Knowledge accumulation in cities : the role of imitation and innovation

The aim of this paper is to develop a spatial model that explicitly incorporates the different types of knowledge spillovers taking place in cities and to show how they affect the migration decision of individuals and the size of cities. We use a static general equilibrium framework with two types of labor (highly and less educated) and two asymmetric locations: The city and the periphery, where only the city provides highly educated workers with the opportunity to exchange knowledge via face-to-face interactions. Our model incorporates two forms of knowledge spillovers happening in these meetings whose intensities are dependent on the similarity of knowledge background of the interacting individuals: First, the individual build-up of skills through the process of learning increases in the similarity of knowledge backgrounds. And second, innovative output generated in a meeting decreases in the similarity of knowledge backgrounds. This reflects the general sentiment that diversity stimulates the emergence of groundbreaking innovations. We see that highly educated workers only focus on the build-up of their personal skills when deciding about the range of individuals in the city they accept to be matched with, whereas innovative output is seen as a by-product of the process of learning. The interplay of agglomeration and dispersion forces determines the allocation of workers in the spatial equilibrium. Moving to the city gives them the chance to increase their personal effectiveness through the process of learning in face-to-face meetings. On the other hand there are two dispersion forces at work: First, the crowding effect in the regional housing and decreasing returns to scale to supplied work. However, the equilibrium allocation of workers across the two regions is socially inefficient. As mentioned above highly educated workers only focus on the build-up of personal skills since the increase in personal effectiveness is directly compensated by firms. A Social Planner however, would recognize that meetings between more diverse individuals in the city would have a positive impact on innovative output. This inefficient decision additionally implicates that agglomeration forces do not reach their optimal extent and create cities that are smaller than socially optimal. The intuition behind this result is simple. People move to the city to maximize their personal outcome, but do not take into account their impact on the emergence of innovations, that are available for everyone. We are the first to explicitly model the impact of different forms of knowledge spillovers on agglomeration forces. We believe that our model's insights on the microfoundations of different types of knowledge spillovers provide a valuable contribution to the understanding of empirical observations like the skill and urban wage premium, because it offers the possibility to look at the forces at work affecting the empirical findings.