Shrinking population and the urban hierarchy

This paper examines whether population shrinkage leads to changes in the urban hierarchy in terms of relative sizes of cities and their functions onomic geography. We work backwards in a racetrack economy with eight cities in a long-run equilibrium. Initial distribution of population is chosen to satisfy both the rank-size rule and central place hierarchy. We have a short-run equilibrium in which firms choose prices and consumers choose consumption taking the number of workers in each region as given. In the long-run equilibrium, workers choose simultaneously where to live and which sector to take a job. After checking for consistency and integrity of the model, we move on to exit from the lock-in state to see what population implosion would entail. In each period, natural changes occur according to the city size and they are followed by social changes in which workers roam across cities in search of higher utility. A generally decreasing trend is apparent, but we find some salient patterns in which small cities previously overshadowed by the primate city become relatively bigger as medium industries spill over on them. This appears to be quite robust against variation in the rates of natural change among cities. Thus, both the rank-size and central place hierarchy are partly disrupted as population keeps shrinking. Regarding the welfare of the residents, a lower demand for land initially causes the rent to go down boosting up the utility. However, the illusion is short-lived because markets soon begin to shrink suppressing wages. We also find it better to maintain a low pace of total population decline in the long-term perspective. More importantly, it is crucial to sustain the relative livability of smaller cities in order to minimize the overall loss of utility.