The way that Perry Anderson describes it in his book, Passages From Antiquity to Feudalism, basically everyone in an urban area is a landowner/proprietor.
“The Graeco-Roman towns were never predominantly communities of manufacturers, traders or craftsmen: they were, in origin and principle, urban congeries of landowners. Every municipal order from democratic Athens to oligarchic Sparta or senatorial Rome, was essentially dominated by agrarian proprietors. Their income derived from corn, oil and wine – the three great staples of the Ancient World – produced on estates and farms outside the perimeter of the physical city itself. Within it, manufactures remained few and rudimentary: the range of normal urban commodities never extended much beyond textiles, pottery, furniture and glassware”
But what about servicing those landowners? What, if any, sort of economy existed for that purpose?
What is the tie period you are interested in? I'm woefully ignorant about the classical period but can talk a bit more about the Hellenistic and Roman period. Are there any aspects of the urban economy you are particularly interested in?
I haven't read any of Perry Anderson, but assuming you represent his claims correctly I wouldn't take him seriously. There were always plenty of shopkeepers, laborers, and the like in the ancient city, and I wouldn't call a view that cities were primarily inhabited by absentee landowners outdated only because no serious scholar of the ancient economy has every presented them as such.