In the study of Philosophy of Economics, I think that four names stand out on this subject: Karl Marx, John Rawls, Robert Nozick, and F.A. Hayek. They each have each put forth some very powerful ideas and represent (more or less) communism, socialism, libertarianism, and (sort of) conservatism respectively. While none of their ideas are perfect and in any case subject to preference, I think each should be studied and the strength and weakness of the arguments understood in order to participate in any debate about economic policy.
Much to my surprise, in a recent informal poll of friends and acquaintances, I've found that very few have heard of any of these other than Marx. While Marx is certainly the most important since his teachings were the instigation for the radical formation of governments in countries containing billions of people, each of the other philosophers' ideas are very important as well.
Here is a quick overview of each of their ideas:
Marx argued that capitalism, like previous socioeconomic systems, will produce internal tensions which will lead to its destruction. Communism, the ultimate heaven of earth with riches for all, will rise from the ashes of capitalism. "From each according to his ability, to each according to his needs" is the slogan popularized by Marx to describe the basic working of communism from the workers point of view.
Rawls makes the case for redistributive justice and socialism in A Theory of Justice. He does this by asking how one might choose to design a fair economic system if we had no clue (he calls this a "veil of ignorance") as to our position in that system. We might be at top in terms of talent and opportunity or we might be at the bottom. If this were the case, he argues that we would design a system that would maximize the position of the worst off (known as "the difference principal") in case we ended up being the worst off, and that such a system would have a great deal of redistribution in order to be just.
Nozick's Anarchy, State, and Utopia (1974), which received a National Book Award, argues among other things that a distribution of goods is just if brought about by free exchange among consenting adults and from a just starting position, even if large inequalities subsequently emerge from the process. He also argues that the only just system of government is a minimalist government dedicated only to the protection of the population, though he argues for progressive taxation to fund that government. Nozick turned Marx's slogan around to become "from each as they choose, to each as they are chosen".
He shared the 1974 Nobel Prize in Economics with ideological rival Gunnar Myrdal "for their pioneering work in the theory of money and economic fluctuations and for their penetrating analysis of the interdependence of economic, social and institutional phenomena." He also wrote extensively on the distribution of information in an economic system and the relationship between that and liberty. He also wrote about evolution of human institutions that support economic activity ("the spontaneous order").
I find that when beginning a discussion about fairness and economics (a favorite topic of Left leaning friends and acquaintances), that a huge part of the effort ends up being dedicated to subtopics already thoroughly addressed by the economic philosophers I've mentioned above. I wish that instead of only teaching Marx in schools, that all four were taught. I think that everybody would then have a much better handle on the economic policy debates that are continually rehashed in the country.