1937 economic paper by John Hicks
John Hicks's 1937 paper Mr. Keynes and the "Classics"; a suggested interpretation is the most influential study of the views presented by J. M. Keynes in his "General Theory of Employment, Interest, and Money" of February 1936. It gives "a potted version of the central argument of the "General Theory"" as an equilibrium specified by two equations (shown as intersecting curves in the "IS-LM" diagram) which dominated Keynesian teaching until Axel Leijonhufvud published a critique in 1968. Leijonhufvud's view that Hicks misrepresented Keynes's theory by reducing it to a static system was in turn rejected by many economists who considered much of the "General Theory" to be as static as Hicks portrayed it.
James Tobin described the "IS-LM" model as:
... the tool of first resort. If you are faced with a problem of interpretation of the economy – policy or events – probably the first thing you can do is to try to see how to look at it in these [IS-LM] terms.
Background.
Publication history.
"Mr Keynes and the "Classics"" was first published in "Econometrica" (April 1937) and reprinted in 'Critical essays in monetary theory' (1967) and again in 'Money, interest and wages' (1982), this time with a prefatory note.
Several of Hicks's other papers deal with the same subject. His review of the "General Theory" was published in the "Economic journal" in June 1936 and reissued in 'Money, interest and wages'. 'The classics again' was published in the same journal in 1957 and reissued in 'Critical essays in monetary theory'. 'IS-LM – an explanation' was published in the winter 1980-1 issue of the "Journal of post-Keynesian economics" and reprinted in 'Money, interest and wages'.
Origins of "Mr Keynes and the "Classics"".
Hicks's paper as first was based on a version read at a meeting of the Econometric Society at Oxford in September 1936, and taking account of the discussion which took place there and later at Cambridge. 
According to Warren Young it should be 'regarded not so much as an original and new piece of analysis but as a synthesis of earlier interpretational attempts by [Roy] Harrod and [James] Meade'. Meade and Harrod 'themselves were intimately associated with the development of the "General Theory"'; Harrod was one of the colleagues to whom Keynes sent proofs of the book for comment. Gonçalo L. Fonseca specifically mentions that "The equations of the "IS-LM" model were written down by Harrod (1937), but the (later) drawing of the diagram by Hicks robbed him of his claims to precedence".
Hicks's own account of the origins of the paper is rather different. He had been working independently on questions overlapping those addressed by the "General Theory" and found much in it which corresponded to his own thinking. It is this convergence of thinking, rather than the prior knowledge supplied by others, which accounts for his rapidly arriving at a clear picture of Keynes's views. This account explains the singlemindedness of Hicks's interpretation, which homes in on Book IV of the "General Theory" and on excessive wages as a cause of unemployment, while other reviewers were struggling to reconcile the different elements of Keynes's thought.
Hicks's relatively classical interpretation of Keynes made him the target of criticisms from more radical Keynesians. He had considered the "General Theory" a more conservative work than Keynes's earlier "Treatise on Money" and given it a favourable review. But he came to have doubts about the formalism he'd presented in 'Mr Keynes and the Classics' and oscillated between retractions and reavowals.
Terminology.
The two curves in Hicks's original diagram are labelled "IS" and "LL", and his original name for the model was "IS-LL" (or possibly even "SI-LL"), but the name which stuck was "IS-LM". It is also known as the 'Hicks-Hansen model', reflecting the importance of Alvin Hansen's 1953 'Guide to Keynes' (which interpreted Keynes's system along the lines of Hicks's model) in introducing Keynesian ideas to America.
Mathematical representation of Keynes's theory.
The "General Theory".
See the article on the "General Theory" for a description of Keynes's economic ideas. Chapters 1–13 and 15 develop the concepts on which Keynes's model is based. The model itself receives an initial statement in Chapter 14 and is 'restated' in Chapter 18: it is these statements which Hicks presented in the mathematical form of an equilibrium specified by simultaneous equations.
The choice of units.
In section I, Hicks presents Keynes's theories in opposition to Pigou's 1933 "Theory of Unemployment". He remarks that:
Professor Pigou's theory runs, to a quite amazing extent, in real terms... The ordinary classical economist has no part in this "tour de force".
But if, on behalf of the ordinary classical economist, we declare that we would have preferred to investigate many of those problems in money terms, Mr. Keynes will reply that there is no classical theory of money wages and unemployment.
This attaches considerable importance to the choice of units, as Keynes himself did when criticising Pigou. The explanation is that the conversion factors – the price level and the wage rate – are not neutral like physical units, but themselves part of the analysis. 
Keynes had avoided real values because their use requires the postulation of a single 'representative' price level. At times in the "General Theory" he allowed every industry to have its own price and elasticity of employment. Hicks split the economy into just two sectors: capital goods and consumption goods. Even this is more than he needed, and in the account below we treat the economy as a single sector.
Hicks assumes that the wage rate is fixed externally ('exogenous').
The variables of the system.
The paragraph in which Hicks sets out his variables is the main point of obscurity in an otherwise readable paper. His variable names are unintuitive and inconsistent with those used by Keynes which we adopt below. 
Some immediate consequences can be drawn. The 'first postulate of classical economics' asserts that the wage is equal to the marginal product, so we might be tempted to write:
Unfortunately this isn't quite correct, since it is necessary to differentiate "real" output and multiply the result by "P" rather than differentiating output in money terms. Hicks avoids this difficulty by giving the equation an unusual form, differentiating an independent with respect to a dependent variable [Px = "w" (dNx/d"x")]. He then gives a further equation [written "I"="wx" (dNx/d"x")+"wy" (dNy/d"y")] in which the price levels by sector determine the relation between output and income; but if we avoid representing income and output by different symbols we can dispense with this equation.
