Arrow Meets Hotelling: Modeling Spatial Innovation

We combine a spatial model of innovation with Hotelling's model of competition. Innovations are vertically and also horizontally differentiated. Potential innovators choose not only whether to innovate but also how to innovate. The bolder they are with a new product, the riskier is the outcome but the softer will be the resulting market competition with existing products. We use the model to explore the interaction of competition and innovation and address several classic questions. The recurring finding is that increased market competition drives not only more innovation but more novel and riskier innovation that offers a higher chance of breakthrough outcomes.