3) The crux of our entire disagreement centers around your “mathematical tautology” version of Say’s Law. For a sample timestamp, at around 32:20 you say “[In a monetary economy] you can still maintain or defend some version of Say’s Law, but it’s no longer a mathematical proof[…]now you have to make an empirical case, and say that as long prices are flexible, markets will clear pretty quickly.”

You are right, of course, that there is no mathematical proof that excess demand for non-monetary commodities must sum to zero. Where I believe you are mistaken is in thinking that this “mathematical proof” angle is particularly relevant in the first place, or that in its absence, we have no choice but to downgrade the discussion to an empirical question. The Classical economists pretty clearly intended the Law of Markets to be an a priori demonstration showing conclusively that there could be no such thing as demand in general failing to keep pace with the volume of goods produced. And they surely would not have bothered to make such a big deal over the Law of Markets if it were only intended to apply to a barter economy.

As I mentioned earlier, my favorite statement of the Law of Markets was given by Ricardo: “Men err in their productions, there is no deficiency of demand.” Here is an example of how he justifies this conclusion:

“Whoever is possessed of a commodity is necessarily a demander, either he wishes to consume the commodity himself, and then no purchaser is wanted; or he wishes to sell it, and purchase some other thing with the money, which shall either be consumed by him, or be made instrumental to future productions. The commodity he possesses will obtain him this or it will not. […] If it will not what does it prove? That he has not adapted his means well to his end, he has miscalculated.”

As you can surely see, there is nothing mathematical about the reasoning here – it is a quasi-praxeological demonstration in the best Misesian tradition! If someone goes to the trouble of producing a good, he MUST either be intending to use it for his own purposes, or to obtain something for it in exchange. In general, supply implies demand, and therefore, abstracting from particular entrepreneurial errors, demand in general cannot fall short of supply.

And more importantly, note that Ricardo’s reasoning applies just as much to money as to any other good. A supplier can intend to sell his product in order to obtain the services of higher cash balances. His designs may be frustrated if too many other “liquidity fetishists” try to pull the same trick – but this merely shows that he failed to anticipate the actual market conditions under which he would be able to realize his transaction.

Like many praxeological theorems that appear at first glance to be little more than a truism, the Law of Markets as expressed in this manner is deceptively powerful. In particular, it remains in my view the clearest, most efficient refutation of the entire Keynesian program. For example, consider the famous passage from Chapter 3 of the GT where Keynes lays out his agenda for the rest of the book: “The outline of our theory can be expressed as follows. When employment increases, aggregate real income is increased. The psychology of the community is such that when aggregate real income is increased aggregate consumption is increased, but not by so much as income” etc. etc. , the point being that we need to find enough investment to serve as an outlet for the increased income.

The Law of Markets immediately exposes this as hogwash. “Aggregate real income” cannot increase without being supported by an increase in production. And if people bothered to produce more, then following Ricardo’s reasoning, they must already have intended to exchange it for something else. Keynes’s attempt to separate the two sides of the transaction is completely invalid.

Apologies again for the length here, but given the subtlety of some of the issues, I wanted to err on the side of excessive clarification. Enjoy your time in Europe – and maybe see if you can find a copy of Kates’s book for the plane ride home. ☺