Bartering is based on a simple concept: Two individuals negotiate to determine the relative value of their goods and services and offer them to one another in an even exchange. It is the oldest form of commerce, dating back to at time before hard currency even existed. (Learn more about how bartering evolved, read The History of Money: From Barter To Banknotes.)
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Anthropologists have argued, in contrast, "that when something resembling barter does occur in stateless societies it is almost always between strangers." Barter occurred between strangers, not fellow villagers, and hence cannot be used to naturalistically explain the origin of money without the state. Since most people engaged in trade knew each other, exchange was fostered through the extension of credit. Marcel Mauss, author of 'The Gift', argued that the first economic contracts were to not act in one's economic self-interest, and that before money, exchange was fostered through the processes of reciprocity and redistribution, not barter. Everyday exchange relations in such societies are characterized by generalized reciprocity, or a non-calculative familial "communism" where each takes according to their needs, and gives as they have.
Barter-based economies are one of the earliest, predating monetary systems and even recorded history. People can successfully use barter in many almost any field. Informally, people often participate in barter and other reciprocal systems without really ever thinking about it as such -- for example, providing web design or tech support for a farmer or baker and receiving vegetables or baked goods in return. Strictly Internet-based exchanges are common as well, for example exchanging content creation for research.
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As Orlove noted, barter may occur in commercial economies, usually during periods of monetary crisis. During such a crisis, currency may be in short supply, or highly devalued through hyperinflation. In such cases, money ceases to be the universal medium of exchange or standard of value. Money may be in such short supply that it becomes an item of barter itself rather than the means of exchange. Barter may also occur when people cannot afford to keep money (as when hyperinflation quickly devalues it).