Simplify massively. Ignore investment, government spending and taxes, and exports and imports. All output is consumed.
Assume a Keynesian consumption function: Cd = a + bY. Draw Samuelson's "Keynesian Cross" diagram. Real consumption demand Cd on the vertical axis, and real output (real income) Y on the horizontal axis. Demand for consumption this current period depends on realised sales of output this current period. "Equilibrium" is where the consumption function crosses the 45 degree line. Because that tells us the level of output at which demand for output equals that same level of output. But that "equilibrium" is not necessarily a full demand = supply equilibrium. Output may be less than "full employment" equilibrium. Firms and households may want to produce and sell more output and labour than they are able to sell, if demand is too low. The multiplier (the change in "equilibrium" output divided by the upward shift in the consumption function that caused it) is 1/(1-b). There is positive feedback in this model, because demand depends on itself.
What does that Keynesian Cross diagram look like in a New Keynesian model, with infinitely-lived consumption-smoothing agents who never face binding borrowing constraints? That depends on how long the "current period" is, and on whether income in the current period affects expected future income.
Assume that the representative agent is perfectly confident that his income will be equal to "full employment" income in all future periods, regardless of what happens to current income. (Yes, this assumption is very questionable.)
If the current period is very short, the consumption function will be almost horizontal (the marginal propensity to consume "b" will be almost zero). Because changes in current income have a negligible effect on permanent income. And if the central bank reduces the current period real interest rate, the consumption function will shift up, causing an increase in "equilibrium" output. If the central bank sets the right interest rate, so the real interest rate equals the "natural rate", the intercept of the consumption function (autonomous consumption "a") will be almost equal to full employment income.
Now let's make the current period longer and longer. So that current income has a bigger and bigger effect on permanent income. Autonomous consumption (the intercept) gets smaller and smaller, and the marginal propensity to consume (the slope) gets bigger and bigger. Less obviously, a given-sized cut in the real interest rate will cause a smaller and smaller upward shift in the consumption function.
Now let's take this lengthening of the current period to the limit. Suppose the current period lasts forever. So my bolded questionable assumption above becomes redundant, because there is no future period. Let us put permanent income on the horizontal axis, and permanent consumption on the vertical axis. Autonomous consumption drops to zero, the marginal propensity to consume rises to one, and the effect of a cut in the real interest rate drops to zero. The budget constraint (plus non-satiation) ensures that permanent consumption must equal permanent income, for any level of permanent income, and for any real interest rate. This means that the consumption function necessarily coincides with the 45 degree line.
And this means that any level of permanent income, between zero and full employment income, is an "equilibrium". Animal spirits are the only thing that determine which of those equilibria will be chosen. Since b=1, the multiplier would be infinite, if it were possible to shift the consumption function up. But the budget constraint says it is not possible to shift the consumption function up, so that infinite multiplier is purely hypothetical.
Now let us introduce a stock of money into the model. The representative agent holds a stock of money. He has a desired stock of money, and an actual stock of money, and the two stocks may not be the same. Introducing money into the model breaks the identity between permanent consumption and permanent income. If an agent holds more money than he wishes to hold, he will plan to run down his stock of money over time, by spending more than his income, so that his permanent consumption will be greater than his permanent income. And if an agent holds less money than he wishes to hold, he will plan to increase his stock of money over time, by spending less than his income, so that his permanent consumption will be less than his permanent income. But even though each individual agent can add to or subtract from his stock of money, by spending less or more than his income, this is not possible in aggregate.
If the desired stock of money is independent of permanent income, an increase in the actual stock of money, so that it is greater than the desired stock, will cause an upward shift in the consumption function. It does not matter if that upward shift is very small, because b=1 and so the multiplier is infinitely big. An extra $1 hot potato in circulation will be enough to expand the economy from 50% unemployment to hit the full employment constraint. And withdrawing a single $1 from circulation would cause the economy to collapse to 100% unemployment.
But a more plausible assumption would be that the desired stock of money is an increasing function of permanent income. This ensures that the consumption function has a slope of slightly less than one, so we get a determinate "equilibrium" level of permanent income where the desired stock of money equals the actual stock.
The model would be more plausible still if we assumed that the desired stock of money depends on permanent nominal income. There is a real stock of money at which equilibrium permanent income is equal to full employment permanent income. Maybe (or maybe not, if it causes destabilising expectations) a slow adjustment of prices, in response to output being greater or less than full employment, would eventually bring the economy to full employment equilibrium.
Keynes understood that demand depended on itself. General Theory chapter 3. Keynes understood that the only thing that might (or might not) bring the economy to full employment income was some sort of real balance effect on aggregate demand (and that the central bank could do the same thing quicker and better than waiting for prices to adjust to get the right level of real money balances). General Theory chapter 17. New Keynesians have forgotten Keynes' two insights about aggregate demand. They have forgotten that demand depends on itself. They have forgotten that some sort of real balance effect is the only thing that might (or might not) bring the economy to full employment automatically. New Keynesians are guilty of an intertemporal fallacy of composition: even if the right rate of interest will ensure full employment in any single period, it does not follow that the right rate of interest will ensure full employment in all periods. New Keynesians just assume, without any explanation, without anything in their models that would make this the only rational expectation, that agents expect that future income will equal full employment income. New Keynesians are the "classical" economists who just assume (the agents in their models expect) an automatic tendency towards full employment. New Keynesians have models of monetary exchange without money. New Keynesians are not Keynesians.
Just continuing my lovely argument with Roger Farmer about Keynes and modern macro.