External spillovers, internal spillovers and the geography of production and innovation

We consider a three-location duopoly model such that (i) firms choose production and innovation locations before (Bertrand) competition takes place and (ii) there are internal and external knowledge spillovers. We show: (1) agglomerations where firms earn negative profits may exist when there are both external and internal knowledge spillovers; (2) greater external spillovers do not necessarily favor agglomeration; (3) decreasing communication costs tend to favor agglomeration; (4) there are exactly two types of agglomeration equilibria: either both firms innovate in the agglomeration, or there is an innovator and an imitator; and (5) if there is a location where both firms produce, then innovation must take place in this location.