Baby Boomers Need to Understand the Exponential Function

In his State of the Union address last night President Obama promised to double exports in 5 years. Is that possible?

Normally this would not worry me too much but I recently watched a series of 8 YouTube video of Dr Albert A. Bartlett Professor Emeritus at the University of Colorado lecturing on the exponential function.

His opening statement is,

“The Greatest Shortcoming of the Human Race is our Inability to Understand the Exponential Function”.

To those that may be mathematically challenged it is all about things that increase at a constant rate and what happens over the long term.

Export Growth Year on Year 1960-1980

He tells us if we can remember just one thing from the lecture let it be the number 70. And when someone tells you your investment returns “on average” will grow at 7% a year you just divide 70 by 7 and that will give you the time it takes to double your investment. In this case 10 years.

Or you can say how long will it take my investments to double if my return is 7% a year. Answer is 10 years.

I urge you to grab a coffee and watch all 8 videos as he explains in simple language the implications of the exponential function.

So when President Obama said he is going to double exports in 5 years I mentally divided 70 by 5 and came up with 14% almost fell off my chair.

What he is saying is that he is going to increase US exports by 14% per year for the next 5 years.

I thought I should check the Export performance of the US over the last few years.

So I decided to check the US Export figures and found the “US Trade in Goods and Services Balance of Payments Tables” since 1960.

I added the % Export Growth Year on Year Column figures and noticed that export growth is quite volatile but in some years has reached 20-30%.

I cannot find a figure for 2009. The US Export fact sheet only states some monthly figures but does admit,

Although the decline in year-to-date figures from 2008 to 2009 has been significant, the monthly figures do show signs of stabilization in U.S. goods and services trade.”

On the surface it looks like Obama can double the exports in 5 years when you look at the growth from 2003 to 2008 when exports increased by 80%. But I wonder how much of that was Banks and Financial Institutions selling “virtual” products and services overseas, products like CDOs and other complex derivatives with meaningless financial numbers attached to them  :-(. This business has evaporated and may never come back.

The other problem is even if he achieves it he might be setting the world up for another boom and bust in 5 years. How will he maintain the 14% growth rate in exports AFTER the five years? I think it would be unsustainable unless he does what China does?

They loan money to poor countries to buy Chinese Goods. I wonder how that will work out in the long run. The US and other western countries have done that on and off for years too.

Isn’t everyone saying the high growth rates are unsustainable because we have Peak Oil, India and China becoming the worlds largest economies and climate change to contend with?

The Professor talks about the electrical energy consumed in the US. It has doubled on average every 10 years. A quick division into 70 shows it has grown at about 7% a year. What will be the energy needs to ensure Obama can double the US exports?

The Professor makes this sobering statement,

“The growth of any doubling time is GREATER THAN the TOTAL of ALL the PRECEDING GROWTH” (In the table below for instance the double from 4 to 8 is greater than the total of 7 already on the board)

Every time the quantity doubles it take more than the total of all the preceding growth. Grains of Wheat on a Chess Board example

Square Number Double Grains on each Square TOTAL Grains on Board
1 1 1
2 2 3
3 4 7
4 8 15

Even if he could grow the economy at 14% a year he is going to need lots of energy and resources and that will upset his Democratic base and the Greens and the Climate Changers.

Always remember the number 70 when listening to politicians and financial people.

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