varies within the city area so too does the amount of floor-space that is supplied per unit of land, this most easily thought of as building height. We allow there to be different construction technologies for residential and commercial structures, noting that technology may also vary across the types of structure needed for different commercial uses, i.e. office blocks versus factories. While focusing on building height, the model also contains the potential for infill, i.e. increasing the built area per unit of land at the cost of open or green space. We also note that the model is comparative static, so does not take into account the fact that construction is a sunk cost, and that decisions therefore depend on expected future rents.<sup>1</sup> The final ingredients are firms who use labor, intermediates, and (commercial) floor-space to produce output. In the benchmark model this is a single composite good, perfectly freely tradable within and outside the city. This good has fixed relative price with respect to ‘outside’ goods (e.g. food, fuels, other manufactures) so can be transformed into consumption goods and intermediates at fixed terms of trade. Central to the model is the possibility that there are agglomeration economies, with productivity in each place depending positively on spillovers from nearby firms. In later sections of the paper we add a second productive sector which can be thought of as consumer services, including retail. This sector is monopolistically competitive and uses labor, floor-space and the perfectly competitive good (as an intermediate) to produce differentiated products which are sold entirely within the city, and are costly to deliver from firms to households.

We show (numerically and graphically) equilibrium patterns of land-use across the city, looking at residential and employment densities, wages, land-rents, and building heights We investigate the way these vary with parameters of the model and may produce different urban configurations (mono- or polycentric). A number of hypothetical policy experiments are undertaken, illustrating the effects of transport improvements, height restrictions, and zoning controls. An illustration of the calibration of this model on data for Dhaka, Bangladesh, is given in Sturm et al. (2021), which discusses the data needed for such an application.

# **2.  The benchmark model**

In this section we set out the benchmark model – with a single production sector – first outlining the economic relationships and determination of equilibrium and then (sub-section 2.1) turning to details of implementation and functional form.

# **2.1 Model structure**

_Geography:_ The city occupies area within a geographical space which is divided into a large number of cells (745 in the simulations and figures that follow). We assume that each cell is a hexagon and the space is the lattice of such hexagons.<sup>2</sup> Cells will be referred to by subscripts _i_ , _j_ , and each of these cells has the same land area, . The distance between the center points of two cells is i , and this will underpin all spatial interactions. Within each cell we set ii i = 0. The cells form an (approximate) circle and the city occupies a mm = mm dd subset of these cells. The size of this subset (i.e. number of these cells occupied as places of residence, work, dd or both and hence inside the city) is endogenous, and this set of urban cells is denoted _I_ .

> 1 See Henderson et al. (2021) for a dynamic urban model in which formal sector construction is durable and incurs sunk costs, while informal sector construction is malleable, and achieves high population density by ‘crowding’ rather than by building tall.

> 2 The hexagonal structure enables a considerably better approximation to a circular city than does a square grid .

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