One Note on Marx on Machinery

The use of machinery for the exclusive purpose of cheapening the product is limited by the requirement that less labour must be expended in producing the machinery than is displaced by the employment of that machinery. For the capitalist, however, there is a further limit on its use. Instead of paying for the labour, he pays only the value of the labour-power employed; the limit to his using a machine is therefore fixed by the difference between the value of the machine and the value of the labour-power replaced by it.

— Karl Marx, Capital Vol. 1 Chapter 15

A throwaway observation which here is only applied to variation between capitalist countries. To restate: the benefit of machines from a social point of view is that they diminish the amount of labor required to produce a product. But in capitalist society, we don't do our accounting in labor-time. Instead, we do our accounting in money, which is a flawed proxy. Consider these two methods of accounting as applied to the employment of a new machine¹1. Without any loss of generality I'll take the value of the constant capital used in producing the machine to be zero.:

The cost of a machine to the buyer = the wages paid to produce the machine (variable capital) (v) + profit to the capitalist producing the machine (s for surplus-value).

The labor-time embodied in the machine = the labor-time required to produce the machine (T).

The profit from adopting the machine = the wages to workers displaced by the machine (v').

So the machine will only be adopted when v' > v + s.

Obviously wages paid are directly proportional to labor time performed where the constant of proportionality is the wage-rate w (take the wage-rate of both industries to be the same for simplicity). So v = wT and v' = wT' (where T' is the displaced labor).

So we have that the machine will be adopted when T' > T + s/w. But from the point of view of society it would be better to adopt the machine whenever T' > T. So capitalism produces produces an inefficiency in use of labor with a size inversely proportional to the wage-rate.

Note that s/w = 0 implies either infinite wage-rate (degenerate solution) or no profit to the capitalist. So the efficient adoption of machinery corresponds exactly to Communism (or at least no profit whatsoever in means of production). And note that while Marx based his argumentation in a labor theory of value it was nowhere actually required in this demonstration.