Well, neither is really applicable. Both are economic philosophies that didn't really exist at the time. But, I understand what your question is getting at.

They were more socialist than communist, but as I said neither term really explains it.

The system was based on bartering, taxes, and providing for yourself. The government provided welfare, but this wasn't done in a way that we'd identify as socialism in modern day.

Their economy is what is described as a 'vertical archipelago' traditional economy. It roughly means an agriculturally based system of public service, which they called "M'ita". Services were conducted by men in the M'ita. M'ita was divided by agriculture, fishing, military service, etc. They worked for the Empire, but were able to provide for their families.

The 'State' did not own everything, as in communism, but did not redistribute wealth, as in socialism.