Innovation and Location: Spatial Agglomeration and Deglomeration

Let us begin with a naive story about an imaginary country named Webertopia. This country is situated along a very narrow valley-corridor h kilometres in length, which makes the geographical territory of Webertopia appear as if it is a horizontal line. At one end of the valley-corridor exists city A which sits continguous to the boundary of country AA, while city B sits at the other end of the corridor contiguous to country BB. In city A, a licensed factory M _A produces the fixed amount q _z of commodity z every day for export to country AA. In city B, we have a licensed factory M _B producing daily the amount q _z of z for export to country BB. The conditions of the licence issued to M _A require that the commodity z produced by M _A should be sold at a fixed unit price p _z to an importer I _A from country AA who comes to city A every day to purchase the product. The similar conditions must be met by factory M _B with respect to importer I _B from country BB. The average cost to produce commodity z is c₁ for both factories when they are operated separately. If the two factories were to go into joint production at a single location within the national boundary of Webertopia, the average production cost would turn out to be c₂.