The trade cost positively depends on the flow of good _n_ across link _j → k_ , _Q_<sup>_n_</sup> _jk_<sup>,subjecttoan</sup> elasticity _β_ , an effect Fajgelbaum & Schaal (2020) describe as ’congestion forces’. It also depends negatively on the level of infrastructure _Ijk_ , subject to an elasticity _γ_ . Following Graff (2024), I set _γ_ = 0 _._ 946.<sup>28</sup> I would also follow him and set _β_ = 1 _._ 177, however, due to the large size of the network, only the dual solution to the model which casts all variables as function of prices is viable, stipulating a maximum of _β_ = 1 for strong duality (Fajgelbaum & Schaal, 2020). As also discussed at length by Fajgelbaum & Schaal (2020), the lagrangian objective of the model is only convex if _β > γ_ , in which case a unique global solution to the network design problem can be computed. If _β < γ_ , the problem becomes non-convex and yields a local optimum, which Fajgelbaum & Schaal (2020) further refine using simulated annealing methods. They denote this case as ’increasing returns to infrastructure’ (IR) and show that the optimal network is more tree-like, with larger investments in fewer links. Graff (2024)’s parameterization implies _β > γ_ . This may, however, not hold for large transnational networks; thus, I also examine the IR case assuming _γ_<sup>_′_</sup> = 1 _._ 2.<sup>29</sup> Fajgelbaum & Schaal (2020)’s model has a normalized inequality-averse Cobb-Douglas utility function giving the utility of a single worker in location _j_ in terms of consumption and housing where _ρ_ controls the level of inequality aversion. Following Graff (2024), I assume _α_ = 0 _._ 7, which is based on estimates by Porteous (2022), and _ρ_ = 0 (no inequality aversion), but I also explore _ρ_ = 2 (moderate inequality aversion). Following Graff (2024), I set _hj_ = 1 _− α_ , i.e., the local housing availability is proportional to the current population. Total consumption in location _j_ is _Cj_ = _Ljcj_ , which in turn is a CES aggregate over _N_ traded goods with elasticity of substitution _σ_ In line with the international trade literature, Fajgelbaum & Schaal (2020) and Graff (2024) use _σ_ = 5, following recommendations by Atkin & Donaldson (2022). Both assume that the largest _N − k_ cities produce their own good and mostly conduct single-country simulations.<sup>30</sup> Since I have few cities per country, it is also plausible to interpret _σ_ as an Armington (1969) elasticity, and here a meta-study by Bajzik et al. (2020) suggests a median value of 3.8. Since the network is very large, even _σ_ = 3 _._ 8 yields equilibria with limited inter-city trade where optimal investments are quite localized around population centers. I thus also run simulations with _σ_ = 2, which is at the low end of empirical estimates (Bajzik et al., 2020). Production of good _n_ in node _j_ is given by Due to lack of better measures,<sup>31</sup> I set city productivity _Zj_<sup>_n_equaltothepredictedInternational</sup> Wealth Index of Lee & Braithwaite (2022) (Figure A2). Since the original estimate is only available

> 28The value for _γ_ is informed by estimates of the costs of road delays to African truckers by Teravaninthorn & Raballand (2009). The value of _β_ is informed by estimates on the cost of traffic congestion by Wang et al. (2011). Fajgelbaum & Schaal (2020) use _β_ = 0 _._ 13 and _γ_ = 0 _._ 1, but their characterization of infrastructure ( _Ijk_ ) in terms of road-lane km yields significantly larger values than the formulation in terms of km/h adopted from Graff (2024).

> 29Fajgelbaum & Schaal (2020) page 1439 simulate an IRS case by inverting the ratio of _β_ and _γ_ keeping _β_ fixed, which, for _β_ = 1, yields _γ_<sup>_′_</sup> = 1 _._ 057. This, however, yields very similar solutions to _γ_ = 0 _._ 946, thus I set _γ_ = 1 _._ 2 to induce stronger effects. There are, as far as I am aware, no studies or empirically accessible data on road congestion in inter-city or international transport.

> 30Graff (2024) sets _N_ = 6 _, k_ = 2 (with one international good produced outside the country and one agricultural good produced by smaller cities) and conducts simulations for every African country. Fajgelbaum & Schaal (2020) set _N_ = 10 _, k_ = 1 and conduct simulations for France, Spain, and Western Europe.

> 31Graff (2024) uses nightlights divided by city population to form the productivity measure. While this is a viable approach, the task of measuring differences in city productivity across countries encourages the use of richer data sources. Lee & Braithwaite (2022) combine daylight satellite imagery and OSM data in an iterative ML framework that has proven able to predict wealth within and across SSA countries reliably. As an attempt to verify, taking a city-population weighted average of the IWI by countries yields a correlation of 0.62 with the 2020 World Bank national GDP/capita estimate and a correlation of 0.73 with the log of GDP/capita. Using NASA’s Black Marble nightlights, on the other hand, only yields a correlation of 0.15 between city-population weighted nightlights/capita and national GDP/capita. However, using the log of nightlights/capita yields a 0.58 correlation with GDP/capita and a 0.65 correlation with the log of GDP/capita. While this appears more promising, a visual comparison, provided in Appendix Figure A10 for the interested reader, shows that the IWI is higher in larger cities in richer countries - in line with much scientific evidence. The nightlights measure appears quite noisy and imprecise.

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