This paper presents a simple Chamberlinian agglomeration model which, like the canonical core-periphery (CP) model, contains two agglomerative forces. However, in contrast to that model, the present model is analytically solvable. Moreover, the present model exhibits a 'supercritical pitchfork bifurcation' rather than the 'subcritical pitchfork bifurcation' of the CP model. This may be a better description for some agglomerative processes than the 'catastrophic' emergence of complete agglomeration predicted by the CP model.