Editing Keynesian economics (section)

==<span id=concepts>Keynesian models and concepts</span>==
===<span id=aggregatedemand>Aggregate demand</span>===
[[File:Keynescross.svg|class=skin-invert-image|thumb|Keynes–Samuelson cross]]

Keynes' view of saving and investment was his most important departure from the classical outlook. It can be illustrated using the "[[Keynesian cross]]" devised by [[Paul Samuelson]].<ref>P. A. Samuelson, ''Economics: an introductory analysis'' 1948 and many subsequent editions.</ref> The horizontal axis denotes total income and the purple curve shows ''C'' (''Y'' ), the propensity to consume, whose complement ''S'' (''Y'' ) is the propensity to save: the sum of these two functions is equal to total income, which is shown by the broken line at 45°.

The horizontal blue line ''I'' (''r'' ) is the schedule of the marginal efficiency of capital whose value is independent of ''Y''. The schedule of the marginal efficiency of capital is dependent on the interest rate, specifically the interest rate cost of a new investment. If the interest rate charged by the financial sector to the productive sector is below the marginal efficiency of capital at that level of technology and capital intensity then investment is positive and grows the lower the interest rate is, given the diminishing return of capital. If the interest rate is above the marginal efficiency of capital then investment is equal to zero. Keynes interprets this as the demand for investment and denotes the sum of demands for consumption and investment as "[[aggregate demand]]", plotted as a separate curve. Aggregate demand must equal total income, so equilibrium income must be determined by the point where the aggregate demand curve crosses the 45° line.<ref>Chapter 3.</ref> This is the same horizontal position as the intersection of ''I'' (''r'' ) with ''S'' (''Y'' ).

The equation ''I'' (''r'' )&nbsp;=&nbsp;''S'' (''Y'' ) had been accepted by the classics, who had viewed it as the condition of equilibrium between supply and demand for investment funds and as determining the interest rate (see [[interest#classicalinterest|the classical theory of interest]]). But insofar as they had had a concept of aggregate demand, they had seen the demand for investment as being given by ''S'' (''Y'' ), since for them saving was simply the indirect purchase of capital goods, with the result that aggregate demand was equal to total income as an identity rather than as an equilibrium condition. Keynes takes note of this view in Chapter 2, where he finds it present in the early writings of [[Alfred Marshall]] but adds that "the doctrine is never stated to-day in this crude form".

The equation ''I'' (''r'' )&nbsp;=&nbsp;''S'' (''Y'' ) is accepted by Keynes for some or all of the following reasons:
* As a consequence of the ''principle of effective demand'', which asserts that aggregate demand must equal total income (Chapter 3).
* As a consequence of the identity of saving with investment (Chapter 6) together with the equilibrium assumption that these quantities are equal to their demands.
* In agreement with the substance of the classical theory of the investment funds market, whose conclusion he considers the classics to have misinterpreted through circular reasoning (Chapter 14).

===<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.

===<span id=liquiditytrap>The liquidity trap</span>===
[[File:Keynesliquiditytrap.svg|class=skin-invert-image|thumb|The liquidity trap]]The [[liquidity trap]] is a phenomenon that may impede the effectiveness of monetary policies in reducing unemployment.

Economists generally think the rate of interest will not fall below a certain limit, often seen as zero or a slightly negative number. Keynes suggested that the limit might be appreciably greater than zero but did not attach much practical significance to it. The term "liquidity trap" was coined by [[Dennis Robertson (economist)|Dennis Robertson]] in his comments on the ''General Theory'',<ref>D. H. Robertson, "Some Notes on Mr. Keynes' General Theory of Interest", ''Quarterly Journal of Economics'', 1936</ref> but it was [[John Hicks]] in "[[Mr Keynes and the Classics|Mr. Keynes and the Classics]]"<ref>"Mr. Keynes and the 'Classics'; A Suggested Interpretation", ''Econometrica'', 1937.</ref> who recognised the significance of a slightly different concept.

If the economy is in a position such that the liquidity preference curve is almost vertical, as must happen as the lower limit on ''r'' is approached, then a change in the money supply ''M̂'' makes almost no difference to the equilibrium rate of interest ''r̂'' or, unless there is compensating steepness in the other curves, to the resulting income ''Ŷ''. As Hicks put it, "Monetary means will not force down the rate of interest any further."

Paul Krugman has worked extensively on the liquidity trap, claiming that it was the problem confronting the Japanese economy around the turn of the millennium.<ref>P. R. Krugman, "It's baaack: Japan's slump and the return of the liquidity trap," ''Brookings papers on economic activity'', 1998.</ref> In his later words:
<blockquote>Short-term interest rates were close to zero, long-term rates were at historical lows, yet private investment spending remained insufficient to bring the economy out of deflation. In that environment, monetary policy was just as ineffective as Keynes described. Attempts by the Bank of Japan to increase the money supply simply added to already ample bank reserves and public holdings of cash...<ref>P. R. Krugman, Introduction to the ''General Theory''..., 2008.</ref></blockquote>

====<span id=islm>The IS–LM model</span>====
[[File:Keynesislm.svg|class=skin-invert-image|thumb|IS–LM plot]]

Hicks showed how to analyse Keynes' system when liquidity preference is a function of income as well as of the rate of interest. Keynes's admission of income as an influence on the demand for money is a step back in the direction of classical theory, and Hicks takes a further step in the same direction by generalizing the propensity to save to take both ''Y'' and ''r'' as arguments. Less classically he extends this generalization to the schedule of the marginal efficiency of capital.

The [[IS–LM model|IS-LM model]] uses two equations to express Keynes' model. The first, now written ''I'' (''Y'', ''r'' ) = ''S'' (''Y'',''r'' ), expresses the principle of effective demand. We may construct a graph on (''Y'', ''r'' ) coordinates and draw a line connecting those points satisfying the equation: this is the ''IS'' curve. In the same way we can write the equation of equilibrium between liquidity preference and the money supply as ''L''(''Y'' ,''r'' ) = ''M̂'' and draw a second curve – the ''LM'' curve – connecting points that satisfy it. The equilibrium values ''Ŷ'' of total income and ''r̂'' of interest rate are then given by the point of intersection of the two curves.

If we follow Keynes's initial account under which liquidity preference depends only on the interest rate ''r'', then the ''LM'' curve is horizontal.

[[Joan Robinson]] commented that:
<blockquote>... modern teaching has been confused by J. R. Hicks' attempt to reduce the ''General Theory'' to a version of static equilibrium with the formula IS–LM. Hicks has now repented and changed his name from J. R. to John, but it will take a long time for the effects of his teaching to wear off.</blockquote>

Hicks subsequently relapsed.<ref>Richard Kahn, ''The Making of Keynes' General Theory'', pp. 160 and 248.</ref>{{Clarify|date=November 2021}}