This paper first appeared as UAB working paper 297.95.This paper examines, both descriptively and analytically, Marx's arguments for the falling rate of profit from the Hodgskin section of Theories of Surplus Value, The General Law section of the recently published Volume 33 of the Collected Works and Chapter 3 of Volume III of Capital. The conclusions are as follows: First, Marx realised that his main attempt to give an intrinsic explanation of the falling rate of profit, which occurred in the General Law section, had failed; but he still hoped that he would be able to demonstrate it in the future. Second, the Hodgskin and General Law sections contain a number of subsidiary explanations, mostly related to resource scarcity, some of which are correct. Third, Part III of volume III does not contain a demonstration of the falling rate of profit, but a description of the role of the falling rate of profit in capitalist development. Forth, it also contains suppressed references to resource scarcity. And finally, in Chapter 3 of Volume III, Marx says that it is resource scarcity that causes the fall in the rate of profit described in Part III of the same volume. The key to all these conclusions in the careful analysis of the General Law section.Financial aid from DGI project SEC 2000-0684 is gratefully acknowledged.