Since the days of David Ricardo economists have discussed the effects of technological progress on employment. Due to a theorem which can be traced back at least to Neisser (1942), these effects can be related to the elasticity of product demand. In this paper we prove the theorem formally in a modern framework and generalize it to the case of many products. This theorem is relevant in many different regards. In particular it may contribute to a better understanding of regional and national (un-) employment.