I imagine one could say they had a communist style 'plan-economy' to simplify, right?

No? I'm not sure why you'd think that?

The Mediterranean economy under the Romans is sometimes called "proto-capitalist" or "proto-industrial," both of which terms probably put too fine a point on it. The Roman state was, even under the Principate, remarkably decentralized. Even under Augustus and later emperors provincial magistrates, who had been almost entirely left to their own devices in the Republic, were largely allowed to do whatever they wanted within fairly general guidelines. When Pliny was governor of Bithynia he frequently was unsure of what to do about things because he had no actual instructions or orders, so he wrote letters back to Trajan to make sure that his policies aligned with Trajan's wishes--most of Trajan's letters basically say "yeah sure that's fine, use your discretion." And by Trajan's time the empire had become much more centralized than under earlier emperors! Trade flowed through the Mediterranean at levels unthinkable until the Modern Period, but not because the emperors were directing it.

The Roman state intervened in the supply and demand of pretty much only one part of the economy, namely the grain supply to the city of Rome. And that intervention was neither very direct nor very strict. In the middle and late Republic state-subsidized grain stores had been instituted, eventually in 58 to be distributed gratis at the rate of 5 modii/month (enough to feed one laborer comfortably, but no more) to the heads of household of, by the end of the century, a really rather restricted number of families. The point was less to provide a free grain ration and more to help stabilize the grain market, which in a pre-Green Revolution agricultural economy could massively fluctuate due to a number of causes. The vast majority of the Roman people's grain had to be purchased on the market, and the provision of a stable grain supply helped keep prices from bouncing all over the place. Moreover, under Augustus and especially Claudius laws and edicts were passed that instituted punishments for private sellers who hoarded their grain to create artificial scarcity. Claudius also worked to incentivize cargo ship owners to carry state grain--the state had no way of transporting its grain by itself, which ought to demonstrate how far from a "command economy" the Roman economy was--by providing them with subsidies to offset the possible losses to storms. But this can hardly be called the regulation of supply and demand. The state was, effectively, just another consumer of grain provided and transported by private middlemen. Even in provinces where grain was provided as part of provincial tribute and therefore did not have to be purchased by the state it was private middlemen who stockpiled it and transported it.