ARRANGEMENT CHANGED FOR PURPOSES OF ACCUMULATION:

B. ARRANGEMENT CHANGED FOR PURPOSES OF ACCUMULATION:

I. 40 c + 10 v + 500 (capitalist’ “consumption fund”) 23 = 6000 9000

c II. 1600 + 800 v + 600 (capitalist’ “consumption fund”) = 3000 Assuming now that “production really goes on with this augmented capital” (511),

the new arrangement yields at the close of the “year,” with s/v = 100%

I. 40 c + 10 v + 10 s = 60

c II. 1600 + 800 v + 800 s = 3200

This represents the new base with (v + s) 1 > c II maintaining the condition for growth. And once more c II must rise to assure equality with a rising v + consump- tion fund of capitalists-I. Marx traces out 5 stages as in Table 2.1. Marx (513–14) points out the following expansions between the end of year zero and the end of year 5:

FINAL TOTAL CAPITAL

ORIGINAL

50 C + 1750 V = 7250 8784 C + 2781 V = 11565

TOTAL SURPLUS 1000 I + 750 II = 1750

1610 I + 1171 II = 2781

Moreover, total capitalist’s consumption rises from 500 I + 600 II = 10 at the beginning of year 1 to 732 I + 746 II = 1478 at the beginning of year 5. But there are more specific patterns to be noted. First, the “profit rates” (s/(c + v) in the two sectors remain steady throughout at r 1 = 20% and r II = 33 1 / 3 %, the constancy in each case imposed by the given c/v ratio in each sector and s/v. Second, whereas the savings to surplus ratio of department I is imposed by assumption at g I = 50%, that in II rises from 150/750 = 20% (year zero) to 240/800 = 30% (year 1) and remains at that level thereafter. (The initial rise is achieved by the absolute fall in the capitalists’ consumption fund from 600 to 560.) Third – and an aspect of what has just been said – the accumulation rate, or yearly percentage increase in c + v, is a steady 10% in department I but rises after year 1 from about 6.6% initially to 10% in department II, remaining at that level thereafter. The same pattern emerges

23 Marx may have adopted the term “consumption fund” from Sismondi 1951: 1, 95.

F. The “Extended Reproduction” Scheme

Table 2.1. ( ∗ = “consumption fund”)

I. 4000 c .+ 1000 v + 1000 s = 6000 END YEAR “0”

c II. 1500 + 750 v + 750 s = 3000

I. 40 c + 10 v + 500 ∗ = 6000 BEGINNING YEAR 1

c II. 1600 + 800 v + 600 ∗ = 3000

I. 40 c + 10 v + 10 s = 60 END YEAR 1

c II. 1600 + 800 v + 800 s = 3200

I. 4840 ∗ c + 1210 v + 550 = 60 BEGINNING YEAR 2

9800 800 v + 560 = 3200

c II. 1760 +

I. 4840 c + 1210 v + 1210 s = 7260 END YEAR 2

c II. 1760 + 880 v + 880 s = 3520

BEGINNING YEAR 3 v + 605 ∗ = 7260

I. 5324 c + 1331

c II. 1936 + 968 v + 616 = 3520

I. 5324 + 1331 + 1331 = 7986 END YEAR 3

c II. 1936 + 968 v + 968 s = 3872

I. 5856 c + 1464 v + 665 ∗ = 7986 BEGINNING YEAR 4

c II. 2129 + 1065 v + 678 = 3872

I. 5856 c + 1464 v + 1464 s = 8784 END YEAR 4

c II. 2129 + 1065 v + 1065 s = 4259

I. 6442 ∗ c + 1610 v + 732 = 8784 BEGINNING YEAR 5

c II. 2342 + 1171 v + 746 = 4259

I. 6442 c + 1610 v + 1610 s = 9662 END YEAR 5

c II. 2342 + 1171 v + 1171 s = 4684

with respect to s I ,s II and total surplus; and, of course, the annual growth rate of capital goods (c 1 + v 1 + s 1 ) is also a steady 10% while that of consumption-goods (c 2 + v 2 + s 2 ) rises from 6.6% to a steady 10%. Total product grows at an initial 8.8% rising to a steady 10%.

The initial adjustments in department II – reduced consumption by capitalists, and increase in savings ratio, in rate of capital accumulation and in surplus – would

80 Elements of Growth Theory

have been excluded had Marx started with end year-1. Those variations reflect the choice of initial values. But the choice does bring to light clearly that for steady growth in Marx’s scheme it is department I that sets the pace (all variables rising by 10%) to which department II must accommodate itself. A savings ratio out of surplus of only 30% in the consumer-goods sector suffices to assure ongoing steady growth of capital-goods (and total output), though 50% is the given savings ratio in the capital-goods sector itself, and this because demand for consumer goods emanating from I does not turn on total accumulation in I but only on the wages- goods component (apart of course from department-I capitalists’ consumption).

