Abstract
In the analysis of many-region spatial agglomeration models, it is practically impossible to find all stable equilibria because the governing equations exhibit complex bifurcation behaviour in line with changes in the level of transport cost. In this paper, a systematic method for finding “trivial solutions,” a special class of equilibria, is introduced. Trivial solutions satisfy the governing equation for any values of the transport cost parameter while retaining their geographical patterns. Trivial solutions can be systematically computed and classified by analysing the group that expresses the symmetry of the governing equations. As a specific example, the trivial solutions on a square lattice economy with boundary is explicitly given. Stability properties of the trivial solutions are studied through numerical experiments employing Forslid and Ottaviano (2003)'s model.
