Abstract
In the final model in this book, I present a simplified version of Ripper and Varaiya (1974) which uses Linear Programming to plan efficient urban development in the presence of multiple industries. The Ripper-Varaiya model assumes an infinitely elastic supply of each factor at a given factor price . As in the Mills model , it incorporates local transportation as one of its industries. The Ripper-Varaiya model uses input-output to represent the production of commodities: similar to Chap. 10. What makes the Ripper-Varaiya model different is that the city can use whatever bill of imports is most efficient. This allows for the possibility that the city is merely a transshipment point (with no production locally) if it is less costly to supply export demands from elsewhere. With a novel twist, the Ripper-Varaiya model is also able to incorporate congestion . The model determines the efficient allocation of land use within the city. While the Ripper-Varaiya model can be solved only numerically, I show how its solution conforms to findings in earlier chapter and at the same time helps us better understand the organization of the urban economy .
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Notes
- 1.
Distance on a rectangular plane between two points, (x 1, y 1) and (x 2, y 2) calculated by the following sum: |x 1 − x 2| + |y 1 − y 2|.
- 2.
I assume here the city is on a map displayed as a rectangular projection.
- 3.
Ripper and Varaiya allow for land uses in Square 1. To me, this complicates exposition of the model without providing any added insight.
- 4.
Total amount of a product produced in a grid square.
- 5.
Ripper and Varaiya allow for any number of alternative production technologies. This might incorporate substitution between inputs where, for example, transportation costs make it valuable. For the purposes of exposition here, two alternatives are sufficient to understand the potential for alternatives.
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Miron, J.R. (2017). An Efficient Urban Economy: The Ripper-Varaiya Model. In: The Organization of Cities . Springer, Cham. https://doi.org/10.1007/978-3-319-50100-0_19
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DOI: https://doi.org/10.1007/978-3-319-50100-0_19
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