it appears likely that at its peak the classical economy was almost as large as that of Western Europe on the eve of the Industrial Revolution...in the more fertile districts of southern Britain and northern Gaul rural population density in the Late Iron Age and the Roman period was as high as in the late seventeenth-century...
The volume of and extent of clalssical trade at its peak in the first centuries AD is visible in a well-preserved ceramic record of mass-produced tableware and oil lamps, and in the dumps containing tens of thousands of amphorae that were discarded when theirir contents were decanted into other vessels for transshipment into the interior. The archaeological record, then, indicates a robust and specialized economy
...renewed analysis of the corpus of Merovingian and Carolingian documents bearing on the status of persons and property in Merovingian and Carolingian Gaul yield a far less catastrophic narrative of the early medieval transition than the one that scholars have constructed from late Roman and early medieval Christian polemics. In particular, the revisions indicate significant political, administrative and economic continuity from the fourth through ninth century, sustained by a surprisingly literate political and administrative elite...While the volume of trade contracted dramatically after 450 AD, the links were never severed.
Meir Kohn pointed me to the paper. Kohn views trade in Smithian rather than Ricardian terms. That is, take it as given that there were high transport costs, which were a barrier to long-distance exchange. Still, you do not necessarily need huge differences in relative factor productivities to generate trade. You can motivate trade with gains from division of labor and the extent of markets.
I seem to have a mental block against a story of a market economy in the Classical period. If Rome imported a lot of products from other parts of its empire, then those regions must have been productive. If, say, Egypt was very productive in grain, and if trade was voluntary, then either Egypt should have enjoyed a high standard of living (with Rome's comparative advantage coming from cheap labor, like China's today) or Rome had products to offer Egypt that the Egyptians really valued.
My instinct--and I seem to be wrong about everything on this topic--was that the flow of goods to Rome was mostly involuntary, consisting instead of plunder and taxes. I have a picture of a wealthy Roman center and an impoverished imperial periphery. Grantham's view is that the periphery also flourished.
Furthermore, Grantham sides with those who view the post-Roman period as a "transformation" rather than a collapse. If we put this all together, we have a picture of an economy that functioned reasonably well in the Classical period, followed by a decline but not a collapse in the Medieval period.
As Kohn put it in his email to me, "I'm afraid he doesn't support your position."
UPDATE: Speaking of medieval times, a reader pointed me to Peter Klein's post about medieval schools that included courses relevant to business.