These are some notes that hopefully clarify, and put into context, the "hydraulic" model of Keynes' theory, I sketched out here.
1. Firstly, I think Keynes' General Theory is overdetermined. In order for the numbers for output, the rate of interest etc generated by Keynes' model to not be determined twice, ie in order to avoid having two contradictory numbers for one thing, some part of the theory needs to be cut. Basically, you can have either the de jure equivalence of savings and investments, or the technically determined schedule of the efficiency of capital, but not both. Orthodox (which for Keynes meant conservative) economics has generally kept the de jure equivalence of savings and investments (in shorthand "S = N") and forgotten about the technically determined efficiency of capital (which Keynes calls the marginal efficiency of capital, "MEC").
2. The MEC schedule basically relates the use of resources to the rate of profit. Keynes' thinking about this is probably somewhat influenced by Piero Sraffa's 1926 paper about the rate of profit in capitalist society, on the basis of which Keynes brought Sraffa to Cambridge. Sraffa's work is strongly influenced by that of Quesnay, Ricardo and Marx. Hence, there's more of a marxist influence on Keynes than one might assume from checking the index of Keynes' book. It's sort of irrelevant to call the schedule of the rate of profit the "marginal efficiency of capital". If capital markets are to be assumed to be reasonably efficient, marginal profit will be the same as actual profit, but calling it "marginal" makes it sound less like marxism.
3. According to the models of Marx or Sraffa, the schedule of the MEC would be upward sloping. Extra investment would increase the rate of profit, calling forth further investment, with a tendency toward full employment. Both writers examine other tendencies in capitalism which are capable of bringing about severe and chronic unemployment, such as has nearly always characterised capitalist society. In the first case technical progress and the business cycle, in the second monopolistic competition.
4. One of Keynes' innovations is in theorising a downward sloping schedule of the MEC, which determines monetary flows such that an economy subject to price rigidities can stall well below full employment, for want of sufficient effective demand. As output increases, the rate of profit falls, and more money becomes idle, setting a brake on the expansion of output. This intelligible, but as we will see false, model was briefly popular in the US after it was exposited in early editions of Paul Samuelson's economics textbook. It is sometimes called hydraulic Keynesianism. Since then, orthodox macroeconomics has been based on the Hicks-Hansen model, which requires that savings must equal investments. Hicks-Hansen essentially drops MEC to include S = N.
5. The notion that S = N is simply false in a credit money economy (it would only be true in very contrived circumstances). Later Keynesian economists, like Kaldor and Minsky, admit this without criticising Keynes very much for perpetuating this error, but whether or not we accept the de jure equality of savings and investments changes everything.
6. In reality there are three factors ordinarily influencing changes in effective demand: debt extended and serviced, saving and dissaving, productivity. Credit money normally expands with accumulation by the banking sector. Inflation is therefore normal in a capitalist economy, and with it the debauch of capitalist profit. Consequently we can only talk about the efficient use of capital in a capitalist economy vaguely and relatively. It is more difficult than Keynes supposed for effective demand to be reversed. A viable model dealing with the problems Keynes was interested in would need to untangle the notions of credit and money that are confused by Keynes, and situate the fluctuations in effective demand in secular history.
7. It might actually be better to think about a capitalist economy as having two currencies: credit money and cash, with a fixed exchange rate. This unfortunately might make capitalism appear bureaucratic, and hence, perhaps, inefficient.
8. I don't believe we can justify the Keynesian welfare state, or, indeed, the Keynesian military economy, on purely economic grounds. Either these things are worthwhile in themselves, or politically useful, or they are not. Keynes' arguments in favour of public works must be somewhat discounted because capitalist finance does anyway what public works were meant to do (l'inutilité, même).
9. Having said that, there might be something in the idea that a more equal distribution of income leads to greater total output. The explanation for this isn't in Keynes though.