The initial savings rate in II of 20% falling short, must be adjusted upwards to assure steady and balanced growth. Does Marx explain how the necessary adjust- ment is achieved? To a degree he does so in a subsequent illustration, satisfying the

initial condition I (v+s) > II c , which traces out the implications should capitalists-II not undertake the additions to c required by a decision on the part of capitalists-I to accumulate:

I. 5000 c + 1000 v + 1000 s = 7000

c II. 1430 + 285 v + 285 s = 2000

Here a savings ratio in I of 50% implies consumption of 1000 v + 500 exceeding c II by 70, so that “it is necessary to add 70” from the surplus value in II (514). This, Marx points out, is not a matter of simple exchange but of a real accumulation requirement on the part of II which if not actually undertaken renders “unsaleable” an equivalent amount of capital-goods (517–18).

Conversely, it is possible that while I (v+s) > II c , satisfying the condition for potential accumulation, yet the sum of consumption expenditures emanating from

I (after the decision is made to save out of surplus s/2), falls short of II c , i.e., that the desired rate of saving in I is so high that consumption requirements do not suffice to provide capitalists-II with the wherewithal – via interdepartmental exchange –

to acquire capital goods sufficient even to replace c II . In this case II must “purchase” its maintenance requirements, referring evidently to a net expenditure of money funds: “I (v+1/2s) is smaller than II c . In this case II does not fully reproduce its constant capital by means of exchange and must make good the deficit by purchase from

I. But this does not entail any further accumulation of variable capital II, since its constant capital is fully reproduced only by this operation. On the other hand, that part of capitalists I, who accumulate only additional money capital, have already accomplished a portion of this accumulation by this transaction” (520). However, apart from the unanswered question relating to the source of money funds for II, the case is anomalous in that only departmental-I is expanding, which is certainly not the Marxian norm, and does not figure at all as an issue in the main illustration.

It is helpful to derive a general expression for the annual growth of capital-goods output. Let k I = (c + v) I ;g I = the (given) proportion of surplus s I converted into

F. The “Extended Reproduction” Scheme

81 net investment; s/v the (given) rate of surplus value; and (c/v) I the organic com-

position of capital, v/(c + v) I or (v/k) I the wage-goods fraction in total “capital” and r I = (s/v · v/k) I = (s/k) I the profit rate. 24 Total-capital goods output in any year t,

= I t−1 I + g I I I s t−1 I t−1 + g I s t−1

= I t−1 + g I s I t−1 I t−1

For example, using Table 2.1 data:

x I 2 = (40 + 1100) + 1100/2)(1 + 1100/5500) = (5500 + 550)(1.2) = 6050(1.2) = 7260 x I 5 = ((5856 + 1464) + 1464/2)(1 + 1464/7320) = (7320 + 732)(1.2) = (8052)(1.2) = 9662

Generalizing: x I t = x 1 0 (1 + g I · r I ) t , 25 capital-goods output in our case growing at

a constant annual rate of 10% determined by the given profit rate (r I = 20%) corrected by the given savings ratio (g I = 50%): ˙x I = g I · r I = 10%. 26 The process is described by Marx, following Sismondi, as a “spiral” (above, p. 8 and note 9).

As for the consumer-goods sector, we recall that the proportion of surplus s II converted into net investment is not a datum, but the “passive” outcome of the investment decisions in department-I, yielding – in Marx’s illustration – an initial

value of 20% rising to a steady 30%. The c/v ratio is given at 2/1 so that (v/k) II = 1/3. Assuming as usual s/v = 1, the formula

x 11 t = 11 t−1 + g II s 11 t−1 II t−1

24 Again there is the ambiguity regarding the c element, whether it represents total capital stock or only the “used-up” portion (see note 21).

25 With r I = the “profit” rate, r I · x I 0 = total “profit” and g I · r I · x I 0 = net additions to the stock of “capital.”

26 In our numerical instances, for end year 2 and end year 5: x I 2 = 60 + 10% · 60 = 7260

x I 5 = 8784 + 10% · 8784 = 9662 Generally: x I t = x I 0 (1 + g I · r I ) t , so that for example we have for the second period – which is

end year 3, the base year being end year 1 (6600) not end year “zero” (6000) since that is not yet an equilibrium situation: x I 3 = 6600(1.1) 2 = 7986.

