Saturday, January 22, 2011

Generation of Work and The Wealth of Nations

If you've been following my previous posts about maximizing the rate of return on work invested, you may be asking yourself the following questions:
a) Which country produces the most work?  (force times distance definition of the word 'work')
b) Which major country has the largest rate of return on work invested?
Before reading on, you probably can guess the answer to both of these question, and most likely your guess is correct. My calculations for each of these questions are below.

I recently went through the data collected on energy use per country per year over the last decade (BP's statistical review of energy). I estimated the total amount of work generated per country per year for each year between 2000 and 2009, for eight major countries: the U.S., China, India, Russia, Japan, Canada, Germany and France. (The UK and Brazil are next on my ToDo list.) I estimated the total work generated by summing the following:
1) Electricity generated that year
2) Work done by vehicles against friction (this value was calculated by multiplying the consumption of petroleum by the average efficiency of 20%. I did not take into account efficiency differences between countries or the fact that there is consumption of petroleum for non-work purposes, such as production of plastics.)
3) Estimated that 70% of natural gas consumption went into generating non-electrical work with an efficiency of 20%. (This includes natural gas for vehicles, but mostly natural gas heating of one's home as an offset for the electricity that would have been required to operate a heat pump to heat one's home during the winter.)

Items not included in the summation, that should be included in a more detailed analysis, are: a) work done by humans & b) work done by animals associated with human projects (horses used for farming, etc...) Rosen and Scott estimated in 2003 that humans consume 20 times less exergy in food than the exergy consumed by the machines they use. So, ignoring human work is a safe assumption.

I'll have more time in the future to refine the estimates of total work. In the mean time, the graph below shows my estimates for the total work done per country:

What you can see is that China's generation of work has been increasing rapidly over the last decade whereas almost all of the other countries, except India, have been stagnant. It appears that China may pass the US as the country that produces the most total amount of work within the next decade, depending on whether it can maintain the rate of increase. I've also graphed the average rate of return on work invested between 2000 and 2009. The average value was calculated using the following formula:

 Rate [%/yr] =  {(Work Generated in 2009)/(Work Generated in 2000)}^(1/9)  - 1

This is the formula for the average rate of return on an investment if the rate is compounded yearly for nine years  (i.e. from 2000 to 2009). The average rate of return is graphed below:

It's easy to see here that China has the largest rate of return of any of the major countries, followed by India. The rate of return from the US, Japan, German and France is zero or less than zero. This means that these countries are not growing, and this is a major problem. In my earlier posts, I've pointed out that money is the capability to do work (in the force times distance sense of work.)
Electricity Backed Currency
[Note that money is not the same as value or utility, and I'll write a post on this topic in the next few weeks. So, value/utility is not the same as the capability to do work, just as the price of an object is not equal to the amount of money/work spent creating the object.]

So, if money is the capability to do work, then the following is true:    the Wealth of a Nation is equal the amount of work it is capable of generating, and hence the wealth of a nation can be calculated by measuring the amount of work it generates each year.

So, I wanted to compare the total work generated with the country's GDP. To do so, I looked up the values of GDP from the World Bank in 2009 and compared these values with the values I calculated for the total work. Often, economists take a ratio between the electricity generated and GDP to determine the overall efficiency of converting electricity into $'s.

However, here's the problem with the standard way of thinking.
1) Work comes in many different forms, and there's no reason to just choose electrical work. For example, there's also the work done by a car against a friction or the work done by humans moving about in the world.
2) The wealth of a nation is equal to the work it generates each year. There is no efficiency factor. The wealth is the work it is capable of doing.

So, I've plotted below a graph that compares the 2009 values of GDP (in trillions of USD) against the total work I calculated that each country generated in 2009. What I found was that the data was rather scattered. I could roughly fit a straight line through the data points for the U.S., Japan, Germany and France, but the data points for the other countries were far away from the line. While I calculated that China's total work was only 68% less than the U.S.'s total work, the World Bank estimated that China's GDP was still three times smaller than the U.S.'s GDP. While the World Bank thinks that China's economy is roughly the same size as Japan's, I estimate that it is twice as large as Japan's economy.

The data points for Russia and India were also far off from the line set by the U.S., Japan, German and France. This leads me to the following conclusion:  either a) my calculations for the total work are incorrect, b) my assumption that money = work is incorrect, c) the calculations of GDP by the World Bank underestimate the GDP of non-Western countries, such as Russia, India and China, or d) some combination thereof.

My guess is that the answer is some combination of a) and c). I recognize that my calculations are very rough, but I also recognize that it's really easy to miscalculate GDP in economies with significant rural or collectivized populations. This is the case for India, China and Russia, but not for the U.S., Canada, Japan and western Europe. I don't know why the data point for Canada is so far below the line, given that I would have expect it to be in line with other Western countries.

In conclusion,
1) The U.S. is the wealthiest country, but perhaps not in one decade.
2) China has the largest rate of return on investment of the work it generates (of the eight countries I studied.)
3) The calculations of GDP significantly underestimate the wealth of China, India, and Russia.
4) It is likely that China's economy is actually twice as large as Japan's and that Russia's economy is comparable to Japan's.

Let me know what you think.

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