In other traditional economies, some sort of private property is respected

A traditional economic system is—here's a shocker—shaped by tradition. The work that people do, the goods and services they provide, how they use and exchange resources… all tend to follow long-established patterns. These economic systems are not very dynamic—things don’t change very much. Standards of living are static; individuals don’t enjoy much financial or occupational mobility. But economic behaviors and relationships are predictable. You know what you are supposed to do, who you trade with, and what to expect from others.

In many traditional economies, community interests take precedence over the individual. Individuals may be expected to combine their efforts and share equally in the proceeds of their labor. In other traditional economies, some sort of private property is respected, but it is restrained by a strong set of obligations that individuals owe to their community.

Today you can find traditional economic systems at work among Australian aborigines and some isolated tribes in the Amazon. In the past, they could be found everywhere—in the feudal agrarian villages of medieval Europe, for example.

Reference: http://www.shmoop.com/economic-systems/types.html