Depression 2008: is This a Trade Cycle’s Recession?

INTRODUCTIONOr, Gt+1 = AYt – BYt-1 ---------------(1)
Many of the writers are of the opinion that theWhere, A = 2 – cw – c
prevailing depression 2008 is the recessive phase of aAnd, B = 1 – cw
trade cycle. I don’t know whether it is so or theRelation (1) represents the condition in which the
depression 2008 is a different phenomenon. All thecyclical fluctuations in the level of income, as
same, I would like to recall the period when theexplained by Samuelson’s model, are extenuated.
world economies were in search of ways and meansThe values of c (= 0.6) and w (= 1.5), which are
to control the then prevailing inflationary pressure. Ifrelated to the numerical example used by Samuelson
that problematic inflation was a consequence ofto show how the cyclical fluctuations in the level of
some trade cycle running that time, the presentincome are generated, give the values of A and B
depressive trend may well be a consequence of theequal to 0.5 and 0.1, respectively.
successive downward phase (after boom) of theTherefore, Gt+1 = 0.5Yt – 0.1Yt-1 -------------(2)
same trade cycle. Then, it needs not be taken as aIf the initial rate of annual autonomous investment
new thing.(G) is Rs 40 which is changed to Rs 50 in (t)th period
An economy is likely to encounter many disturbancesand if the rate of autonomous investment (G) is
whereby all methods of maintaining employment andplanned as per the relation (2) for (t + 1)th and
national income as steadily rising involve certainonward periods, the level of income will experience a
difficulties and weaknesses depending upon thesteady growth as shown in the table given in the end
nature and size of the disturbances. The periodicalhereof.
rise and fall in the level of economic activities,CONCLUSION
employment and national income is the mostIt is widely accepted that the interaction between
frequent type of the disturbances and is known asmultiplier and accelerator causes the generation of
trade cycle. This type of cyclical fluctuations has beentrade cycles and that the Samuelson’s model is
experienced by all industrial countries since thethe true explanation of the network. If it is so, the
nineteenth century. While governments may haveextenuation of cyclical fluctuations on account of
the greatest difficulty in overcoming the effects oftrade cycles becomes possible, fully and easily, by
major structural changes in the economy, they shouldregulating the autonomous investment according to
be able at least to mitigate cyclical fluctuations bythe relation (1) explained hereinabove. In this way the
means of suitable monetary and fiscal measures.myth of bringing out the economy from the depths
SAMUELSON’S THEORY OF TRADE CYCLEof depression becomes converted into reality. This
Among various theories of trade cycle propoundedwill enable the national income to grow without
by different economists the theories base on thefluctuations on account of a trade cycle caused by
principle of accelerator allied with the multiplier principlethe multiplier-accelerator interaction. Therefore, it may
have paved the way for more accurate analysis ofwell be concluded that if the depression 2008 is the
trade cycle. Economists like R. F. Harrod, A. H. Hansen,recessive phase of a trade cycle, it can easily be
J. R. Hicks and P. A. Samuelson have made fairlytreated in the way suggested above.
successful attempts to establish that the interaction
of the accelerator with the multiplier is capable, underThe table showing the planned autonomous
certain circumstances, of generating continuousinvestment and the stabilized growth of national
cyclical fluctuations.income
Paul A. Samuelson studied the multiplier-accelerator 
interaction in greater detail and derived a model inPeriod
which a series of equations expresses the way in 
which the two forces interact to affect income,Autonomous
consumption and investment over a time. AccordingInvestment
to him, the multiplier and the accelerator combine in a(G)
series of endless possibilities depending upon theConsumption
values of the multiplier and the accelerator. In other 
words, the initial increase in autonomous investment(C)
(Ia) works through the multiplier (K) to cause anInduced Investment
increase in income (Y), say dY = K x Ia {where, K=1(In)
(1 - c) and c represents the marginal propensity toIncome
consume (MPC)], and this increase in income (dY) 
brings an increase in consumption (C), say dC = c x(Y)t-2
dY (where c which works through the accelerator40
(w) to cause a change in induced investment (In),60
say dIn = w x dC, which, in turn, further increases0
income by K x dIn and so the action and the reaction100t-1
continue. The process is super cumulative because40
one initial increase (or decrease) will set off a60
snow-ball effect where income and investment0
interact to magnify the impact at each successive100t
level. Samuelson used lagged functions for investment50
and consumption and derived income function which60
gave various patterns of change in income level, for0
different combinations of the values of the marginal110t+1
propensity to consume (MPC) and the accelerator,45
for a given change in autonomous investment66
(government spending).9
EXTENUATION OF CYCLICAL FLUCTUATIONS120t+2
The present study aims at finding out the condition49
related to the change in autonomous investment that72
extenuates the cyclical fluctuations by making plain9
the ebbs and flows of a trade cycle, explained by130t+3
Samuelson’s model. The change in autonomous53
investment in accordance to the so derived condition78
will provide the steady rate of income growth.9
The income function derived by Samuelson reads as140t+4
–57
Yt = Gt + cYt-1 + w (Ct – Ct-1)84
Where, Yt = Aggregate income or output during a9
period t.150t+5
Gt = Autonomous investment incurred by61
government during the period t, c = Marginal90
propensity to consume (MPC), w = Capital output9
ratio or the accelerator and Ct = Aggregate160t+6
consumption during the period t.65
Yt-1 and Ct-1 denote the income and the96
consumption, respectively, in previous period.9
Therefore, Yt+1 = Gt+1 + cYt + w(Ct+1 – Ct)170t+7
But, Ct = cYt-1 and Ct+1 = cYt69
Therefore, Yt+1 = Gt+1 + cYt + cwYt – cwYt-1102
Or, Yt+1 – Yt = Gt+1 + cYt + cwYt –9
cwYt-1 – Yt180t+8
Or, Yt+1 – Yt = Gt+1 + cw(Yt – Yt-1) –73
(1– c)Yt108
Or, dYt+1= Gt+1 + cw dYt – (1– c)Yt9
[Where, dYt+1 = Yt – Yt-1 and dYt = Yt –190t+9
Yt-1]77
Or, dYt+1 – dYt = Gt+1 + (cw – 1) dYt114
– (1– c)YtdYt+1 and dYt represent the rise in9
income in (t + 1)th and (t)th period, respectively. If200
the cyclical fluctuations in the level of income are---  
extenuated, there will be established a steady rate ofREFERENCES
income growth.1. Brooman F.S., ‘Macro Economics.’
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Or, dYt+1 – dYt = 0Economics.’
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c)Yt = 0Macro Economics.’
Or, Gt+1 = (1– c)Yt – (cw – 1) dYt4. Kurihara K.K., ’Monetary Theory and Public
Or, Gt+1 = (1– c)Yt – (cw – 1)(Yt –Policy.’
Yt-1)5. Rana K.C. and Verma K.N., ‘Macro-Economic
Or, Gt+1 = (2 – cw – c)Yt – (1 –Analysis.
cw)Yt-1