We document that sales of individual products decline steadily throughout most of the product life cycle. Products quickly become obsolete as they face competition from newer products sold by competing firms and the same firm. We build a dynamic model that highlights an innovation-obsolescence cycle, where firms need to introduce new products to grow; otherwise, their portfolios become obsolete as rivals introduce their own new products. By introducing new products, however, firms accelerate the decline of their own existing products, further depressing their sales. This mechanism has sizable implications for quantifying economic growth and the impact of innovation policies.