Are ethics and economics compatible? Certainly.

The agents and 'players' in the economic sphere play by rules that they have not given themselves. I'd even say that this is impossible because the economy is not a sphere of its own, apart from the rest of society - like sport - but it is intimately linked to all aspects of our daily lives; all of us are part of the economy, we are economic players : when we buy or sell something, when we rent a flat, or as employees.

These rules the economy plays by are devised and enacted in politics (legislature). And in drafting these laws, ethical considerations very often (I would even say in most cases) play an essential role (example: what kind of bankruptcy law is just?).
In this respect, ethical considerations have always been implicitly present in the rules under which business operates.
That is the implicit level.

There is an explicit level to this: when actors in business act explicitly and purposefully according to ethical standards (such as the so-called 'bio' industry or 'fair trade), because customers expect and reward this sort of doing business.

It is therefore wrong to claim that both areas, ethics and business, have nothing to do with each other. What undoubtedly exists is a tension between the two spheres. But this is trivial, because in every area of human activity there is a tension between what is and what ought to be. There are laws, norms, rules everywhere where people act, and there are always people who disregard and break these laws and rules.