I was thinking about the term 'late stage capitalism' the other day, and I think I've got an idea for a semi-rigid (heh) definition of the term. Forgive my autism below.
OK, so first of all, let's assume that von Mises is partially right - total demand is infinite under capitalism. That is, the mechanics of capitalist accumulation mean that every individual person under capitalism wants every possible resource in the world under their personal control. Since there is only one 'everything', not everyone can have it, and everyone ends up with less than they demand.
Next we assume that total demand across the population would be finite under communism. Communism is defined here as a system that has completely dispensed with the Law of Value (i.e., markets, money, wage labour), with no private property and free access to all resources. We justify this assumption by noting that hoarding is impossible without the private holding of storage space, accumulation of goods beyond that which is needed is pointless without exchange, and free access to abundant goods eliminates the perception (and reality) of scarcity and the concomitant desire to hoard goods. Let's call the finite total demand of the global population under a hypothetical full communism D. We'll note that D is the sum of each the demands of each individual person, D_i.
Now let's talk about the current system. Let's say we have a way of doing a global audit of the Earth's total accessible resources, energy production/distribution capacity, factors of production, and labour force/composition. We'll call the result of that audit S_max, or the total current supply capacity of human civilisation. You can think about it in terms of dollars if you like, or as a complicated sum of individual resources, energy sources, etc in natural units. Now of course we are aware that capitalism doesn't operate at full efficiency all the time, so S_realised < S_max. We also note that S_max increases over time, as our technology allows us to access further-flung resources and capture more energy, our labour pool grows, and we build more factories.
Now that we've defined a demand term and a supply term, we can start talking about comparison-based conditions. We start off by assuming that S_max < D at the dawn of capitalism, reflecting the low level of the development of the productive forces. We can call the period during which this condition is satisfied 'early capitalism'. As capitalism develops, however, it can be readily observed that productivity increases vastly outstrip population growth. That is, S'_max > D'. If S_max is growing faster than D, it stands to reason that there either will or has come a time when S_max >= D. We can call the period during which this condition is met 'late capitalism'. Of course due to the inefficiency of the market system, capitalism in this period likely simultaneously satisfies S_realised < D and S_max > D. This is a highly undesirable situation - capitalism at this point acts as a fetter on production.
To conclude (also tl;dr): it may be useful to define 'late capitalism' as the period where the productive forces have developed enough to materially support a direct transition to 'higher stage' communism.
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