mid-15c., apparently from Old French barater "to barter, cheat, deceive, haggle" (also, "to have sexual intercourse"), 12c., of uncertain origin, perhaps from a Celtic language (cf. Irish brath "treachery"). Connection between "trading" and "cheating" exists in several languages. Related: Bartered; bartering. The noun is first recorded 1590s, from the verb.
In England, about 30 to 40 cooperative societies sent their surplus goods to an "exchange bazaar" for direct barter in London, which later adopted a similar labour note. The British Association for Promoting Cooperative Knowledge established an "equitable labour exchange" in 1830. This was expanded as the National Equitable Labour Exchange in 1832 on Grays Inn Road in London. These efforts became the basis of the British cooperative movement of the 1840s. In 1848, the socialist and first self-designated anarchist Pierre-Joseph Proudhon postulated a system of time chits. In 1875, Karl Marx wrote of "Labor Certificates" (Arbeitszertifikaten) in his Critique of the Gotha Program of a "certificate from society that [the labourer] has furnished such and such an amount of labour", which can be used to draw "from the social stock of means of consumption as much as costs the same amount of labour."
It’s hard to answer that without actually seeing a modern gift economy in action. Luckily, modern gift economies actually do exist. On a small scale, they exist among friends, who might lend each other a vacuum or a cup of flour. There’s even an example of a gift economy on a much larger scale, albeit one that’s not always in operation: The Rainbow Gathering, an annual festival in which about 10,000 people gather for a month in the woods (it rotates among various national forests around the country each year) and agree not to bring any money. Groups of attendees set up “kitchens,” in which they prepare and serve food for thousands of people every day, all for free. Classical economists might guess that people would take advantage of such a system, but, sure enough, everyone is fed, and the people who don’t cook play music, set up trails, teach classes, gather firewood, and perform in plays, among other things.