> If I give you a dollar for a burger, then I've lost a dollar and gained a burger, and you've gained a dollar and lost a burger. Assuming this was a fair trade (that dollars and burgers are of approximately equal value), then as a result of the transaction we've simply rearranged who has which good, and no additional value was created in the process.

This is incorrect. I sell a burger because I value it less than your dollar, and you buy a burger because you value it more than one dollar. Win-win. It is a positive sum game, not a zero sum one.