His incorrect argument may be summarised as:
In order to see this one has to go back to the most elementary configuration, that is, the pure consumption economy which consists only of the household and business sector.**The root of the problem is that he has confused cash flow for profits. In a two sector economy, if one sector has a financial surplus, the other sector has to have a corresponding deficit, since the sum of financial flows has to equal zero. (In published economic data, there can be measurement errors that create residuals.)
In this elementary economy three configurations are logically possible: (i) consumption expenditures are equal to wage income C=Yw, (ii) C is less than Yw, (iii) C is greater than Yw.
In case (ii) monetary saving Sm is positive and the business sector makes a loss, i.e. Qm is negative.
However, a financial flow is not the same thing as profits. For an economy divided between a household sector and a business sector (that is, the external and governmental sectors are assumed out of existence), there are two main cash flows out of businesses that are not expenses, and which create a wedge between cash flow and profits.
- Dividend payments are flows to the household sector (which allows for the purchase of business output) that are emphatically not expenses.
- Capital expenditures by businesses are a outward cash flow by businesses that do not immediately give rise to an expense. (Depreciation expenses will arise in the future, however.)
For example, a business can pay a $1000 dividend to its owner, and the dividend is saved in the bank. The household sector has $1000 in savings, and there is no effect on business sector profits.
These two exceptions are not minor; they drive a lot of the action in the national accounts, and in the possibilities for outcomes in model economies. Dividends in particular pose a lot of potential theoretical difficulties. If we have a model in which all transactions in a period settle simultaneously, and all entities are purely forward-looking, there is little to stop dividends from becoming arbitrarily large -- since all output can be immediately purchased with dividends.*
This is a rather silly example, but it underlines why we always have to keep the cases of dividend and fixed investment flows in our minds when discussing the national accounts.
* Anyone with a background in control systems engineering will recognise this as being the highly annoying case where the "D matrix" is non-zero. About 90% of the annoyance factor of controls proofs deals with that case.
(c) Brian Romanchuk 2016