In the modern version of an old legend, an investment banker asks to be paid by placing one penny on the first square of a chessboard, two pennies on the second square, four on the third, etc. If the banker had asked that only the white squares be used, the initial penny would have doubled in value thirty-one times, leaving $21.5 million on the last square. Using both the black and the white squares would have made the penny grow to $92 million billion.
People are reasonably good at forming estimates based on addition, but for operations such as compounding that depend on repeated multiplication, we systematically underestimate how quickly things grow. As a result, we often lose sight of how important the average rate of growth is for an economy. For an investment banker, the choice between a payment that doubles with every square on the chessboard and one that doubles with every other square is more important than any other part of the contract. Who cares whether the payment is in pennies, pounds, or pesos? For a nation, the choices that determine whether income doubles with every generation, or instead with every other generation, dwarf all other economic policy concerns.
You can figure out how long it takes for something to double by dividing the growth rate into the number 72. In the twenty-five years between 1950 and 1975, income per capita in India grew at the rate of 1.8 percent per year. At this rate, income doubles every forty years because 72 divided by 1.8 equals 40. In the twenty-five years between 1975 and 2000, income per capita in China grew at almost 6 percent per year. At this rate, income doubles every twelve years.
These differences in doubling times have huge effects for a nation, just as they do for our banker. In the same forty-year time span that it would take the Indian economy to double at its slower growth rate, income would double three times—to eight times its initial level—at China’s faster growth rate.
From 1950 to 2000, growth in income per capita in the United States lay between these two extremes, averaging 2.3 percent per year. From 1950 to 1975, India, which started at a level of income per capita that was less than 7 percent of that in the United States, was falling even farther behind. Between 1975 and 2000, China, which started at an even lower level, was catching up.
China grew so quickly partly because it started so far behind. Rapid growth could be achieved in large part by letting firms bring in ideas about how to create value that were already in use in the rest of the world. The interesting question is why India could not manage the same trick, at least between 1950 and 1975.