There comes a time in every endeavour when it becomes imperative that one does a bit of arithmetic. As the late John McCarthy used to say, “Those who refuse to do arithmetic are doomed to speak nonsense.” Doing a bit of arithmetic is important not only to avoid nonsense but also to get a feel for what we normally would miss since our brains are not naturally attuned to figuring out the state of the world without the help of numbers. In this piece I lean upon a few sums to help me understand the broad implications of one facet of economies — their growth rates.

The notion of the gross domestic product (GDP) of an economy has become a familiar one. Yet it is of fairly recent vintage. It was developed by Simon Kuznets for a US Congress report in 1934, and “refers to the market value of all final goods and services produced within a country in a given period. GDP per capita is often considered an indicator of a country’s standard of living,” as the wiki explains. (See this for more on GDP, its measurement and its meaning.)

GDP is an aggregate measure of economic activity and it should not be taken as a comprehensive measure of social well-being or happiness or any such abstract notion. GDP is like the annual income of a person. While personal income is an indicator of how economically successful a person is, it does not define the person in any comprehensive way. But knowing that a person is doing well economically tells us whether he has the material wherewithal to live a decent life or not. This holds true for a country also. If the GDP is below a certain threshold, it is unlikely that the people are prospering.

One of the features of the modern world is that GDP grows with time. GDP growth is a recent phenomenon, actually. Over pretty much the entire existence of human civilization, there was scant progress in the material standard of living. From generation to generation, people lived pretty much like their ancestors did. Only after the Industrial Revolution (mid-1700s) did things change – and changed astonishingly rapidly compared to the past.

Instead of things improving at the rate of 0.01 percent or so, the average long term rate of growth of the production of stuff (goods and services) began to be in the low single digits. That’s a rate two orders of magnitude higher than before the Industrial Revolution. The implications of that higher growth rate are impossible to overstate. It is hard for us to get our minds around the idea of exponential growth. So we have to do the arithmetic, and in some cases, even after doing the sums, the results still strain belief.

So let’s do the numbers. I want to do a counter-factual exercise. Start off with India’s per capita GDP (estimated in 2010 US$) in 1947. I assume that to be $250. I assume the population of India in 1947 to be 350 million. How accurate are these numbers? I think they are ball park figures, and even if they are off by 10 or 20 percent, our exercise is robust and the conclusions do not critically depend on the starting numbers since we are more interested in estimating magnitudes rather than exact figures.

To begin, I hunt around for a pencil and some paper. OK, got it. Now I assume a per capita GDP growth rate of 2.1 percent per year. Multiply that with $250, the per capita GDP for year 1, and I get $255 as the per capita GDP for year two. I assume 2 percent population growth rate. So in year 2, the population is 357 million, and the GDP in year 2 is $89.25 billion (the product of population 357 million times the $255 per capita GDP.) For year 3, I repeat the exercise. Then I realize that doing arithmetic by hand is not very much fun. It is tedious and error-prone. So I start looking for an easier way. Ah ha! Let’s use a spreadsheet.

Spreadsheets are fun, if you know how to use them. I don’t. But then I rarely use them. One can do rough estimations in one’s head but when it comes to long series of calculations – and especially when one wants to do various scenarios – it is best to use a spreadsheet. Anyway, to cut a long story short, I pulled out the Google spreadsheet. (The link to my masterpiece of a spread sheet appears below.)

OK, so here’s what I did. Starting with $250 as the per capita GDP at year 1, at 2.1% growth rate, by year 62, I get a per capita GDP of $900. That looks reasonable to me. If year 1 is 1947, year 62 is 2009. (Note that I am using actual GDP numbers, not “Purchasing power parity” numbers since the PPP numbers don’t make any sense.) I am using 2% as the annual rate of growth of population since at that rate, 350 million in year 1 grows to around 1.2 billion in year 62. That is approximately the population of India.

Here are the numbers I crunched. GDP for each of the 62 years. For 2009, the GDP of India works out to be $1.061 trillion, which is the product of 1.2 billion population and $900 annual per capita income. That’s about right. Then I repeated the exercise with the same population growth rate but a different per capita GDP growth rate: 6% instead of 2.1%. With that, in 2009, I get a per capita GDP of $9,300. That’s an order of magnitude higher than $900 number. That is the per capita income of a middle-income country.

Then I did another thing. I computed the cumulative GDP. With 2.1% per capita GDP growth rate, the cumulative GDP of years 1947-2009 works out to be $24.5 trillion. Compare that to with 6% per capita GDP growth rate: the cumulative works out to be $143 trillion. That’s a difference of $120 trillion.

Let’s ponder those numbers for a moment. What do they mean? What are the implications? Is 6% growth of per capita GDP possible for such an extended period? What would have been possible given that? What about poverty? Global power and influence? What about the impact on the lives of hundreds of millions of people? In the next bit, we will discuss those and other bits.

(Click to see the spreadsheet.)

Go to part 5 of this series where I calculate the loss.

The MindsetWednesday February 8, 2012 / 10:57 pmwaiting for the next bit …..^-^

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MallikarjunaThursday February 9, 2012 / 2:12 amAwesome,

What could have been & What we are?

Looking forward to next part.

I’m forwarding this (Link & Spreadsheet) to all my friends.

mkssrajasthan@gmail.com

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SuramyaThursday February 9, 2012 / 5:16 pmAtantu,

Great articles. Thanks for spreading the knowledge.

FYI.. In the spreadsheet, you have calculated numbers assuming 6% GDP growth, but the title of the column is 7%.

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RCThursday February 9, 2012 / 6:03 pmBut what about numbers in PPP, Sir?? (Toung in cheek 🙂 )

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