In discussions on the rate of profit and its tendency to fall and its role in Marxist theory, a number of phrases are often employed without clarifying what these might really mean. Primary among these are such phrases as ‘the rate of profit must ultimately fall’ and ‘the counter-acting factors cannot possibly offset the tendency in the long run’. As a result of this ambiguity, and as a result of a legacy of confusion concerning Marx’s own ideas on the profit rate beginning with the Western reception of Okishio’s (1961) famous theorem, research on the actual mathematical conditions for the profit rate to rise or fall, especially in the long term, has all but ceased. However there is very strong evidence that the rate of profit has, in fact, been falling in most industrialised economies for some considerable time, and there is good reason to suppose this has at least some bearing on the origins of the present prolonged phase of stagnation in these economies. The time is therefore ripe to return to a rigorous study of the general mathematical conditions that might govern the long-term movement of the profit rate. In particular, I will attempt to give mathematical meaning to the two concepts above
