in rents.<sup>10</sup> Another difference is that households can choose between different transport modes (a discrete choice model is used to compute modal shares). A third difference comes from the introduction of transaction costs and a rent border which have an influence on rent levels and city size.

We use this model calibrated on the Paris urban area, with a grid of 100km2 with cells of 0.25 km2. The model accounts for land-use constraints on the Paris agglomeration. Transportation costs include monetary costs such as the cost of gasoline and the cost of time. We assess them using the spatial structure of the Paris transportation networks (roads and public transport).

As described in Appendix D, a validation of the model over the 1900–2010 period shows that the model reproduces the available data on the city’s evolution fairly faithfully and captures its main determinants. It also reproduces the spatial distribution of dwelling size, population density, and rents in the urban area fairly well. These results suggest that this tool can be used to inform policy decisions. This model, calibrated on Paris, has been used in several other studies (Viguié and Hallegatte, 2012; Viguié, 2012; Avner et al., 2013; Viguié et al., 2014).

# _3.2. Increase in the speed of one local train_

Let us analyze the effects of a theoretical increase by 25 % in the speed of one local train line (“RER B”) of Paris urban area. "RER B" is one of the main transport axis of Paris urban area, crossing Paris city, and linking this city with many of its suburbs. It has 47 stations, and an average 900,000 commuters daily traffic, which makes it the second most used public transport line in the Paris urban area.<sup>11</sup> Due to the planned important development of the places this line crosses, important modernizing works have been launched.<sup>12</sup> The 25 % speed increase we are considering here is a theoretical example, that we will simply use as an illustration of potential improvement. Whereas we call it a “speed improvement”, it is important to note that, in the simulations, this improvement simply corresponds to a decrease in generalized transport costs, which could equivalently be interpreted, for instance, as improvements in comfort (AC, security etc.).

_Closed city case._ Let us first do an analysis in a closed city case, i.e. let us suppose that city population is exogenously determined and is not impacted by the transport investment. Fig. 4 shows a map of rents change due to the improvement in transport. As was observed in Sec. 2.3, rents increase in places with improved accessibility, and this is counterbalanced by a general decrease everywhere else. Rents decrease occurs over a much wider area (5800 km2) than rents increase (1000 km2), but the value of the decrease is extremely small and almost negligible compared to the increase : taking into account population density, averaged housing price decrease and increase

> 10To sum up, two main mechanisms drive the model. First, households choose where they will live and the size of their accommodation by assessing the trade-off between proximity to the city center and housing costs. Living close to the city center reduces transportation costs, but housing costs (per unit of area) are higher there. Second, we assume that landowners combine land with capital to produce housing: they choose to build more or less housing (that is, larger or smaller buildings) at a specific location depending on local real estate prices and construction costs.

> 11Source: RATP (www.stif.org/IMG/pdf/Presentation_de_la_SNCF_et_de_la_RATP_au_comite_de_ ligne_du_RER_B_du_3_novembre_2009.pdf).

> 12 See for instance http://www.modernisation-rerb.fr/.

11