Inada (1963) provided properties of the production function that are useful in the study of economic growth. Shephard (1970a) provided an axiomatic approach to the study of production theory. He applied these axioms to give a formal statement of the law of diminishing returns (Shephard, 1970b). In this paper we demonstrate that the Inada conditions and the law of diminishing returns, as articulated by Shephard, are fundamentally inconsistent. Thus one is forced to make a choice between the two models when studying productivity and growth.