Or, "Profits = Expenditure - Income". Those are just alternative ways of saying the same thing, for a closed economy, if investment and saving include government investment and saving.
Most economists will say that's wrong. And it is wrong by standard definitions, where aggregate expenditure and income are the same thing, and investment and saving are also the same thing (for a closed economy, including government investment and saving).
But let me tell you a story:
There are firms and households (ignore government and foreigners). Firms rent land and labour from households, and use it to produce food which they sell to households (ignore capital). There is a fixed stock of currency that is used to buy and sell everything. Food cannot be stored. No other assets.
In any given year, if households spend $100 more buying food than the income they earn from rent and wages, then at the end of the year households own $100 less currency and firms own $100 more currency than at the beginning of the year. Firms have made a profit exactly equal to the $100 difference between households' expenditure and income. Or, firms' $100 profits are equal to households' negative saving (there is no capital and no investment in this story).
But who owns the firms?
If households own the firms, we can say that firms' assets are owned by households, and firms' profits are included in households' income. And if we do that, then we are back at the standard definitions where Expenditure = Income, and Investment = Saving, must always be true.
Or we could adopt an intermediate position: we could say that firms' profits are part of household income only if firms actually distribute those profits to the households that own them. In which case we get: Undistributed Profits = Expenditure - Income = investment - Saving.
There's a number of different ways we could add things up. Which is the best way? It depends.
Suppose firms were like a strange religious cult; they save all their profits for six years, then on the seventh year they blow the lot by spending it all on food which they burn as a sacrifice to the gods. None of the households want firms to do that; it's just what firms do, following some weird internal logic of their organisational structure. If so, you had better build that fact about firms' behaviour into your macroeconomic model. And it would not make sense to include firms' profits as part of households' income, because households know they will never be able to consume firms' profits. (And a corporate profit tax might really be a tax on corporations, and not on the households who own them, work for them, or buy from them.) So Profits = Expenditure - Income = Investment - Saving.
There is no one right way to do the accounting (though there are conventional ways, and it's easier to understand what others are saying if we all follow the same conventions). The accounting can't tell you what the world looks like (though it can help you keep your head straight when you are looking at the world). First decide what the world looks like; then do your accounting accordingly.
[An economist will probably make a comment on this post, and that comment will go automatically into the spam folder. Because Typepad, and history, across this and other macro blogs. But if it's a reasonable comment I will fish it out, after a short delay.]
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