There are four goods produced in an economy by four individuals:

Good: apples, bread, shoes, hats

Producer (in order): Orchard Owner, Baker, Cobbler, Hat Maker

If the orchard owner only wants to initially trade for hats and bread, the baker only wants to initially trade for hats and shoes, the cobbler only wants to initially trade bread and apples and the hat maker only wants to initially trade for apples. Will any trade between these four persons take place in a barter economy? If so, explain your answer in terms of the double coincidence of wants and the idea of transaction costs. Also, explain the trades that will take place with two producers who wants all four good at the end.