According to Caroline Humphrey, there is actually no anthropological or ethnographical evidence has ever shown that a pure barter economy has ever existed. Throughout history only credit and monetary systems have ever been seen. I think it is clear to most of us how our own market economies use money as a medium of exchange, but in societies (both historical and present) without money no apparent bartering occurs. Instead, most exchange happen between neighbors who trust one another to pay back their debts in due time. Because there is little travel of people from village to village and small populations where everyone knows one another, it is easy to keep track of who owes whom and how much. Even over a long period of times, a person leverages their own reputation as collateral on a debt.
For example, I would ask the local diary farmer for a gallon of milk, and he would give it to me, trusting that someday I might give something of equal value later down the road. If I do not give him anything, or I short change him with a single egg, word will get around the village that I'm a cheap moocher and no one will give me what I need because I am untrustworthy. But if I do pay him with something he might need, say a large bundle of firewood, then word will get around that I am an honorable and helpful neighbor, and more people will be willing to help me out.
In short, a barter system is not the historical precedent of the modern market economy.