Economics in the pre-industrial era

I had some questions regarding economic development before the industrial revolution. First, how do we measure growth? Like, we obviously can’t say “Rome’s GDP grew at 2.5% in AD 117,” but what’s our proxy? Second, how do we measure relative wellbeing and development statuses of given societies, say of Imperial Rome compared to the Islamic world in the Golden Age? Finally, how good are our sources for this kind of thing and what are they?
 
According to: https://en.m.wikipedia.org/wiki/List_of_regions_by_past_GDP_(PPP)

In the absence of sufficient data for nearly all economies until well into the 19th century, past GDP cannot be calculated, but at best only roughly estimated. In a first step, economic historians try to reconstruct the GDP per capita for a given political or geographical entity from the meagre evidence. This value is then multiplied by estimated population size, another determinant for which as a rule only little ancient data is available.

A key notion in the whole process is that of subsistence, the income level which is necessary for sustaining one's life. Since pre-modern societies, by modern standards, were characterized by a very low degree of urbanization and a large majority of people working in the agricultural sector, economic historians prefer to express income in cereal units. To achieve comparability over space and time, these numbers are then converted into monetary units such as International Dollars, a third step which leaves a relatively wide margin of interpretation.

The formula thus is: GDP (PPP) = GDP per capita (PPP) x population size

It should be stressed that, historically speaking, population size is the far more important multiplier in the equation. This is because, in contrast to industrial economies, the average income ceiling of premodern agrarian societies was quite low everywhere, possibly not higher than twice the subsistence level.
 
I would say using population as a compass for.ore industrial economics is.......complicated. certainly you can see China and India and say their economies were massive but they weren't productive, at least not on the level that the European and Middle Eastern Economies. As such the answer is complicated. I will write a more detailed answer later.
 
Generally speaking, subsistence, where you have enough wheat-equivalent to live and work as adult (about half of children died) - note, that you can suffer from bad nutrition, you need to be able to work your field and remain alive, not be in good health - lies around 400$ (1990 purchasing power parity $) per year.

If I remember this right. Italy around the peak of the Roman Empire is estimated by scholars at about 2.1 times subsistence; Byzantine Empire around 1000 AD at around 1.7 subsistence. Somewhat around 800$ per person annually (but 1990 Int$, as Maddison used these), if we must try to express in dollars (so 66$ per month).
 
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