Some of the comparative static results are straightforward, for example that stronger agglomeration economies create higher rents and a denser cluster of employment in the CBD. Some involve trade-offs between forces pulling in opposite directions. Transport improvements enable concentration of employment and dispersal of residency, as raising income and thereby attracting population; their effects on CBD rent and density are ambiguous. Population growth raises productivity and CBD density, but also the average length and cost of commuting. Rents increase, but both real wages and average per capita income (the sum of wages and rents) fall with population size. Building technology and the ability to use land to produce floor-space are important for city productivity and income.

Policy measures have direct effects – for example costs saved in faster travel – and also determine the shape of the city. This can be quite fundamental as, for example a radial road network reinforces the urban center. The model indicates the direction and possible long-run magnitude of such effects and also gives estimates of their implications for income and welfare. These income changes can be quite large, both because the change in location of activities in the city are non-marginal, and because these changes interact with market failures, above all the externalities created by agglomeration. Thus, appropriate zoning that concentrates employment can raise productivity and welfare. The full equilibrium effects of a transport improvement may be several times larger than the direct ‘user-benefits’.

Sections 6 – 8 of the paper explore extensions of the model. The most important is adding a consumer services sector, representing activities including retail, domestic services, hospitality, maintenance services, and the informal sector. There are intra-city transport costs in accessing and supplying consumer services and these costs create their own agglomeration force, favouring central locations and hence possibly forcing employment in tradable sectors to the edge of the city. This is one factor – but not the only one – that can create polycentricity, as demonstrated in section 8.

The extended model contains multiple drivers of city shape. There are the spillovers that are captured in the benchmark model, the shape of transport systems (e.g. the centripetal force created by radial roads), and the effect of transport costs in consumer services. All of these operate through the choices made by households of where to live and where to work. We show (section 6) both the sensitivity of results with respect to parameters of the household choice function and, more fundamentally, the powerful additional clustering forces that are created if employment considerations enter households’ location choices not just by wages offered in each place, but also by the number of jobs in each place. These are all forces for clustering, and the contribution of each needs to be better understood.

Finally, this paper is an ‘exploration’; numerous further questions need to be addressed (for example the interactions between different policy measures) and extensions made. The most challenging are to do with multiple equilibria and the possibility of securing ‘transformative change’ through policy measures, particularly so in a dynamic environment where investments are long-lived and expectations matter.

# **References**

Ahlfeldt, Gabriel M., Stephen J. Redding, Daniel M. Sturm, and Nikolaus Wolf (2015), ‘The economics of density: Evidence from the Berlin Wall’, _Econometric_ a, 83(6), 2127-2189

> Allen, T., and C. Arkolakis (2014): ‘Trade and the Topography of the Spatial Economy,’ _The Quarterly Journal of Economics_ , 129(3), 1085-1140.

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