Big or small? A new economic geography model with an endogenous switch in the market structure

We present a new economic geography (NEG) model with a linear demand function where firms may change the perception of their relative dimension with respect to the local market. If they perceive themselves as big, they behave as Cournot oligopolists, otherwise they behave as monopolistic competitors. We first compare the pure cases in which only one market form prevails in the two-region economy. Comparing these pure cases of monopolistic and oligopolistic competition only a quantitative difference emerges. Subsequently, we assume that firms switch behavior and start to interact strategically when the number of local firms is below a threshold; in that case, the market form evolves endogenously. Results change substantially. ‘Break’ and ‘sustain’ points are separated as in standard NEG models with an isoelastic demand function leading to a co-existence of equilibria. Stable partial agglomeration and oscillations with small amplitude are possible. The dynamics are described by a 1D piecewise smooth map, which can be continuous (in the pure monopolistic or oligopolistic cases) or discontinuous (when the market structure evolves endogenously). We analyze the bifurcation structure of the parameter space of the map comparing these cases. We show that the continuous maps have rather standard dynamics, while the discontinuous map is characterised by border collision bifurcations of fixed points and cycles, which lead to rich and complex bifurcation structures.