Barter system

Barter system is exchanging goods without money. It still persisted probably still persists when we use money by and large. During harvest seasons, in my village people used to buy vegetables by exchanging grains. Even now, we exchange our time by seeing ads for services provided by youtube. The barter system will work in the greater philosophy of everybody needs to give something to get something. The need for exchanged goods (say you have only bags but I have enough of them), the perishability of exchanged goods all pose problem. Here , a market place, where people meet at a common place and exchange various goods may help to certain extent. But pricing for exchanged goods becomes difficult. 

Assume Person A has built a few identical huts which he is good at and he is ready to sell them. He is interested in buy some cattle in exchange for each cattle. Person B comes with 3 cows and 2 goats and buy a hut from him. Person B comes with 2 cows and 8 goats and buy another hut from him. Person C has got some goats. How many goats he needs to exchange get a hut?

Putting into algebra we will get 3x+2y=1 and 2x+8y =1...A simple transaction straight away introduces algebra and gives linear simultaneous equations to solve. (A quick scan gives 1 cow compensates 6 goats...So he needs to give 18+2 =20 goats)Its just two items to exchange for a hut. Imagine the transactions where one exchange 5-6 items and get 3-4 items.

Now consider about modern day economic activities like a spine surgery, a bridge construction. How can we price them if we have only barter system? How many variables will be involved?

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