19. An Efficient Urban Economy: The Ripper-Varaiya Model

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.