  ## Natural Resources Management

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

Oct 08

### Natural Resources Management - Assignment 1

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

Jul 02

### Natural Resources Management - Course Outline

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