Rate and Mass of Surplus-Value

In this chapter, as hitherto, the value of labour-power, and therefore the part of the workingday necessary for the reproduction or maintenance of that labour-power, are supposed to be given, constant magnitudes.

 This premised, with the rate, the mass is at the same time given of the surplusvalue that the individual labourer furnishes to the capitalist in a definite period of time. If, e.g., the necessary labour amounts to 6 hours daily, expressed in a quantum of gold = 3 shillings, then 3s. is the daily value of one labour- power or the value of the capital advanced in the buying of one labour-power. If, further, the rate of surplusvalue be = 100%, this variable capital of 3s. produces a mass of surplusvalue of 3s., or the labourer supplies daily a mass of surpluslabour equal to 6 hours.

 But the variable capital of a capitalist is the expression in money of the total value of all the labour-powers that he employs simultaneously. Its value is, therefore, equal to the average value of one labour-power, multiplied by the number of labour-powers employed. With a given value of labour-power, therefore, the magnitude of the variable capital varies directly as the number of labourers employed simultaneously. If the daily value of one labour-power = 3s., then a capital of 300s. must be advanced in order to exploit daily 100 labour-powers, of n times 3s., in order to exploit daily n labour-powers.

 In the same way, if a variable capital of 3s., being the daily value of one labour-power, produce a daily surplusvalue of 3s., a variable capital of 300s. will produce a daily surplusvalue of 300s., and one of n times 3s. a daily surplusvalue of n x 3s. The mass of the surplusvalue produced is therefore equal to the surplusvalue which the workingday of one labourer supplies multiplied by the number of labourers employed. But as further the mass of surplusvalue which a single labourer produces, the value of labour- power being given, is determined by the rate of the surplusvalue, this law follows: the mass of the surplusvalue produced is equal to the amount of the variable capital advanced, multiplied by the rate of surplusvalue, in other words: it is determined by the compound ratio between the number of labour-powers exploited simultaneously by the same capitalist and the degree of exploitation of each individual labour-power.

 Let the mass of the surplusvalue be S, the surplusvalue supplied by the individual labourer in the average day s the variable capital daily advanced in the purchase of one individual labour-power v, the sum total of the variable capital V, the value of an average labour-power P, its degree of exploitation

  
a' (surplus-labour)
—————————————
   a (necessary-labour)

and the number of labourers employed n; we have:

     
/  s
      | —- x V
      |  v
 S =  |
      |        a'
      |  P  x —- x n.
              a

It is always supposed, not only that the value of an average labour-power is constant, but that the labourers employed by a capitalist are reduced to average labourers. There are exceptional cases in which the surplusvalue produced does not increase in proportion to the number of labourers exploited, but then the value of the labour-power does not remain constant.

 In the production of a definite mass of surplusvalue, therefore the decrease of one factor may be compensated by the increase of the other. If the variable capital diminishes, and at the same time the rate of surplusvalue increases in the same ratio, the mass of surplusvalue produced remains unaltered. If on our earlier assumption the capitalist must advance 300s., in order to exploit 100 labourers a day, and if the rate of surplusvalue amounts to 50%, this variable capital of 300s. yields a surplusvalue of 150s. or of 100 x 3 workinghours. If the rate of surplusvalue doubles, or the workingday, instead of being extended from 6 to 9, is extended from 6 to 12 hours and at the same time variable capital is lessened by half, and reduced to 150s., it yields also a surplus-value of 150s. or 50 x 6 workinghours. Diminution of the variable capital may therefore be compensated by a proportionate rise in the degree of exploitation of labour- power, or the decrease in the number of the labourers employed by a proportionate extension of the workingday. Within certain limits therefore the supply of labour exploitable by capital is independent of the supply of labourers.¹ On the contrary, a fall in the rate of surplusvalue leaves unaltered the mass of