The rate of creation and failure of start‐up firms can be modeled as a search and matching process as in labor market matching models. Setting out an endogenous growth model with entrepreneurship, we derive an entrepreneurship Beveridge curve. We use this to illustrate that whether or not a start‐up is successful depends on the efficiency with which entrepreneurial abilities are matched with business opportunities. The entrepreneurship Beveridge curve is a potentially useful analytical contribution to the formalization of the economics of entrepreneurship. We identify a number of extensions and applications.