David Glasner again argues against the identity between saving and investment. He finds some quote by Scott Sumner where it sounds like Sumner claims that the profession has just decided to define saving so that it means the same thing as investment. I don't really think that is true.
I certainly see saving and investment as quite different things. Saving is that part of income not spent on consumer goods. Investment is spending on capital goods. They aren't anything like the same sort of thing. That they must always be equal as a matter of arithmetic is a bit remarkable. But it is true.
In my opinion, there was a tendency by Keynes and some of his followers to confuse the identity with an equilibrium process by which a change in planned saving or investment causes output to change until planned saving again equals planned investment. Worse, very poor arguments were sometimes made against the orthodox view that interest rates adjust to bring saving and investment into equilibrium on the grounds that saving and investment are always equal.
Planned saving doesn't have to equal planned investment. It is certainly possible that interest rates might change to bring planned saving and planned investment into equilibrium. It is even possible that output and income might adjust to bring planned saving and planned investment into equilibrium.
Purchases and sales are equal by definition. But quantity supplied and quantity demanded can be different. Quantity supplied is planned sales and quantity demanded is planned purchases. They don't have to be equal, but the price can adjust to bring them into equilibrium. It would be a very poor argument to say that the price cannot adjust to bring quantity supplied and quantity demand into equilibrium because purchases and sales are always equal by definition. And then to insist that the quantity will adjust to the amount purchased at a given price and call that equilibrium. That might be what would happen, but it is what we call "surplus."
Suppose there is an all service economy. Further, everyone is an independent businessman. Everyone's income is someone else's expenditure. Everyone's expenditure is someone else's income.
The barber's expenditure on massages is the income of the masseuse. The expenditure of the masseuse on haircuts is the income of the barber. The expenditures of the barber and masseuse on musical performances is the income of the musician.
And, further, the expenditure of the musician on music lessons is the income of the teacher of music.
Income and expenditures are equal. It is like receipts from sales are equal to spending on purchases. No, it is exactly the same thing as receipts from sales are equal to spending on purchases.
Now, that part of income not spent on services that start with the letters A to M must equal spending on services that start with letters N to Z. It isn't that anyone must spend some particular amount on any particular service, it is rather that the economist is partitioning income and expenditure.
And really, it is just a partition of expenditure. To say "that the part of income not spent on services that start with the letters A to M" is the same thing as saying "that part of expenditure that is not expenditure on services that start with the letters A to M." The other part of expenditure must be expenditure on services that start with the letters N to Z.
If we define that part of income not spent on services that start with letters A to M as saving and spending on services that start with N to Z as investment, then saving and investment must be equal by definition.
Further, in a four service economy, that part of income not spent on haircuts, massages, or musical performances must be equal to the amount spent on music lessons. That part of income not spent on haircuts, massages, or musical performances is saving. Spending on music lessons is investment. Saving equals investment.
Does adding entrepreneurs hiring workers to produce the services make a difference? No. Because the revenues of the firms will equal wages plus profits--income to the employees plus income to the entrepreneurs.
Does the production of goods make a difference? Well, there is the possibility that goods will be produced and not sold. But that doesn't really matter either. What is in fact done is that unsold goods are counted as purchased by the producer, and included as inventory investment. What this implies is what is actually produced results in a matching income and as well as matching expenditures. Income equals output and output equals expenditures, so income equals expenditures. But consideration of the all service economy where unsold output isn't an issue shows that income equals expenditure anyway.
Nothing in this argument says that expenditure equals potential output--which is more or less the same thing as saying quantity demanded equals quantity supplied. The prices need to be right for that to happen. The interest rate has to be right for planned saving to equal planned investment while expenditure equals potential output. Again, this is the same thing as the prices have to be right so that quantity supplied equals quantity demanded. And finally, the nominal quantity of money very much impacts which money prices and wages are the ones that keep quantity supplied and demanded equal.