Yes, the state could not afford to equip soldiers with bronze arms due to their prohibitive cost and the state's relative lack of revenue. Instead, it would probably decree that those fulfilling a certain property qualification would be bound to fight (alongside the aristocrats who had fought of their own volition since the dark ages) on pain of losing their citizenship.

There was, to my knowledge, no such thing as 'units'. We have phalanges , or ranks, and the first manifestations of the phalanx.

Source: Snodgrass, A. (1980) Archaic Greece: The Age of Experiment pp 101f