Steven Medema know more about the history of the Coase theorem than many of us know about our spouses.
So whether you are distantly or intimately familiar with the idea, you are likely to pick up some insights in his article, "The Coase Theorem at Sixty" (Journal of Economic Literature, 2020, 58:4, pp. 1045-1128, subscription required).
In the 1960 article by Ronald Coase, "The Problem of Social Cost," the Coase "theorem" was not actually a theorem, nor does it seem to be the main point of the entirely verbal essay. Coase was working on various questions of regulatory economics, which might be summarized as the question of the appropriate government reaction in situations where market don't perform well. For example, it had been recognized since the 1920s and the work of A.C. Pigou that some economics activities might involve "externalities," where social costs were imposed on others who were not part of the market transaction. Pollution is an obvious example. The common policy prescription was that the government should estimate the value of this additional social cost, and then impose a "Pigovian tax" so that the firm producing the externality would face the actual social cost of its action--in effect, it would no longer be able to dump its pollution garbage into the environment for free.
Coase approached the problem of social cost from a different angle. Medema writes:
The article makes three basic points. First, externalities are reciprocal in nature. Yes, A’s actions impose costs on B, but to restrain A in favor of B imposes costs on A. The economic problem, Coase emphasized, is to avoid the more serious harm. ... Second, if the pricing system works costlessly and rights are assigned over the relevant resources, agents will negotiate a solution that maximizes the value of output, and this outcome will be reached irrespective of to which party those rights are assigned—the idea that came to be known as the Coase theorem. ... In the frictionless world of welfare economics circa 1960, the negotiation result shows that Pigouvian remedies are completely unnecessary for an efficient resolution of externality problems. Third, in the real world of positive transaction costs, all coordination mechanisms—markets, firms, and government—are costly and imperfect, meaning that there is no route to the optimum. The best that we can do is to choose among imperfect alternatives ... Comparative institutional analysis, then, becomes the method of choice, and the goal, from an economic perspective, is to select the coordination mechanism that maximizes the value of output for the problem under consideration.
Here's how I tried to convey the Coase "theorem" insight in an article I wrote last summer about "Are Property Rights a Solution to Pollution? (PERC Reports, Summer 2020). In my words:
In one famous example, Coase discussed the hypothetical situation of a railroad running beside a farmer’s field. Sparks from the train would sometimes start fires in the crops. How should this external cost—a kind of pollution “externality”—be addressed?
For non-economists, an obvious answer is for the government to pass a law. For example, the government might require that the railroad company install spark arrestors on the smokestacks of its locomotives, use a different blend of fuel or a new engine, leave a buffer zone beside the field, or relocate the rails altogether. Alternatively, the government might declare that the farmer should build a fence to protect the field, install a sprinkler system, change crops, leave a buffer zone, or perhaps even relocate the farm.
Rather than viewing anti-pollution efforts in terms of how governments should choose which rule to impose, Coase took an altogether different approach. He pointed out that the problem could be rephrased in terms of property rights—in other words, who has what rights? For example, the government could say that the railroad company had a right to emit sparks, in which case the farmer would have to figure out the most cost-effective way of protecting the fields. Alternatively, the government could say that the farmer had a property right not to have sparks land among his crops, in which case the railroad would have to figure out an answer—which might include installing spark arrestors or other technology to prevent fires from occurring, or even just paying the farmer to put up with the annoyance.
In Coase’s approach, the question of how to respond to problems of pollution such as unwelcome railroad sparks did not need to be delegated to a government vote or board of experts. Nor did the problem of pollution, in Coase’s view, need to be solved by regulators imposing a Pigouvian tax to account for the “externality” imposed. After all, governments or any outside groups will inevitably possess much less detailed and hands-on information about the range of possible options—and how those options might be tweaked or combined—than railroads and farmers. Moreover, any choice of specific government regulations will be affected by politics and lobbying. Instead, Coase argued that once property rights were clearly defined, then one party or the other would have an incentive to seek out the most cost-effective way of reducing this form of “pollution.”
Coase's work often pushed back against a common assumption (common both then and now), that direct government actions and mandates are the appropriate answers to problems with markets. He emphasized that governments often lacked both detailed knowledge of how to resolve issues with markets, and also that government acting under political pressure might lack the incentive to resolve such problems appropriately. Instead, the role of government could be to set up a system in which the economic actors themselves would use their detailed private information to reach a better decision.
In other classic examples, Coase argued in the 1950s that when it came to allocating spectrum rights, it was better for the government to auction those rights rather than to allocate them by an administrative decision-making process. Such auctions would cause private actors to reveal their true preferences, rather than just deploy their lobbyists. In another paper, Coase argued that although economists often invoke lighthouses as an example of where markets can't work well, as a historical fact many lighthouses were built by the private sector once the government gave them the right to collect tolls.
It's perhaps useful to note that Coase is certainly not claiming that real-world markets are perfect, and that private negotiations will resolve any issues. His prescriptions often involve the active intervention of government: for example, in setting the rules over whether railroads or farmers are responsible for dealing with sparks, or setting up auctions for spectrum rights, or giving lighthouse builders a right to charge tolls. Coase is arguing against "blackboard economics," as he later called it, where market problems and government solutions are sketched out in a classroom like a solved problem. Instead, Coase favored of a comparative institutional economics, where the specific details of situations take on a central role and thus it becomes important to think about details of information and incentives is possessed by the actual parties involved.
Coase did not refer to his result as a theorem: instead, this label was bestowed by George Stigler a few years later. Medema writes: "[T]he Coase theorem is neither prediction nor testable hypothesis nor descriptor nor policy prescription. It is, and can be nothing more than, a benchmark—a generator of predictive, testable, descriptive, and policy insights."
Medema describes in detail the unfolding of the Coase result over time, as the issues of potential problems, involved parties, information, and incentives have been explored in many contexts--including contexts outside of economics. Here, I'll close with Medema's overall summary of this process.
The Coase theorem is, by any number of measures, one of the most curious results in the history of economic ideas. Its development has been shrouded in misremembrances, political controversies, and all manner of personal and communal confusions and serves as an exemplar of the messy process by which new ideas become scientific knowledge. There is no unique statement of the Coase theorem; there are literally dozens of different statements of it, many of which are inconsistent with others and appear to mark significant departures from what Coase had argued in 1960. ...
The theorem has never been given a generally accepted formal proof; yet it has been the subject of scores of attempts to “disprove” it in a stream of analysis and debate that continues to this day. It has been labeled a “tautology” and the “Say’s law of welfare economics” (Calabresi 1968, pp. 68, 73), an “illuminating falsehood” (Cooter 1982, p. 28), and even a “religious precept” (Posin 1993, p. 810). Halpin (2007, p. 339) calls the theorem “theoretically degenerate … and ideologically charged.” Usher (1998, p. 3) bundles these various charges together, claiming that the theorem is ”tautological, incoherent, or wrong,” with the specific verdict resting upon to which version of the theorem one subscribes. ...
The nature of the theorem’s underlying assumptions is often said to make its domain of direct applicability nil; yet, it has been invoked, criticized, and applied to legal-economic policy issues in thousands of journal articles and books in economics and law ... as well as in journals spanning fields from philosophy (Hale 2008) to literature (Minda 2001) to biology (Frech 1973a). Indeed, the Coase theorem may be the only economic concept the use of which is more extensive outside of economics than within it.