Interactions between the Multiplier Analysis and the Principle of Acceleration Author(s): Paul A. Samuelson
Source: The Review of Economics and Statistics, Vol. 21, No. 2 (May, 1939), pp. 75-78 Published by: The MIT Press
Stable URL: http://www.jstor.org/stable/1927758 .
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INTERACTIONS BETWEEN THE MULTIPLIER ANALYSIS
AND THE PRINCIPLE OF ACCELERATION
woulddeny that the "multiplier" analysis of the effects of governmental deficit spending has thrown some light upon this important problem. Nevertheless,
there would seem to be some ground for the
fear that this extremely simplified mechanism
is in danger of hardeninginto a dogma, hindering progress and obscuring important subsidiary relations and processes. It is highly desirable, therefore, that model sequences,
which operate under more general assumptions,
be investigated, possibly including the conventional analysis as a special case.' In particular, the "multiplier," using this
term in its usual sense, does not pretend to give
the relation between total national income induced by governmentalspending and the original amount of money spent. This is clearly seen by a simple example. In an economy (not
necessarily our own) where any dollar of governmental deficit spending would result in a hundred dollars less of private investment than
would otherwisehave been undertaken,the ratio
of total induced national income to the initial
expenditureis overwhelminglynegative, yet the
"multiplier" in the strict sense must be positive. The answer to the puzzle is simple. What the multiplier does give is the ratio of the total
increase in the national income to the total
amount of investment, governmental and private. In other words, it does not tell us how much is to be multiplied. The effects upon private investment are often regarded as tertiary influencesand receive little systematic attention.
In order to remedy the situation in some
measure, Professor Hansen has developeda new
model sequence which ingeniously combines the
multiplier analysis with that of the acceleration
principle or relation. This is done by making
additions to the national income consist of three
components: (i) governmentaldeficit spending,
private consumption expenditure induced
by previouspublic expenditure,and (3) induced
' The writer, who has made this study in connection with
his research as a member of the Society of Fellows at Harvard University, wishes to express his indebtedness to Professor Alvin H. Hansen of Harvard University at whose suggestion the investigation was undertaken.
private investment, assumed according to the
familiar acceleration principle to be proportional to the time increase of consumption. The introductionof the last component accounts for
the novelty of the conclusions reached and also
the increased complexity of the analysis.
A numerical example may be cited to illuminate the assumptions made. We assume governmental deficit spending of one dollar per unit period, beginning at some initial time and
continuing thereafter. The marginal propensity to consume, a, is taken to be one-half. This
is taken to mean that the consumption of any
period is equal to one-half the national income
of the previous period. Our last assumption is...
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