Arnold Kling isn't buying into this. He writes,"I just don't believe that over a thousand years ago human beings had the trustworthiness, discipline, numeracy, and institutional base to engage in what we would today recognize as free trade." I'm not sure why. In his book, The Origins of Human Society, Peter Bogucki writes
One of the major advances in Maya research has been the identification of early trading networks, since the procurement of status goods such as jadeite, marine shell, quetzal feathers, and obsidian was linked with the emergence of elites. The site of Cerros, on the Caribbean coast of Belize, is particularly significant (Robertson and Friedel 1986). It lies on Chetumal Bay near the mouths of the New River and Rio Hondo, which lead into the interior of Belize. Not only was it well-suited to engage in coastal trade between the salt-producing areas of Yucatan to the north and the source area of obsidian and jade in Guatemala and El Salvador to the south, but from this location goods could also move into the interior of Belize and northern Guatemala. (p.348)
I'm willing to be wrong. But here is my alternative to the view that the Mayans (or the Romans) had a market economy.
Way back when, most people had to live primarily on what they produced within the household. Within extended families and small villages there was also some reciprocal exchange. But no markets.
Then one day, a clan living near an oasis or a salt source said, "Hey. Everybody needs this stuff. If we take control of the access to it, then we can collect a toll, and we won't have to work so hard any more." Thus was born what Mancur Olson called a "stationary bandit."
In some locations, it took a relatively large organization to control access to critical resources. In order to exercise control, the stationary bandits had to evolve to be relatively well-organized--heading in the direction of what we would now term "progress" and "civilization."
This civilization evolved further when, in some areas, stationary bandits formed associations and hooked up with roving bandits, creating empires. The roving bandits collected booty from distant neighbors and the stationary bandits collected tolls from local subjects. The booty and the tolls took the form of goods and slaves. If the empire got really big and powerful, the goods and slaves could be distributed and traded in a central location.
You might call the central location where the bandits distributed and exchanged stuff a "market." But it was not a market in the sense that people voluntarily produced the goods in order to sell them for cash into the market. Instead, people had their stuff stolen, and when a lot of stolen goods were collected in one place, the thieves had a "market."
Again, I'm willing to be wrong. And it could very well be that the difference between voluntary trade and stolen goods is more of a continuum than a sharp distinction. It could be that markets have always been a mix of goods produced for voluntary trade and stolen goods. But for what it's worth, my picture of pre-modern markets is that they consisted mostly of stolen goods. My picture of modern markets is that they consist mostly of goods produced voluntarily with the intent of selling.