The basic reason that we have a problem is due to exponential growth which creates a strongly non-equilbrium use of our resources. ( Although some "professors" suggest that consumer behavior is not at fault but instead corporate greed is at fault. This is an easy path to buy into because it absolves the individual from blame. Its bullshit. All consumers bear responsibility for their use of resources and the consumer base rises exponentially)

Its not to great of simplification to state that the failure to understand the concept of exponential growth by planners and/or legislators, is the single biggest problem in all of Environmental Studies and/or Management.

The Two Principle Problems with Resource Management:

• Failure for policy makers to understand the concept of exponential growth.
• Failure for legislation to be formulated and passed to give us a long term energy strategy

Exponential growth drives resource usage for a very simple reason:

Human population increases exponentially:

Accurate trend extrapolation is the most important part of future planning. However, failure to assume exponential growth will always lead to a disaster so always assume exponential growth when planning anything! ( Remember the California Example ).

70/n years; n =% growth rate

Its important to recognize that even in the slow growth period, the use of the resource is exponential. If you fail to realize that, you will run out of the resource pretty fast.

T_e = 1/k * ln (Rk/r_o +1)

where k = growth rate
R = total resource available
r_o = initial consumption rate

The basic problem is that we substitute Disney's First Law for this arithmatic reality of resource depletion.

Some examples to do in Excel. Calculate resource depletion time scales for various values of k.

Let's start out with the Hubbard Curve. Note that peak production occurs on a timescale of 1/2 of T_e as the production curve is assumed to be symmetric.

• Measured Growth rate of oil production in the US over period of 1945-1955 was 3% (.03)
• Starting period of calculation is 1946
• Hubbard estimates the ratio of R/r_o in 1946 to be 120
• From this, what do you find as the year of peak production?

Other Examples:

• Oil (World): R = 2000 r_o = 28 (2001)
  
  
  
• Coal (US): R = 250 (billion tons) r_o = 1 (2001)

• Natural Gas (US): R = 200 (tcf) r_o = 22
  Natural Gas (World): R=161 (tcm) r_o = 2.5 (2002)

• Cooper (US): R = 45 (million tons) r_o = 2 (1996)
  World: R = 320 r_o = 9

• Cell Phones (US): R = 1E10; r_o = 150E6; k =0.30 when do we run out of 10 digit cell phone numbers?

  
  
  
  

• Earth Carrying Capacity:
  • R =1E12 (1 trillion total humans integrated over time)

  • Worlds population starts growing exponentially in the year 1800

  • Population at that time was about 500 million people (500E6)

  • What's the remaining lifetime of humans given our planetary resources at a growth rate of only 1%?

    
    
    
    
    
    
    Now in the real world, consumption curves are modified by economics and so may look something like this.

    And this makes trend extrapolation difficult.

    However, in the case of resource usage (as opposed to market economics), underlying exponential growth is usually the basis for resource usage, unless some new technology comes into play that makes the use of that resource more efficient.

    
    

    A good example of this is provided by the pattern of historical energy consumption in the US.

    

    Note that this energy usage above includes energy for heating, cooking and transportation. These are large energy sinks.

    In more "modern" times, an increasing fraction of our energy use is devoted to generating electricity: