Economic Growth Over the Past 500 Years
One Hundred Interesting Mathematical Calculations, Number 4
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
Comments
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...
Brad DeLong
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 |
