Marx after Okishio : falling rate of profifit with constant rate of exploitation

Can cost-reducing, technical change lead to a fall in the long run rate of profit if class struggle manages to keep the rate of exploitation constant? In this paper we demonstrate, in a general circulating capital model, that if (a) the technical change is capital-using labor-saving (CU-LS), (b) the real wage bundle can change, and (c) the decline in the unit cost of production is bounded above by the change in the nominal labor cost associated with the new technique of production, then viable technical change can be consistent both with a constant rate of exploitation and a fall in the long run rate of profit. This result vindicates Marx's claim in Volume III of Capital, that if the rate of exploitation remains unchanged then technical change in capitalist economies can lead to a fall in the long run rate of profit.