By the way, here is what must surely be a slam-dunk refutation of the Lange/Becker/Baumol version of Say’s Law (the version that you outline in the lecture).
To recap, this version starts with Walras’s Law, that the excess demands in all markets have to sum to zero, and then defines Say’s Law as the additional assumption that excess demand in the money market is zero. A corollary of Walras’s Law, of course, is that general overproduction is logically impossible in a barter economy. (I’m not putting words in anyone’s mouth here, Baumol says exactly this in his 1977 paper on Say’s Law).
But something is obviously wrong here. Take the simple case of a two-good economy, where Smith produces more of Good A than Jones is interested in buying at any exchange rate, and Jones also produces more of Good B than Smith is interested in buying at any exchange rate. Sure, you can say that they will probably learn from their mistakes and stop doing this, but how on earth can you say that it is logically impossible?
The answer here is that the “proof” of Walras’s Law is based on a budget constraint equation, where it is simply assumed that each individual demands as much as he possibly can given his budget. This is not a problem in the context of establishing the possibility of general equilibrium, which is how Walras originally used the equation. But in the context of Say’s Law, the question of whether or not an individual will spend his whole income is kiiiiind of the whole point!! So in order to take Walras’s Law as a starting point for Say’s Law, you have to assume that Say’s Law is essentially true. But once you do that, there is no need to bother with Walras’s Law at all, let alone add the highly unrealistic assumption of perpetual monetary equilibrium.
This paragraph will admittedly be an argumentum ad hominem, so please take it as somewhat tongue-in-cheek. (I believe I have given sufficient proof of the case above).
Recall that this definition of Say’s Law (as Walras’s Law + assumed monetary equilibrium) traces back to Oskar Lange’s 1942 article in a compilation called “Studies in Mathematical Economics”. Given that this is Liberty Classroom, where we explore the superiority of free-market economics over the fallacies of the mainstream, is it really all that hard to believe that a socialist doing “mathematical economics” might simply have been completely wrong?
Edit to add: You don’t need to take my word for it on Walras’s Law. Sowell notes that it is based on James Mill’s behavioral theory, that people only produce in order to buy things with the income they receive. What he fails to realize is that this “behavioral theory”, if true, already suffices to show all that the Classical economists intended to show! So either it is false, in which case Walras’s Law is also false, or it is true, and Walras’s Law is superfluous.
Just to be really clear about all this, let’s return to the two-good Smith-Jones economy above. J.S. Mill would have no problem handling the mutual overproduction case – in fact, this is exactly what he was responding to in the War Expenditure essay. He would say that the fact that Smith and Jones both went to the trouble of producing their respective goods (we’re assuming here that Smith and Jones never consume the goods that they themselves produce, and that they derive no inherent utility from the production process) proves that they intended to exchange with each other – therefore there must be some exchange rate that would satisfy each party, even if there is not necessarily one that satisfies both simultaneously.
Lange could then say “Aha, so Walras’s Law is a legitimate starting point after all!” But the point is that this added piece of behavioral logic already shows that supply implies the willingness to purchase (at some exchange rate) and gives the supplier the power to purchase (at some exchange rate). Supply is therefore a sufficient condition for ex ante demand. The only question is whether the suppliers have correctly anticipated the exchange rate at which the other party will agree to transact – this determines whether or not their ex ante demand will be realized ex post. But this is a problem that is well handled by the standard microeconomic tools of pricing and profit/loss. Mill’s point – and the entire reason that we should care about Say’s Law at all – is that there is no mysterious extra dimension of economic analysis where we have to worry about ex ante demand (i.e. demand in general) being insufficient.
Note also, in contrast to Lange’s approach, that this reasoning handles money without any problem. Perhaps Smith produces certain increments of Good A because he wants to add to his real cash balances. There is nothing special about this – either he has calculated correctly, in which case there is no problem, or he has not, in which case he suffers a loss, and either learns or goes out of business.
So the entire money/barter dichotomy is just a byproduct of Lange’s fallacious approach. In my opinion, this whole episode is a testament to the power of verbal deductive logic in economics, and to the dangers of attempting to translate it to mathematics.