Prosperity and Depression.pdf

Recent Developments in Trade Cycle TheoryPart IIIIn this table the diagonal sums, as those indicated by the arrow,' representthe successive income generated by the primary expenditures.They approach lOa. _I_= 500, if continued long enough. The hori-I-%lontal sums (in each line) represent the sum total of income generatedin the period which corresponds to the line in question by the initialexpenditure in that periodptus the indirect contribution to the periodin question of all the previous original expenditures through the reexpenditurein each period of four-nfths· of the receipts in the precedingperiod. This sum too approaches eventually. (for remote periods) 500dollars. The ratio of this sum to the primary expenditure again can beregarded as the multiplier. It measures the income per unit periodwhich will eventually be generated by a continual stream of primaryexpenditures. 1 Obviously this multiplier is different from the onemeasured diagonally in our table. But the two meanings are not distinguishedcarefully enough in the, literature on the subject. 2A number of baflling question~ arise in connection with this serialinterpretation of the multiplier. First, is it possible at all, in this case,1 For further exercises in the mechanics or rather arithmetics of these schemessee J. M.' Clark and F. Machlup, 10(. dt. There is one further property of theseries which is worth pointtng out because it has been the source of a tangle ofconfusion. It will be observed that the sum of the successive differences of thediagonal series is equal to the initial investment expenditure which started theseries: (100-80) + (80-64) + (64-51.2) + (51.2-40.96) ... = 100. Ingeneral terms, the sum of the successive differences of the series I + C + c+ 2c 3 ••• is: (I-d + (c-c 2 ) + (C 2 _C 3 ) +. (C 3 _C 4 ) + ... :::: I. It will alsobe observed that these successive differences are nothing but the amounts savedin successive periods-saving in each period being defined in the Robertsoniansense as income received in the preceding period minus consumption of the givenperiod. Hence we may say: aggregate saving induced in successive periods byany act of investment approaches the amount of the initial investment, implyingthat S and I. are different for any finite period, the difference becoming smallerwith the length of the period. It is interesting that Mrs. Robinson and Mr. Kahn,both champions of the Keynesian equality or rather identity of S and I, haveadopted that way of looking at the matter. (See J. Robinson, Introduction to theTheory of Employment, pages 20 and 21, and Mr. Kahn's first statement of themultiplier theory, "The Relation of Home Investment to Unemployment" (E(onomkJournal, June 1931). They deduce that nobody needs to worry lest investmentmight exc~ed saving and thus cause inflation, because each act ofinvestment automatically draws' all the necessary saving in its wake. It is probablyno longer necessary to unravel at length the tangle of confusion contained in thisargument. .2 The reason is probably that they are numerically equal, if we have a constantstream of primary expenditures. If this stream is not constant, diagonaland lateral sums will not tend to be equal.