82 Elements of Growth Theory

where g II is the “required” savings to surplus ratio and (s/k) II the profit rate in department II, yields for year-5:

x 11 5 = (3194 + 3/10 · 1065)(1 + 1065/3194) = (3513)4/3 = 4684

The general rule applies: the growth rate of output in department I = (r · g) I = 20% × 1/2 = 10%, becomes the growth rate in department II required to assure balanced inter-departmental exchanges. This growth rate, given the profit rate of

33 1 / 3 %, dictates a savings ratio of 30%. Marx’s main illustration therefore does not presume that capitalists-II attempt – like capitalists-I – to save 50% of surpluses, but treats their savings decisions as responses to those made in sector I – in effect the “lead” sector – required to assure ongoing or flawless growth. Morishima refers to Marx’s “very peculiar investment function, such that . . . capitalists of department I devoted a constant proportion of their surplus value to accumulation . . . and capitalists of department II adjusted their investment so as to maintain the balance between the supply and demand for capital goods” (Morishima 1973: 118; also Luxemburg 1951 [1913]: 120–38). But Marx was obliged to proceed in this fashion by the structure of the departmental

analysis, for to impose a g II ratio renders the system over-determined. This same characteristic also made it impossible to start out with a Simple Reproduction scheme, for example:

I. 4000 c + 1000 v + 1000 s

c II. 2000 + 500 v + 500 s

and trace out the implications of decisions by capitalists in each sector to engage in saving and net accumulation, i.e., to examine the transition from a static to a growing system; rather it was necessary to select initial data in the main scheme

whereby (v + s) I > c II (see above, p. 75). Had Marx started out with the Simple Reproduction scheme, there would have been no way to set the system in motion. First, an assumed common increase in g from zero (say to 1/2) in each sector implies that total demand for consumer goods by department-I falls short of total demand for capital goods by department II:

I. 40 c + 10 v + 500 (consumption fund)

c II. 20 + 550 v + 250 (consumption fund) But even g = 1/2 in department I alone is problematic, since I’s savings ratio implies

consumption of 1600 falling short of c II . This problem, that part of department-II’s product is rendered unsaleable, is taken up by Marx thus: “Instead of 2,000 I (v+s) , only 1,500, namely (1,000 v + 500 s ) I, are therefore exchangeable for 2,000 II c ; 500 II c cannot be reconverted from the commodity form into productive (constant) capi- tal II. Hence there would be an overproduction in II, exactly equal in volume to the

83 expansion of production in I” (503–4). Marx goes on to suggest that the “overpro-

G. Concluding Comment

duction” in question might even impede the ability of II to buy the capital-goods’ counterpart of v I (504). The transition to growth remained for Marx an enigma.

What now of the economic logic for regarding department-I as lead sector by treating the savings ratio g – not only the profit rate r – as a datum? No reason is given by Marx for this decision, whereas it would appear intuitively possible to fix the savings ratio in II so that the growth rate of the economy is determined in that sector, with I coming into line. However, if one carries out this exercise it is not clear that the required interdepartmental balance can be satisfied. For example,

using as base (Table 2.1) the end year-one data II. 1600 c + 800 v + 800 s – year zero is below “par” as we have seen – assume that department II saves 1/2 of surplus (g II = 50%) and allocates the new accumulations ( = 400) according to c/v = 2/1 so that c rises by 266.6 and v by 133.3. At the beginning of year 2 we now have:

II. 1866.6 c + 933.3 v + 400 consumption fund Inter-sectoral balance requires that consumption by workers and capitalists in

department I must equal 1866.6. Applying the principle that the growth rate of the economy is determined once the departmental savings rate as well as the profit

rate are given, g II · r II will determine the growth rate at one half 33.3% = 16.6%. The savings rate required of I must guarantee this same growth rate. Thus with the original end year 1 data for I: 40 c + 10 c + 10 s = 60 with r = 20%, g I is determined thus:

g I · 20% = 16.6% ∴ g I = 83%

This savings rate implies that “required” net investment – and corresponding con- sumption – in I = 83/100 × 10 = 913, which, with c/v = 4/1, is allocated between c and v in the ratio 730.4/182.6 yielding:

I. 5130 c + 1282.6 v + 187 (consumption fund) = 6600. But the sum of consumption requirements thus emanating from department I ( =

1469.6), falls short of the capital-goods requirements of department II (c II = 1750). It is not clear whether this imbalance is an inherent feature of the system precluding treatment of II as lead sector and, if so, why.