Matt asks this question. I am a bit on the run, so I will do this in link-less form, but all the sources should be easily googled. Here goes:
1. He developed the “theory of clubs,” which sets out the conditions under which private associations supply excludable public goods at optimum levels.
2. For his time he had the best and most rigorous analysis of the incidence of public debt.
3. With Gordon Tullock he pioneered the economic analysis of voting rules in terms of transactions costs and external costs imposed on others. Any current blogosphere discussion of say the filibuster will rely on this approach, though we now take it so for granted we don’t realize how impressive it was at the time.
4. He had pioneering economic analyses of bicameralism, logrolling, and other aspects of legislatures, again with Tullock.
5. Along with Harsanyi, he formulated aspects of the “original position” before Rawls did and he was a major influence on Rawls. By the way, I have seen Buchanan numerous times with top professional philosophers, and he has no problem holding his own or better.
6. He helped pin down, including on the technical side, the economic concept of externality.
7. He provided the most important revision to optimal tax theory since Ramsey, namely the point that supposedly efficient methods of taxation can be too easy to use. That was in The Power to Tax, with Brennan. His piece on static vs. dynamic versions of the Laffer curve, with Dwight Lee, is also significant.
8. He provided a public choice analysis of why Keynesian economics would not lead to the appropriate budget surpluses during good times and thus would contain dangerous ratchet effects toward excess deficits.
9. He thought through the conflict between subjective and objective notions of value in economics, and the importance of methodologically individualist postulates, more deeply than perhaps any other economist. Most economists hate this work, or refuse to understand it, either because it lowers their status or because it is genuinely difficult to follow or because it requires philosophy. Yet it stands among Buchanan’s greatest contributions even if a) I do not myself agree with his approach, and b) I do not think it is easily summarized or even well-explained. Buchanan took Knight and Shackle very seriously and he understood that the typical pragmatic dismissal of their caveats was not in fact well-founded.
10. His Hayekian work on “order defined only through the process of emergence” and “economics as a science of exchange and catallactics” is a very important take-down of the scientific pretensions of much of economics. It doubted whether the notion of efficiency could be independently conceptualized at all. Again, this work is disliked or ignored. Buchanan may be going too far, but it is a very important and neglected perspective.
11. He thought more consistently in terms of “rules of the games” than perhaps any other economist. This point remains underappreciated and underapplied. It makes technocracy out to be a fundamentally different endeavor.
12. He did important work in the history of economic thought, reviving interest in the Italian school of public finance and public choice.
13. His late papers with Yoon on the work ethic, increasing returns, and economic growth remain underappreciated. I also admire his work with Yoon on the anti-commons.
There is more, but that is a start. Try his article on why pollution should be taxed for Pigouvian reasons. I could add that Buchanan understood the importance of monetary rules, and favored a regime where the supply of money would be elastic in response to negative economic circumstances.
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