access steady-state equilibrium bio-economic equilibrium

19. Open-access steady-state equilibrium

20. HMSY = eEMSYS H1 = eE1S H2 = eE2S H2 H1 S1 SMSY =SMAX/2 S2 S Steady-state equilibrium fish harvests and stocks at various effort levels

21. HPP H=(w/P)E HOA EOA E Steady-state equilibrium yield-effort relationship zero economic profit equilibrium

22. Steady-state harvesting: private property

23. Steady-state harvesting: private property in steady state dp/dt = 0 difference between market price and marginal costs of an incremental unit of harvested fish reduction in total harvesting costs, by having one more unit of resource, additional fish grows by dG/dS value at the net-price profit foregone not harvesting) marginal cost of investment marginal benefit of investment

24. Steady-state harvesting: private property

25. Steady-state harvesting: private property the value of the reduction in harvesting costs that arises from a marginal increase in the resource stock natural rate of growth in the stock from a marginal change in stock size opportunity costs fundamental equation of renewable resources

30. Renewable Resource Policies • 1. Command and Control • reducing fishing effort • restriction on fishing gear • spatial restrictions • fleet size reduction • quantity restrictions on catch

34. Where the forests go

35. Community ownership and administration of forests

36. Forestry Funds

37. A possible global forest situation: 2050

38. A single rotation forest model • Stand of timber of uniform type and age • All trees are planted at the same time • All trees are to be cut at the same time • Once felled the forest will not be replanted • The land has no alternative uses: • All costs and prices are constant • The forest generates only timber as a value, other possible values are ignored • Felling of the forest has no external effects

39. A single rotation forest model

40. Maximisation of profit present value

41. Maximisation of profit present value

42. Example

43. Figure 18.1 (a) The volume of timber in a single stand over time (Perman et al., page 603)

44. Figure 18.2 Present values of net benefits at i = 0.00 (NB1) and i = 0.03 (NB2)(Perman et al.: page 606)

45. Figure 18.3Variation of the optimal felling age with the interest rate, for a single-rotation forest (Perman et al.: page 607)

46. Infinite rotation forestry models

47. Infinite rotation forestry models: NPV

48. Infinite rotation forestry models: NPV

49. Infinite rotation forestry models: NPV

50. Infinite rotation forestry models: NPV