Natural Resources Management

Natural Resources Management

Understanding human relationships with, and impact on, the natural environment, and defining rational and informed analysis toward reducing undesirable outcomes.

 

Given the competitive exploration and extraction problem:

Year

Production

(106 br/yr)

Price

($/br)

Reserves

106 br

1997

552

54

7170

1998

557

51

9240

1999

554

52

9460

2000

551

68

9801

2001

548

75

9830

2002

544

79

9900

2003

522

85

8500

2004

493

90

6400

2005

458

94

6500

2006

417

95

4300

2007

368

100

4000

2008

312

101

3000

2009

251

102

2800

2010

185

107

1500

2011

113

109

1300

2012

22

110

800

Required:

Determine the optimal terminal time using the formula

aT – a(1 – e-dT)/d = R0

Where:

a is the intercept term for the downsloping demand curve

d = 0.05, which is the discount rate reflecting the time value of money

R0 is the reserve level at 1997

The solution should be submitted before the last lecture on 28/10/2013

 

Natural Resource Management

Objectives:

The primary objectives of this course is to introduce students to the theory of Natural Resource Management


Course content:

  1. Integral calculus with some aoolications
  2. Introduction to differential equations
    • The homogenous case
    • The nonhomogenous case
    • Variable coefficient and variable term problems
    • Dynamic stability analysis
    • Application to nonlinear fishery model
  3. Caclulus of variation
    • The Euler equation
    • Generalization of Euler equation
    • The transversility condition
  4. Optimal control theory
    • The maximum principal
    • The current value Hamiltonian
  5. Renewable resources
    • Growth function
    • Production and yield function
    • Objectives of management
      • Constant prices
      • Downward sloping demand
    • Spawner recruit models
    • Optimal investment strategy
    • Common property resources
    • The theory of resource regulations
    • Optimal forest rotation
  6. Non renewable resources
    • Pure depletion and discovery
    • Pure depletion
    • Competitive and monopolistic mining industries
    • Extraction costs: The case of a single mine
    • Scarcity from an economic perspective
    • Exploration

References

  • Jon Conrad and Colin Clark: Natural Resource Economics. Cambridge
  • Colin Clark: Mathematical Bioeconomics: The Optimal Management of Renewable Resources

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