Hayes(H)presents a reinterpretation of Keynes's GT which is both worthwhile and error filled all at the same time.It is worthwhile in that he corrects a number of the minor errors in the literature on Keynes's theory of effective demand made by Sidney Weintraub,Paul Davidson,Geoffrey Harcourt,Victoria Chick,etc.,while at the same time reinforcing the two major errors originally made by Dennis Robertson.These same errors were repeated by Hugh Townshend in a private letter of correspondence to Keynes in the late 1930's.The two errors are,first, that Z,the expected aggregate supply function,equals pO,where p is the expected price level and O is real output and second,that Z,the aggregate supply function ,is also the aggregate supply curve.Any reader, who can integrate derivatives(take the anti derivative so as to obtain the original function as it was first defined by Keynes)can simply go to footnote 2 on pp.55-56 of the GT and/or to p.283(one can also successfully use the derivatives on pp.284 and 285 )and easily discover what Keynes's Z function has to be.There will be only one answer.Of course,since the economics literature consists of many different answers about what Z is,all these other answers will be demonstrated to be mathematically false.This is the result the economics profession fears.There is only one answer possible.The answer is that Z= WN+P ,where W is a constant money wage,N is total aggregate employment,and P is equal to expected economic profit.Robertson actually came very close to correctly specifying Z in his 1936 Quarterly Journal of Economics article on p.168 when he stated that "...(Z)is the proceeds the expectation of which will just make it worthwhile to give that amount of employment,and for simplicity may be regarded as made up of factor-cost(F)and associated profit(P)(pp.24-25)." Robertson is refering to pp.24-25 of the GT.Contrary to Robertson,P is EXPECTED profit,not actual profit.Robertson then started talking about Z being equal to pO in later work.All economists,who have written on Keynes's theory of effective demand or the aggregate supply function,Z, or the aggregate supply CURVE,D=Z,which is the locus of all the different possible D=Z intersections that specifies a series of multiple equilibria,since every D=Z intersection point satisfies both the necessary and sufficient first and second order conditions for an EXPECTED profit maximum ,have, since that time, invariably confused the Z function with the D=Z locus .The Y function,which stands for the actual aggregate demand,is equal to PO,where ,in the context of the Y-Multiplier model of chapter 10,P is the actual price level. On p.189 of his book,H commits the exact same mathematical error later made by Robertson, both in a book published in 1941 and in a series of exchanges on Keynes's theory published in the Economic Journal of 1954-1956.Based on his erroneous belief that Z=pO,H substitutes this into Y(GT,P.209) to obtain p=Z/O .This gives the incorrect answer that Y=Z.Of course,only D can equal Z at an optimum point that maximizes expected profit.Y deals with actual,not expected,profits.H is mixing up the two different sub models in the GT,the Y-multiplier model,which is Keynes's simplest model, and the D-Z model,which is the most advanced.Similar errors occur on pp.91-93 when H attempts to deal with footnote 2 on pp.55-56 .
It is a strange and bizarre world where the use of simple integration rules,that would yield the obvious answer that Z=WN +P and D= pO,are not used by an economics profession that claims that they are highly developed mathematicians.There should be no more " What did Keynes mean ? " claims .Yet these claims have been going on in the economics profession since 1936.Interestingly,not a single economist in the 20th century, or so far in the 21st century,has applied the simple and straightforward integration technique just to see what the answer would be if they went ahead and integrated Keynes's derivatives on pp.55-56,ft. 2 and on p.283(or in footnotes 1 and 2 on p.283).
I have appended two discussion sections below for the interested reader.However,to make use of them you will have to be able to use simple,easy integration.