Income = value of output = consumption + investment.Clearly there is a problem with Keynes's calculus. Certainly one cannot invest what one has not saved, but what one has saved is not necessarily invested. So the final equation isn't necessarily true, even if it can be true. It's possible to just sit on one's money and not invest it.
Saving = income - consumption.
Therefore saving = investment. (63)
Keynes in fact goes on to repeat that "in the aggregate the excess of income over consumption, which we call saving, cannot differ from the addition to capital equipment which we call investment" (64). Well, of course it can. For the business owner, who Keynes is talking about here, it makes sense to have savings in case of emergency. Perhaps in the end all the savings really do end up as investments in the company. Over time. But that does not mean that savings is really and at all times the same as investment. If the mathematical logic is good, as it certainly is, then there is a problem with the premises.
Perhaps I am failing to see something in chapter 6, but when Keynes argues that
During any period of time an entrepreneur will have sold finished output to consumers or to other entrepreneurs for a certain sum which we will designate as A. He will also have spend a certain sum, designated by A1, on purchasing finished output from other entrepreneurs. And he will end up with a capital equipment, which term includes both his stocks of unfinished good or working capital and his stocks of finished goods, having a value G (52)It seems that he is arguing A = income from sales, and A1 = purchases, and G = capital (made homogeneous). Then he argues that Income = A + G - A1, which may simply mean something like final income or profits. But he then goes on to say that aggregate consumption (C) = SUM(A - A1), and I = SUM(A1-U), where -U is the entrepreneur's investment in equipment "exclusive of what he buys from other entrepreneurs" (54-55). I'm certainly unsure of what such an investment could possibly be. Whatever an entrepreneur invests is necessarily either wages or purchases. If so, then Income = Purchases + Wages(?). Income may go toward such things, but do they need to? What about profits?
But note above Keynes defines income as consumption + investment. So I = A - A1 + A1 - U, or I = A - U. Thus A - U = A1 - U and A = A1. So sales = purchases. If sales equals purchase, there is no savings. If Savings = A1 - U - (A - A1), then Savings = Investments - Sales. So if Saving = Investment, Sales must = 0. And if sales = purchases, purchases = 0. If A = 0, and A1 = 0 then C = 0 - 0, or C = 0.
Clearly something has gone horribly awry. I don't discount the possibility that it's my reasoning and calculations.
In any case, if saving is the same as investment, and people saving causes recessions, then Keynes seems to make the strange argument that investing causes recessions.
Finally, one thing I can say for certain is that Keynes is wrong when he argues that price equilibirum must be reached for a sale to take place. If such an equilibirum does occur, it necessarily must be reached by actual buyers and sellers interacting -- meaning people are buying at prices outside the equiibrium price prior to and causing the convergence of prices to the equilibrium. But I reject price equilibrium as a reality anyway, so he's doubly wrong as far as I'm concerned. People do make purchases without prices being at equilibrium, because prices are always fluctuating and differ from place to place. Entrepreneurs make money by finding such disequilibria and attempting to bring prices into equilibrium, but the second that happens, it goes out of equilibrium from the actions of people buying and selling.