December 13, 2002
One Hundred Interesting Mathematical Calculations, Number 4

#### One Hundred Interesting Mathematical Calculations, Number 4: Economic Growth Over the Past 500 Years

Suppose that Virginia Postrel is an average contemporary American, with daily economic resources to spend of \$100 or so, and that she can buy a five-pound bag of flour containing 7500 calories for \$0.69. What fraction of her daily economic resources does she have to spend in order to obtain one calorie?

This calculation is simple. If \$0.69 gets her 7500 calories, then \$0.69/7500 = 9.2 x 10-5 dollars will get her one calorie. With daily economic resources of \$100, that amount is equal to 9.2 x 10-7 of her daily economic resources.

Now consider a typical person among our ancestors of half a millennium ago--a Eurasian or African peasant circa 1500. Something like three-quarters of the value of what they and their villages produced was foodstuffs. They were close to the Malthusian edge, and that three-quarters of their production was just enough to get them an average diet of perhaps 1875 calories a day. What fraction of their daily economic resources did they have to devote to the task in order to get one calorie's worth of nourishment?

If getting foodstuffs took 3/4 of their economic resources, and if that 3/4 of their economic resources get them 1875 calories, then the fraction of daily economic resources to get one calorie would be (3/4)/1875 = 4 x 10-4.

How much larger a fraction of daily economic resources did our ancestors of 1500 have to spend to get calories than does Virginia Postrel today? The answer is straightforward. Simply divide (4 x 10-4) by (9.2 x 10-7). The answer is 434.8. That--on the wheat-flour standard--is a measure of economic growth since 1500, of how much richer we are today than our ancestors of half a millennium ago.

Do you think this number--about 435--is an overestimate or an underestimate of "true" economic growth since 1500? Why?

Posted by DeLong at December 13, 2002 11:30 AM | Trackback

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Over 500 years, a 438.3-fold increase represents a meager 1.224% annual growth rate. That is

(1.01224)^500 = 438.3

Many economist would find a 1.2% annual growth rate to be a bit anaemic, no?

But, over the long haul, even a relatively "anaemic" rate of growth can produce some subtantial benefits.

(Does this count as yet another "interesting math problem"?)

Posted by: Jacques Distler on December 14, 2002 12:07 AM

When did civilization invent the lost leader and is it the modern the ancient roman practice distributing grain to the mob? Now there's a question for the new SAT short essay section.

I gather that during the middle ages the technology for making bread was lost and they ate only gruel. I believe that was in "On Food and Cooking", but I don't see it there in a casual glance. This makes me wonder a bit if picking the 1500 as a starting point isn't telling us more about what a back water Europe was at the time.

There is a nice chart showing the price of wheat in units of real wages in Braudel's Structures of Everday Life (page 135 in my copy). It reports that the labor to buy a unit of wheat was reasonably stable from 1400 thru 1540. At that point it began rose to a peak in 1710 and then slowly fell back, it didn't return to the price levels of the 1500's until the 1920s. There are many thought provoking charts of this kind in Braudel's work.

Sadly work like his work is PI (pre-internet) and requires some calories to get over it's barrier to entry.

Posted by: Ben Hyde on December 14, 2002 07:04 AM

>>I gather that during the middle ages the technology for making bread was lost and they ate only gruel.

No. The rich ate bread. But making bread is rather complicated: you've got to cut the wheat, thresh the wheat, mill the wheat, find the yeast, mix the wheat with the yeast and the water, knead the dough, let the dough rise, knead the dough again, let the dough rise again, and cook the dough.

If you aren't rich in 1500, you may well not have the available work time to do this--in which case it's back to gruel...

Posted by: Brad DeLong on December 14, 2002 07:30 AM

>Over 500 years, a 438.3-fold increase represents >a meager 1.224% annual growth rate. That is

>(1.01224)^500 = 438.3

>Many economist would find a 1.2% annual growth >rate to be a bit anaemic, no?

Yeah but the calculation becomes pretty impressive when you realize that the vast bulk of that growth actually took place in the last 200 years instead of the last 500.

That makes the growth rate closer to 3%.

Posted by: James Chapman on December 14, 2002 04:51 PM

A friend passes on this comment:

It's too late in the evening for me to suss this out for myself, but how does this square with the notion that hunter-gatherers typically spend (I'm making this up) 3-4 hours a day to meet their basic needs, while agriculturalists etc, spend far more?

Jared Diamond (Guns, Germs, and Steel, et.al.) makes the point that _of course_ no one in the developed world would trade their lifestyle for that of a Kalahari bushman. But how much worse off would an Indonesian rice farmer be?

Posted by: jda on December 15, 2002 07:43 AM

Re:

>>Jared Diamond (Guns, Germs, and Steel, et.al.) makes the point that _of course_ no one in the developed world would trade their lifestyle for that of a Kalahari bushman. But how much worse off would an Indonesian rice farmer be?

Perhaps not at all. There is a respectable argument (I don't know whether it's true or not, and neither does anybody else, but it is respectable) that the invention of agriculture was a disaster for the standard of living of the median human.

