Coase Theorem vs. the two fundamental theorems of welfare economics

As Paul Krugman would say, this post is "somewhat wonkish."

Two facts that came together for me in the last few days are the following:

(1) It has occurred to me that the Coase Theorem, depending on how one states it, is simply a special application of either the First Fundamental Theorem of Welfare Economics or the Second Fundamental Theorem.  (In the Wikipedia link to the Coase Theorem that I've provided here, versions 1 and 2 of the Coase Theorem are the First Fundamental Theorem at work, while version 3 involves the Second Fundamental Theorem.)  I'm probably not the first person to think of this, but I don't recall seeing it stated anywhere, and it leads to an interesting question, which is why people who were familiar with those theorems nonetheless initially found the Coase Theorem surprising and counter-intuitive.  This in turn may help to illuminate what made Coase important.

(2) I was recently contacted, along with a number of other people (many of them with Chicago connections) in law and economics, with regard to a forthcoming tribute to Ronald Coase that I believe will be appearing in the University of Chicago Law Review.  The tribute pieces are meant to be very short (e.g., 500 words), although they are permitted to be longer.

It therefore occurred to me that, by very briefly writing up (1), and including a punchline regarding the questions that I note above, I could also do my part with regard to (2).  So I wrote it up today, in between doing other things, and have sent it in.

The final is just 750 words long (including footnotes), and I will plan to post or link to it here at some point.