Using smooth profit functions to characterize production possibilities, we extend the concepts of regularity and fixed point index to economies with very general technologies, involving both constant and decreasing returns. To prove the genericity of regular economies we rely on an approach taken by Mas-Colell that utilizes the topological concept of transversality. We also generalize the index theorem given by Kehoe. Our results shed new light on the question of when an economy has a unique equilibrium.