Editing Keynesian economics (section)

===<span id=multiplier>The Keynesian multiplier</span>===
Keynes introduces his discussion of the multiplier in Chapter 10 with a reference to Kahn's earlier paper (see [[#multorigins|below]]). He designates Kahn's multiplier the "employment multiplier" in distinction to his own "investment multiplier" and says that the two are only "a little different".<ref>p. 115.</ref> Kahn's multiplier has consequently been understood by much of the Keynesian literature as playing a major role in Keynes's own theory, an interpretation encouraged by the difficulty of understanding Keynes's presentation. Kahn's multiplier gives the title ("The multiplier model") to the account of Keynesian theory in Samuelson's ''Economics'' and is almost as prominent in [[Alvin Hansen]]'s ''Guide to Keynes'' and in [[Joan Robinson]]'s ''Introduction to the Theory of Employment''.

Keynes states that there is ...
<blockquote>... a confusion between the logical theory of the multiplier, which holds good continuously, without time-lag ... and the consequence of an expansion in the capital goods industries which take gradual effect, subject to a time-lag, and only after an interval ...<ref>p122.</ref></blockquote>
and implies that he is adopting the former theory.<ref>p. 124. See a discussion in the work by G. M. Ambrosi cited below, and also Mark Hayes's statement that "the 'sequence' multiplier of Old Keynesian economics cannot be found in ''The General Theory''" (''The Economics of Keynes: A New Guide to The General Theory'' (2006), p. 120).</ref> And when the multiplier eventually emerges as a component of Keynes's theory (in Chapter&nbsp;18) it turns out to be simply a measure of the change of one variable in response to a change in another. The schedule of the marginal efficiency of capital is identified as one of the independent variables of the economic system:<ref>Chapter 18, p. 245.</ref> "What [it] tells us, is ... the point to which the output of new investment will be pushed ..."<ref>Chapter 14, p. 184.</ref> The multiplier then gives "the ratio ... between an increment of investment and the corresponding increment of aggregate income".<ref>Chapter 18, p. 248.</ref>

[[G. L. S. Shackle]] regarded Keynes' move away from Kahn's multiplier as ...
<blockquote>... a retrograde step ... For when we look upon the Multiplier as an instantaneous functional relation ... we are merely using the word Multiplier to stand for an alternative way of looking at the marginal propensity to consume ...,<ref>''Time in economics'' (1958).</ref></blockquote>
which G. M. Ambrosi cites as an instance of "a Keynesian commentator who would have liked Keynes to have written something less 'retrograde{{'"}}.<ref>G. M. Ambrosi, ''Keynes, Pigou and Cambridge Keynesians'' (2003).</ref>

The value Keynes assigns to his multiplier is the reciprocal of the marginal propensity to save: ''k'' &nbsp;=&nbsp;1 / ''S'' '(''Y'' ). This is the same as the formula for Kahn's multiplier in a closed economy assuming that all saving (including the purchase of durable goods), and not just hoarding, constitutes leakage. Keynes gave his formula almost the status of a definition (it is put forward in advance of any explanation<ref>On p115.</ref>). His multiplier is indeed the value of "the ratio ... between an increment of investment and the corresponding increment of aggregate income" as Keynes derived it from his Chapter&nbsp;13 model of liquidity preference, which implies that income must bear the entire effect of a change in investment. But under his Chapter&nbsp;15 model a change in the schedule of the marginal efficiency of capital has an effect shared between the interest rate and income in proportions depending on the partial derivatives of the liquidity preference function. Keynes did not investigate the question of whether his formula for multiplier needed revision.