Several significant contributions have already been made in economic literature. Atkin & Donaldson (2015) show that the effect of log distance on trade costs within Ethiopia or Nigeria is 4-5 times larger than in the US, and _≤_ 30% of this effect is explained by the availability and quality of roads. Using 10 years of disaggregated monthly price data, Porteous (2019) estimates a dynamic model of agricultural storage and trade comprising 6 grains traded across 230 regional markets in 42 SSA countries, connected in a network with 413 links to 30 international ports. He finds median trade costs 5x higher than elsewhere in the world. Reducing trade costs to the world average would yield a 46% reduction in grain prices and a welfare gain equivalent to 2.17% of GDP. He further shows that 88% of the welfare gain can be achieved by lowering trade costs through ports and links representing just 18% of the trade network, supporting corridor-based approaches.

Graff (2024) studies spatial inefficiency in African national road networks using a regular 0.5<sup>_◦_</sup> grid-network parameterized with Open Street Map (OSM) routes between adjacent cells. Employing data on population, nightlights (productivity) and ruggedness (Nunn & Puga, 2012), and the quantitative framework of Fajgelbaum & Schaal (2020), he generates ideal national networks, and estimates that Africa would gain 1.3% of total welfare from better organizing its national road systems (with national welfare gains ranging between 6.6% for Somalia and 0.5% for South Africa), and 0.8% from a 10% optimal expansion. He also documents that colonial infrastructure projects skewed trade networks towards a sub-optimal equilibrium and that regional favoritism and inefficient aid provision hinder optimal network investments (Graff, 2024). The latter is consistent with findings by Jedwab & Moradi (2016); Jedwab et al. (2017), Burgess et al. (2015), and Bonfatti et al. (2019). Similarly, Gorton & Ianchovichina (2021) analyze trade network inefficiencies and optimal expansions for Latin America closely following Fajgelbaum & Schaal (2020). They find average welfare gains of 1.6% from optimal reallocation and 1.6%/1% from a 50%/10% optimal expansion of national road networks. They also consider transnational networks in the MERCOSUR and Andean Community trade blocs. Disregarding borders, they find that optimal expansions better connect major cities across countries at welfare gains of 1.5%-1.9%. Throughout, they find that optimal network investments reduce spatial wealth disparities.

An emerging policy literature evaluates the effects of planned road interventions in Africa. Notably, Fontagn ́e et al. (2023) model the effects of planned trade (AfCFTA) and transport (PIDA) integration and find that AfCFTA alone would raise exports by 3.4% and GDP by 0.6%, whereas concurrent completion of PIDA priority road projects up to 2040 would raise exports by 11.5% and GDP by 2%. The novel analysis incorporates data on border frictions and trade through ports. Further similar works investigate West-Africa (Lebrand, 2023) and the Horn of Africa (Herrera Dappe & Lebrand, 2023) regions. Lebrand (2023) finds that upgrading the DakarLagos road corridor yields benefits 3x the estimated costs, and 6x with reduced border delays. Herrera Dappe & Lebrand (2023) find a 1% welfare gain from road investments along 4 corridors, which is raised to 4.3% if border delays are reduced by 50%, and to 7.8% with added electrification.

Many further works such as Jedwab & Storeygard (2022), Peng & Chen (2021), Abbasi et al. (2022), Fiorini et al. (2021), and Moneke (2020) study the economic effects of past road interventions in Africa. The latter two find that road network expansion in Ethiopia enhanced the impact of trade liberalization/electrification on local firm productivity/industrialization, respectively. A vast further literature studies the effects of road interventions in other world regions, particularly in China (Faber, 2014; Baum-Snow et al., 2020) and India (Asher & Novosad, 2020; Alder, 2016).

This paper does not examine planned or past interventions but instead characterizes optimal investments.<sup>1</sup> Apart from the partial equilibrium simulations by Porteous (2019) on a heuristic agricultural trade network, and the general equilibrium work by Graff (2024) examining hypothetical optimal reshuffling and 10% expansion of national road networks on a regular 0.5<sup>_◦_</sup> grid parameterized in a way that has limited resemblance to optimal routing (see Section 4), the literature has not yet (to my knowledge) seen a detailed quantitative attempt to compute what should optimally be done to improve or extend Africa’s present road network. This paper attempts to fill this void.

Starting from a precise continental grid of 12,016 cells with centroids exactly 50.28km apart, I

> 1Eyeballing the results of this paper against PIDA investments (Fontagn ́e et al., 2023) suggests that they resemble optimal general equilibrium trans-African road network investments under (unrealistically) low trade elasticities.

2