The first serious challenge to Keynes's General Theory came from those closest to him analytically: the "Wicksellians". Bertil Ohlin's (1937) Economic Journal articles claimed not only that the "Stockholm School" had anticipated the main elements of Keynes's theory but that, more importantly, there remained the problem of reconciling savings and investment while the multiplier was working itself through.
Ohlin's claim of precedence, can be reasonably dismissed. While there are many points of contact between the Stockholm School and Keynes (who was himself a "Wicksellian" in his pre-1936 macroeconomics, after all), the Swedes did not have a theory of effective demand as the determinant of output, which was the essence of the General Theory after all.
Ohlin's second claim - which was also made by the other "English Wicksellian", Dennis H. Robertson (1937, 1940) - was substantially more serious. The problem can be viewed in the following manner: suppose there is an exogenous increase in effective demand; consequently, via the multiplier, output will rise to meet it. However, during the process of adjustment towards the new equilibrium, planned savings and planned investment are not equal. Of course, as Keynes reiterated several times (and perhaps made more forcefully clear by Lerner, 1938, 1939, 1944), actual savings is investment in the General Theory, thus they are equal at all times.
In principle, it is easy to see that this is correct: suppose there is an injection of investment of $10. By the multiplier theory, this implies that in the first round of the multiplier, say, $1 of this extra income will be saved and $9 will be spent - thus planned investment exceeds planned savings by $9. What Keynes insisted upon is, of course, that the $9 that will be spent are not yet spent and thus constitute "savings" - unplanned but still actual savings. Thus, actual investment is always equal to actual savings even if planned investment and planned savings diverge during the multiplier process.
However, we can start thinking of Ohlin's argument in the following way: suppose, indeed, that there are $9 of actual but unplanned savings that agents intend to get rid of in the next round of the multiplier process. Would not these $9 consequently be out of the loan market and thus unavailable for lending? This is a delicate point, but let us suppose that they are not available for lending. Then, although actual savings may indeed have increased by $10, planned savings only increased by $1 and if only planned savings make it to the loan market then, consequently, there is a disequilibrium in the financial books, even if its only a temporary one. Consequently, one ought to imagine that in order to keep the financial books in order in the interim, the rate of interest will rise. But then, if this is granted, planned investment will decline as a result and the multiplier will be set in reverse before it has even had a chance to work itself through.
As it happens, Ohlin's (1937) original argument was a bit more complicated -- and confused. He argued that interest rates were determined by ex ante investment and ex ante savings where "ex ante" does not exactly mean "planned" but rather "expected". The difference is important for it exposed a weak spot in Ohlin that Keynes (1937) used to attack in his rejoinder: namely, it might be understandable that ex ante investment (i.e. expected investment) ought to lead to a greater demand for loans as entrepreneurs normally arrange for financing before they carry out investment projects, but how on earth can "ex ante" (i.e. expected) savings make it into the financial markets? Ohlin's theory was simply counter-intuitive as the notion of "expected" savings having any impact on the loan market was ludicrous - one cannot, after all, supply what does not exist. Ohlin's categories, Keynes concluded, were muddled and his objections misplaced.
However, the earlier possibility of "unplanned" savings not making it to market might have been in the back of Keynes's mind -- and, as a result, he made a rather strange concession to Ohlin, namely:
"During the interregnum -- and during that period only -- between the date when the entrepreneur arranges his finance and the date when he actually makes his investment, there is an additional demand for liquidity without, as yet, any additional supply of it necessarily arising. In order that the entrepreneur may feel himself sufficiently liquid to be able to embark on the transaction, someone else has to agree to become, for the time being at least, more unliquid than before." (Keynes, 1937: p.665).
Of course, as Keynes notes, "finance is essentially a `revolving fund'. It employs no savings. It is, for the community as a whole, only a book-keeping transaction." (Keynes, 1937: 666). Thus, the financing of a new investment project is obtainable from this "fund" and this fund is replenished as investment projects are actually undertaken and loans repaid. Does this mean that a rise in planned investment will lead to a rise in interest rates? Ostensibly, it could as the rise in money demand via this "finance demand" channel could increase interest rates directly and could potentially kill the multiplier unless this "revolving fund" expands.
Now, Dennis Robertson (1937, 1940) had raised similar objections to Keynes's theory. Specifically, he believed that Keynes's theory of liquidity preference and the Wicksellian theory of loanable funds were one and the same thing, to the point which he innocently noted that:
"I have suggested that even from the momentary market point of view, the Keynesian formulation tends to obscure unduly the parts played by productivity and thrift" (Robertson, 1940: p.24).
However, Keynes was adamant about savings not affecting interest rates:
"If there is no change in the liquidity position, the public can save ex-ante and ex-post and ex-anything-else until they are blue in the face, without alleviating the problem in the least - unless, indeed, the result of their efforts is to lower the scale of activity." (Keynes, 1937: p.668),
However, he contradicts himself with his finance demand for money for, in the same article, Keynes notes that the finance demand for money applies to all planned activity, "whether the planned activity by the entrepreneur or the planned expenditure by the public is directed towards investment or towards consumption." (Keynes 1937: p.667). To use Robertson's terms, this implies that, via the finance demand for money, higher "productivity" (more planned investment) could lead to a direct rise in interest rates and "extra thrift" (less planned consumption) could lead to a direct fall in interest rates. This was a contradiction which Keynes seemed not to have spotted - and few economists have spotted since (albeit, see the attempts to incorporate finance demand for money in Paul Davidson (1965, 1972) and S.C. Tsiang (1956, 1966, 1980)).
Finally, we should mention a further criticism which led John Mayndard Keynes to revise a portion of his thesis. Specifically, in the General Theory, Keynes had accepted the "second classical postulate" that the real wage and the level of employment were negatively related. Specifically, Keynes had accepted the notion that the real wage would be equal to the marginal product of labor, so that w/p = FN. Naturally, we must remind ourselves that Keynes's causality goes the other way: aggregate demand determines the employment level N first, which then determines the marginal product and consequently the real wage. However, by accepting that marginal product of labor was downward sloping, the implication is that the real wage is counter-cyclical: i.e. when employment N rises, the marginal product of labor declines and hence the real wage must decline.
This was challenged by John T. Dunlop (1938) and Lorie Tarshis (1938) who argued that the real wage was, in fact, procyclical. Keynes responded to this with a 1939 paper "Relative Movements of Real Wages and Output" in the Economic Journal, where he recanted his earlier acceptance of this "first classical postulate" (Keynes, 1936: p.5) and agreed with the Dunlop-Tarshis contention that the real wage was, in fact, pro-cyclical (implying that the labor demand function is not the downward-sloping marginal productivity of labor curve, but rather an upward-sloping one).