Urban production functions, often used to indicate optimal city size, usually deal with one city in isolation. This paper introduces differing production and transport costs and demand intensities in order to generate an urban hierarchy of differing urban sizes and market areas. It then distinguishes between continuous hierarchies with a single production function and discretely stepped hierarchies with differing production functions. The model is then applied in order to generate a seven-level hierarchy for 464 urban centres in Saskatchewan, but this is outperformed by the corresponding continuous hierarchy model. The policy implications for self-sustaining urban growth and the potential non-viability of small communities are then discussed.
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