I'll address the household model first, because it's the first one to have come into existence. In the household model, every family is a self-sufficient community. The head of the household (originally Adam) provides leadership. He owns all the property, and he assigns duties or offices. I think that we can assume that Adam assigned Cain to the office of farmer so that the world's first household would have a supply of grain. He then assigned Abel to the office of shepherd to provide a supply of milk and wool (no meat until after the Flood). I'm sure that various daughters were assigned to care for the fowl (for eggs) and to process the grain, milk, and wool (to get bread, butter, cheese, and fabric for clothing and shelter). And of course the producers Cain and Abel were responsible for returning to God the firstfruits of their produce. All in all, we can visualize a smooth-running (until the murder of Abel) household that made efficient use of the land into which Adam and Eve were driven from the Garden of Eden.
Households may legitimately expand pretty dramatically beyond this. A household may include servants (who are not family and are therefore paid for their service to the household) and various employees who contribute such products and skills as specialized cooking, metalworking, mechanical arts, printing, and, of course, preaching and teaching. The point is, each household produces everything it needs to exist comfortably. It may import raw materials and products, but these are always extras.
The village is much like the household except that it is de-centralized. Authority lies not with the head of the household but with some form of government (of course fatherhood or patriarchy is itself the first and most basic form of government), whether elected or hereditary or whatever else. A village is made up of households, but each household is not self-sufficient. Instead of the household employing servants or assigning children to perform specialized tasks, each household in the village is itself specialized, most engaged in farming but some dedicated to various trades and arts, including the Preaching Office. These specialized households, when banded together to form a village, become a self-sufficient community. Really, the village is just the household on a larger scale and with fewer bonds of blood-relation. By the way, the household as a component of the village is what Dr. Luther assumes when he says that each Chief Part of the Catechism is presented "as the head of the family should teach it in a simple way to his household."
Why is this important? Other than being simply beautiful and the way in which we were created to live, I consider it an economic necessity. We cannot continue as we've been doing, with every laborer integrated not into a small and self-sufficient community but into a huge and global community--which becomes no community at all. I have an inkling that smaller communities are more efficient than larger ones. Yes, the larger the community, the greater the division of labor. But a small community can react so much more quickly and meaningfully to crises among its members, and the leader of a small community can be more effective and personal in his administration than can the leader of a "community" of millions.
There is vastly more to say about this, and I hope to do so eventually.
