Coase makes arguments that regulations are never beneficial assuming there are no transaction costs or wealth effects. He knows these are unrealistic assumptions.
Of course. All arguments make simplifying assumptions and are invalid in cases where those assumptions don't apply to an extent that swamps the mechanisms of the argument. Nevertheless, I find Coase's criticism of Pigovian taxes to be devastating. But if you like them, by all means advocate for them. Though I think they're a bad idea, they're fully consistent with a free market.
Prohibitively expensive to get everyone to write private contracts covering all types of polluting behaviors and enforce them in courts (this is a txn cost) -> legal regulation can improve welfare
It's only prohibitively expensive if you don't optimize it. But again, I agree that pollution is a hard problem and one that has little to do with a free market. The only relevance a free market has is that it would mean that pollution of one's own property that doesn't affect other people's use or enjoyment of their property would be allowed. Otherwise, it would be handled much the same way.
Children may be born with no wealth and be unable to borrow to finance their education (this is a wealth effect) -> free public education can improve welfare
And people may be born with no wealth and be unable to borrow to finance starting a business. Education is an investment with an expected return like any other investment. If nobody is willing to make the investment with their own money, it's probably a bad investment. And I genuinely believe that for most of the recipients of public education, it does them almost as much harm as good. I consider public education more or less a failed experiment.
I don't believe public education is a better investment than whatever those who were taxed to pay for it would have done with their money. So I don't think it will improve welfare overall.
If you want a definition of the free market that includes public education and government regulation, then fine. However, you must then admit that this makes 'free market' a very fuzzy concept.
I agree, it's a fuzzy concept. It can't be explained in a buzzword or two.
My 'free market' can be this, while your 'free market' can be that. Similarly my 'communism' can be this, while your 'communism' can be that; ask the Chinese. It is more productive to talk about specific policy issues rather than use loaded words. Of course, the ideologues will disagree.
Well, that's why earlier in this thread, there was a list of core policy issues that relate to what we mean by a "free market".
But yes, I agree, you can't make a simplistic list of buzzwords and say "that's what I mean by a free market". Complex issues are complex.