He remarks (in our notation) that since "Y" is a (monotonic) function of "N", once it is given "N" is given; but, since he is working in money units, there is an implicit assumption that "P" is given.
The 'classical' theory.
Hicks starts with the quantity theory of money:
where "V" is the velocity of money. [He himself writes "M"="kI" (where "k"=1/"V"). "k" is Keynes's symbol for the multiplier.]
His second equation can be written:
where I ("r") is 'the amount of investment (looked at as the demand for capital)' which is 'what becomes of the marginal-efficiency-of-capital schedule in Mr. Keynes's work'. "S"("Y","r") is the propensity to save (expressed as a function of money income). He suggests that the presence of "Y" as an argument to "S" is unnecessary given that it is by now determined by the quantity theory.
[This equation is expanded into two due to Hicks's proliferation of symbols. One equation in words is 'Investment = Saving': in symbols the two equations are Ix="C"("i") and Ix="S"("i","I"). "C" stands for 'capital' whereas for Keynes it stood for 'consumption'. So Hicks's "C"("i") is our I ("r") while his "S"("i","I") is our "S"("Y","r").]
The two equations as we have given them can be solved together for "Y" and "r"; and total employment is considered as determined by income "Y". 
Hicks sums up:
I think it will be agreed that we have here a quite reasonably consistent theory, and a theory which is also consistent with the pronouncements of a recognizable group of economists... Historically this theory descends from Ricardo... it is probably more or less the theory that was held by Marshall...
This is historically questionable; see below. 
In fact both of the equations Hicks takes from Keynes are part of the classical analysis. The quantity theory has precisely the sense Hicks gave to it. In classical theory the equation I ("r") = "S"("Y","r") is the equilibrium condition of the loans market and determines the rate of interest rather than the level of employment (see Keynes's Chapter 14). Hicks's pair of equations in money terms are complete as he gave them, containing only two variables, but this property would not necessarily apply to their classical counterparts in which some quantities would be given in real terms (see the "General Theory").
Mr Keynes's 'special' theory.
Hicks moves on to discuss industrial fluctuations in his §II, remarking that changes in the velocity of circulation can be related to changes in confidence, and asking whether velocity has not 'abdicated its status as an independent variable' [strictly he refers to his uninterpreted variable "k", which can be recognised as the reciprocal of velocity in classical theory]. He adds that 'this last consideration is powerfully supported by another' since 'on grounds of pure value theory, it is evident that the direct sacrifice made by a person who holds a stock of money is a sacrifice of interest'.
He now quotes Lavington (who also said that "It's all in Marshall, if one only digs deeply enough") as arguing that an individual will hold money up to the point at which the convenience of doing so is equal to the rate of interest. 
The demand for money depends on the rate of interest! The stage is set for Mr. Keynes.
He contrasts the equations of 'classical' theory:
with those adopted by Keynes:
These differ from the classical equations in two ways. On the one hand, the demand for money is conceived as depending upon the rate of interest (Liquidity Preference)...
and more surprisingly, as depending "solely" on the rate of interest, with no possible influence from the level of income. And:
On the other hand, any possible influence of the rate of interest on the amount saved out of a given income is neglected... this second amendment is a mere simplification, and ultimately insignificant.
The liquidity preference doctrine is that of Keynes's Chapter 13, rapidly superseded by his more comprehensive doctrine of Chapter 15. Its role in Keynes's theory is unclear. It provides no mechanism for ensuring equilibrium between supply and demand of loans, but Hicks argued elsewhere that this equilibrium would be ensured anyway by Walras's law.
Mr Keynes's 'general' theory.
Hicks revises the equations to take account of the Chapter 15 theory of liquidity preference:
'With this revision, Mr Keynes takes a big step back to Marshallian orthodoxy.' In fact Keynes considers liquidity preference to be the sum of two functions so that it may be written:
Here "L"1 is the sum of transactions and precautionary demands and "L"2 is speculative demand. The form "L"("Y","r") is slightly more general than Keynes's "L"1("Y") + "L"2("r") but the difference is purely notational.
The IS-LM model.
Having analysed Keynes's equilibrium system as a pair of simultaneous equations, Hicks then represents it graphically as two intersecting curves. The IS curve joins all the pairs (Y,r) which satisfy the "IS" equation I(r)=S(Y) and the LM curve joins the pairs which satisfy the "LM" equation L(Y,r)=M. The point of intersection of the two curves tells us the income Ŷ and the rate of interest r̂.
Under Keynes's Chapter 13 liquidity preference doctrine the LM curve will be a horizontal line. Under his Chapter 15 doctrine, if "L" is an increasing function of "Y" and a decreasing function of "r", then the LM curve will slope upwards. The IS curve always slopes downwards.
Source of the equations.
In Chapter 14 Keynes identified the equation I("r") = "S"("Y") as the main determinant of employment once its dependence on "r" has been eliminated through the liquidity preference function.
The discussion is presented in connection with a complicated diagram whose essential components are shown on the right. The vertical axis is saving/investment and the horizontal axis is the rate of interest. For a few representative levels of income he draws a curve showing the amount of saving which will take place for each level of income. One of these is shown as a solid red line; another, corresponding to a higher level of income, is shown as a dotted line. Both curves are increasing functions of "r", which may be no more than a concession to the