Competition as a discovery procedure: Hayek in a model of innovation

I model a mechanism through which competition can encourage innovation and growth. Although the often-cited 'Schumpeterian effect' of competition is to decrease the expected rents from an innovation, the competitive process also acts to uncover better ways of satisfying consumers and lowering costs. When firms are uncertain about the best direction in which to innovate, more competition results in better innovations. By endogenizing the level of competition and introducing this uncertainty into a general equilibrium model of vertical innovation, I show how this Hayekian effect of competition works against the Schumpeterian effect, resulting simultaneously in a positive relationship between competition and growth, and an inverted-U relationship between competition and firm-level innovation.