Simplified Alonso-Mills-Muth model with a monopoly vendor

One important but unrealistic assumption in the simplified Alonso-Mills-Muth (AMM(0)) model is that the composite good is ubiquitous and thus there is zero shopping cost for residents. This paper assumes that the composite good is only sold by a monopoly vendor inside the city and hence a shopping cost is inevitable for residents. It is shown that the vendor will locate at the city boundary in equilibrium. In contrast to the symmetric land rent pattern in the AMM(0) model, the current AMM(k) model offers an asymmetric land rent pattern in equilibrium. Moreover, this paper shows that a rent-maximizing government either regulates the vendor to locate at the central business district (CBD) (when income is high) or does not enact any regulation (when income is low).