I'm going to say right off the bat that this chapter was pretty confusing. As such, I'd be indebted to anyone who can point out anything I've missed or just plain gotten wrong. Here goes.
Keynes introduces us to his multiplier: "For in given circumstances a definite ratio, to be called the Multiplier, can be established between income and investment and, subject to certain simplifications, between the total employment and the employment directly employed on investment (which we shall call the primary employment)." We'll see shortly that his idea of investment is not what we might suspect by the term, but more on that in a moment.
Section I: Another term is introduced, the marginal propensity to consume, which is defined as: dCw/dYw. Cw is the consumption in terms of wage-units and Yw is income in term of wage units. As usual, Keynes is doing his best to confuse us. All he's saying here is that man spends some percentage of his income; if I make 50 grand a year and I spend 45 grand, then my marginal propensity to consume is 9/10. Actually, as Keynes defines this in terms of wage unit, we cannot even say this much, but Keynes forgets his own definition and treats this propensity as if it were defined in monetary terms, so we can be forgiven the mistake.
From calculus, we know that the d is supposed to represent a rate of change; this is curious because Keynes tells us that "This quantity [the marginal propensity to consume] is of considerable importance, because it tells us how the next increment of output will have to be divided between consumption and investment." Obviously there is no such law. I can increase my propensity to consume by spending my next paycheck at the casino; I could also decrease it.
Using some math, Keynes tells us that: "we can write ΔYw = kΔIw, where 1 - (1/k) is equal to the marginal propensity to consume." He then proceeds: "Let us call k the investment multiplier. It tells us that, when there is an increment of aggregate investment, income will increase by an amount which is k times the increment of investment."
It's not immediately clear what he's done here. As Iw stands for investment, he's simply written the same equation a bit differently. In my previous example, we noted that my marginal propensity to consume is 9/10; using this, as well as the amount of wage units I spend on consumption, we can arrive at my income. Keynes is doing something similar with his multiplier by using the amount of money I invest--5 grand--and, using the multiplier, arriving at my income. The precise importance of the multiplier escapes me. Keynes can do math, but he's a lousy economist.
Not only is the multiplier worthless, it's also essentially arbitrary. Hazlitt points this out in The Failure of the New Economics, but we could make any division we wish and then create a multiplier based on this division. Let us say that I spend 50 a year on socks. The sock multiplier is then 1000. We can now use this fact to stimulate the economy through "investment" in socks by the government.
If the marginal propensity to consume is 1, then the multiplier becomes infinite. If the people in an economy never save at all, it will only be necessary for the government to invest the smallest amount and full employment shall reign. Here again we see Keynes's preposterous hatred of the saver rear its ugly head.
Just what happens when the savings rate becomes negative is anyone's guess. I suppose the multiplier becomes negative and any "investment" undertaken by the government hurts the employment rolls. At last, truth can be extracted from something Keynes has said.
Section III: The multiplier is an idea Keynes took from someone named Kahn. But his multiplier is different as it deals with employment. No matter. Keynes can make the necessary assumption to ensure that these will actually be the same. Whether or not these assumptions are well founded is irrelevant, since the idea of the multiplier is patently absurd.
Keynes writes: "It follows, therefore, that, if the consumption psychology of the community is such that they will choose to consume, e.g., nine-tenths of an increment of income, then the multiplier k is 10; and the total employment caused by (e.g.) increased public works will be ten times the primary employment provided by the public works themselves, assuming no reduction of investment in other directions." Since the marginal propensity to consume can be measured, we need only use it to find the "multiplier", after which the government knows how much to "invest" to bring the economy to full employment. If our multiplier is 10, and there are 10 million works unemployed, if the government employs the first million, the private sector will pick up the slack for the other nine.
A few points here. First, it's important that Keynes offers no conditions as to what sort of investment need occur. Presumably, full employment can be restored whether the unemployed are set to work digging holes in the ground--and filling them up again--or helping build roads. Only an ignoramus would be concerned with what is being produced; the important thing is to get people up and consuming.
Second, Keynes doesn't tell us whence this investment will come. If the money comes from taxes, this may cause a reduction in the propensity to consume, thereby decreasing the multiplier--according to Keynes. If the money comes from the printing pressed of the central bank, we would expect inflation, although he tells us that: "When full employment is reached, any attempt to increase investment still further will set up a tendency in money-prices to rise without limit, irrespective of the marginal propensity to consume; i.e. we shall have reached a state of true inflation." We'll deal with his definition of inflation later; for now, we note that it can only apply if full employment has been reached; and then it occurs suddenly all at once.
Third, we should be able to verify whether or not this works. And we see that Keynes does try to do this a bit later.
Section III: Keynes clarifies that the multiplier may not always take full effect: "If, therefore, we wish to apply the above without qualification to the effect of (eg.) increased public works, we have to assume that there is no offset through decreased investment in other directions,-and also, of course, no associated change in the propensity of the community to consume." He then goes on the sketch out some of the reasons, but as an implementation of Keynesian policies never seems to produce anything akin to the multiplier effect, I think it clear that government investment causes so many disparate changes in the economy as a whole that we can't possibly list them all. Keynes's theory assumes that government may act in a vacuum, but we know that every economic action undertaken produces innumerable effects on the other economic actors.
Section IV: I don't find anything worthy of especial comment in this section.
Section V: Using the little data available, Keynes can attempt to verify his theory. "Taken in conjunction with estimates of national income these [numbers] suggest, for what they are worth, both a lower figure and a more stable figure for the investment multiplier than I should have expected. If single years are taken in isolation, the results look rather wild. But if they are grouped in pairs, the multiplier seems to have been less than 3 and probably fairly stable in the neighbourhood of 2.5. This suggests a marginal propensity to consume not exceeding 6o to 70 per cent. — a figure quite plausible for the boom, but surprisingly, and, in my judgment, improbably low for the slump." In other words, the marginal propensity to consume has absolutely no relation to employment numbers. Don't think that the inability of the data to confirm his theory would slow Keynes down for a bit. Not in the least.
Section VI: Here we have a rhetorical aside, and a reminder that Keynes can be a clear an engaging writer when he takes the time to do so. Unfortunately, the subject of this section is an attack on gold. Since gold is and has been a valuable commodity for the purposes of economic exchange, I have little doubt that it will continue to be useful to humans for quite awhile, certainly longer than our fiat currency. It shall outlast the influence of Keynes himself.