c 4000 + v 1000 + s 1000 = 6000 units
c 2000 + v 500 + s 500 = 3000 units.
c 2000 + v 500 + s 500 = 3000 units.
If productivity in producing means of production falls by 20%, these units, as values would become:
c 4800 + v 1200 + s 1200 = 7200
c 2400 + v 500 + s 500 = 3400
The 4000 units of c in Department I now has a value of 4800, reflecting the 20% additional labour-time required for its production. The variable capital in Department I rises to 1200, because 20% more labour has to be used to produce the output. If the rate of surplus value remains the same this additional labour creates additional surplus value. This additional labour means more appears as revenue, in the form of wages and profit, in Department I, which means it consumes additional consumer goods.
As a result of the fall in productivity, the cost of the constant capital consumed by Department II rises to 2400, equal to the new value produced by labour in Department I. This additional value passes into the value of Department II output. The new value added by labour in Department II is unchanged as productivity there is unchanged.
But, it can now be seen that where constant capital previously comprised two-thirds (66.6%) of the value of its output, it now comprises 24/34 = 70.6%. The effect can be seen in price per unit. The price of producer goods was, if we assume 1 hour = £1, £1 per unit, and now rises to £1.20 per unit.
Department I takes the 4000 units it requires out of its own production, with a value now of £4,800. It exchanges the remaining 2000 units with Department II, obtaining £2,400 in exchange. Department II's output of 3,000 units now has a value of £3,400 reflecting the the higher value of constant capital, so the value of a unit of its output is equal to 3400/3000 = £1.133 per unit.
With its £2,400 Department I now buys 2117 (2117 x £1.133 = £2399) units of consumption goods. With its £1,000 Department II can now buy only the 883 units left.
In reality, the increase in the price of consumer goods from £1 per unit to £1.13 per unit, would mean that the value of labour-power would have risen. Workers would still require the same quantity of commodities for their reproduction, and the value of those commodities has risen. Consequently, in Department II, for example, wages would have to rise to 500 units x £1.13 = £565, but because only £1,000 of new value is created, surplus value falls to £435. Although the drop in productivity was only in Department I, therefore, because this affects the level of social productivity, by increasing the labour-time required also for producing consumption goods, not only is a greater proportion of social labour-time required to reproduce means of production, but a greater proportion is required to produce consumption goods too, which leaves a smaller proportion of social labour-time left over as surplus production and surplus value.
Marx gives another example of this. How is it he asks that even where productivity in say spinning, does not change, it appears to have fallen when measured in its own product. Say 5 kg of cotton are spun into 5 kg of yarn in ten hours, and this productivity remains the same. Assume also that the 5 kg of cotton itself requires ten hours of labour to produce. The total value of the yarn is equal to twenty hours of labour or four hours per kg.
If the value of cotton rises by 50%, the total value of yarn rises to 25 hours, or 5 hours per kg. Yet, the spinner still spins 5 kg of cotton into 5 kg of yarn in 10 hours, as before. It appears that the productivity of the spinner's labour has fallen only because social productivity has fallen. More labour-time is required to produce yarn, because more labour-time is required to produce cotton.