- Different utility functions. E.g. I have a baseball glove that is worth $80 on the open market, and you have some software that is worth $80 on the open market. We both value what we have in the sense that we get some utility from having these things, but we both would value $80 worth of other things even more. So we sell them; or we trade with each other if doing so is less costly and if we have a double-coincidence of wants. There has been no production of goods in this example, no specialization, no division of labour, no comparative advantage. All that has happened is that we have realized that we have different utility functions and that we will both increase our utility by trading, either with each other or with others in the marketplace.
- Comparative Advantage. Even if you are better than I am at producing everything, you cannot easily be self-sufficient. And even if you could be self-sufficient, you would be better off producing the things at which you are comparatively better and trading with me (and I would be better off producing the things at which I am comparatively better). Comparative advantage can arise from different productivities in labour, land, and/or capital, even though most of the examples we present in our classes involve only labour.
- Specialization and division of labour. Even if there are no comparative advantages whatsoever, we might find it advantageous to specialize and trade. As an example, consider this question: why don't I produce my own food (assume I have the ability and knowledge to do so, and assume those who do produce food are just as capable of being economics professors as I am)? Furthermore, why don't we all produce our own food (assuming away the comparative advantage explanation)? The primary reason for this flows from indivisibilities, economies of scale, and high transaction costs. We don't rent 15 minutes on a combine to harvest the crop from the 1/4 acre of a wheat field that we might rent.... etc. etc. because the transaction costs to capture those economies of scale are just too high.
For more, see this at Cafe Hayek.