Posted by: Brad DeLong on December 15, 2002 02:00 PM

Or, perhaps, agriculture, rather than being a disaster (in the sense of a mistake, in the sense that there was some other, better, option available) simply became necessary. Perhaps rising population meant that a hunter/gather existence would no longer bring in enough food to feed the people. Or perhaps agriculture was a disaster for the common man but a boon for the elite, perhaps it was something inflicted on the population by the rulers of that population. To increase total wealth and concentrate it upwards means improvement for the lives of the rich, even if no one else.

Braudel says that for the average European peasant life got harder from the 1590s to the 1820s, or perhaps even the 1840s. Then, finally, things turned around and began to improve.

Posted by: Lawrence Krubner on December 15, 2002 08:12 PM

Well, that certainly squares with the fact that the Indians who came into contact with European settlers, although interested in useful manufactures like guns etc., were not particularly keen on giving up their nomadic hunter-gatherer ways, even in full view of the "benefits" of settled agriculturalism...

Posted by: jimbo on December 16, 2002 07:30 PM

Surely the problem here is assuming that Calories are a good approximation for Quality of Life.

Most of us Westerners are trying (unsuccessfully) to reduce our intake of calories; and our failure to do so is the cause of many health problems.

So a more realistic calculation would be to work out the price of sufficient calories for the lifestyle 500 years ago. And the price of sticking to the equivalent now while supplying the rest of our dietry requirements (either through buying more expensive health foods or membership of a gym to work off that excess)

Posted by: phil jones on December 17, 2002 05:19 AM

This is probably an underestimate of the growth rate. Not only do I have to spend less of my resources per calory in 2003 than I would have had to in 1500, but I also have to spend less of my resources per automobile, computer, telephone, etc. Obviously, back in 1500 even 100% of my resources wouldn't have been able to get me any of those things because they hadn't been invented. These technological goods are infinitely cheaper today than they were in 1500. This is a common criticism of using GDP growth as a measure of economic growth. GDP is a measure of quantity, not quality.

Posted by: Dan on January 17, 2003 11:03 AM

This is probably an underestimate of the growth rate. Not only do I have to spend less of my resources per calory in 2003 than I would have had to in 1500, but I also have to spend less of my resources per automobile, computer, telephone, etc. Obviously, back in 1500 even 100% of my resources wouldn't have been able to get me any of those things because they hadn't been invented. These technological goods are infinitely cheaper today than they were in 1500. This is a common criticism of using GDP growth as a measure of economic growth. GDP is a measure of quantity, not quality.

Posted by: Dan on January 17, 2003 11:06 AM

>>>
This is probably an underestimate of the growth rate
>>>

Or it greatly overstates it. It all depends on what you want to measure.
Sahlins' research showed that the Bushmen of the Khalahari worked only about 20 hours a week. They had a great deal of leisure time. To make an estimate of how much that leisure time is worth in a monetary economy you'd have to make some kind of estimate. There would be several ways of making that kind of estimate, several methodologies that you could use, and, this is important, many of them would be valid, yet they would yield very different results. For instance, do you compare their 20 hours of work with what an average American works (44 hours a week, last time I checked)? Do you multiply those hours by a standard American wage? If not, what amount would you choose? Why?

Progress is not linear. Although much has been gained over the last 500 years, other things have been lost. Species have gone extinct at an incredible speed, a speed at least an order of magnitude above the average background speed of the last million years. How do you put a price on that? Is it necessary to? Some leisure, or at least certain types of leisure, have been lost. Women from 3rd World countries complain that there is no community in America, no web of support to help in the task of raising children. If it is true that modern life is more atomized and less community oriented, then is this a loss, and should it be subtracted from the total of overall progress? How would you measure it?

So much of all pre-industrial life was informal, I've often wondered how any of it can be formally measured.

In 1776 only 22% of the American population participated in the monetary economy, but that number had reached 66% by 2000. Therefore when one speaks of the median wage in America, it refers to an unrepresentative group (wage earners were a minority) in the early decades, but an increasingly representative group in the later decades. Is it fair to compare the two numbers (the median wage of 1776 compared to the median wage of 2000)?

I've spent the last 15 years puzzling over the same question: things have certainly changed, and some things have been lost, and some things have been gained, but how can you measure it?

Posted by: Lawrence Krubner on February 2, 2003 05:40 PM

>>>>>
In 1776 only 22% of the American population participated in the monetary economy, but that number had reached 66% by 2000.
>>>>>

Really poor writing on my part. The numbers 22% and 66% refer to the number of people who work for money, not the number, obivously, that participate in the monetary economy. That number, I'm sure, is just about 100%.

Posted by: Lawrence Krubner on February 15, 2003 02:32 PM

>>>>>
In 1776 only 22% of the American population participated in the monetary economy, but that number had reached 66% by 2000.
>>>>>

Really poor writing on my part. The numbers 22% and 66% refer to the number of people who work for money, not the number, obivously, that participate in the monetary economy. That number, I'm sure, is just about 100%.

Posted by: Lawrence Krubner on February 15, 2003 02:34 PM