Appendix to provide estimates of how floods affect household utility, aggregate land values and populations compared to a no flood city, when floods are not necessarily distributed proportionally to the distance to the city center (Table 2).

||||||C|ities||||
|---|---|---|---|---|---|---|---|---|---|
|||(a)|(b)|(c)|(d)|(e)|(f)|(g)|(h)|
||CCA|-43.5|-33.7|-3.4|-3.3|-0.001|-0.001|-32.3|-28.4|
|Household<br>|CCP|-43.5|-33.7|-3.4|-3.3|-0.008|-0.007|-34.0|-29.4|
|utility<br>|OCA|0|0|0|0|0|0|0|0|
||OCP|0|0|0|0|0|0|0|0|
|<br>|CCA|0|0|0|0|+0.008|+0.008|-10.2|-6.22|
|Aggregate<br>l<br>|CCP|0|0|0|0|+0.10|+0.10|-12.2|-7.55|
|and<br>l<br>|OCA|-99.1|-96.7|-24.8|-24.2|-0.004|-0.003|-96.5|-94.2|
|vaues<br>|OCP|-99.1|-96.7|-24.8|-24.2|+0.038|+0.037|-97.2|-94.9|
||CCA|0|0|0|0|0|0|0|0|
|li<br>|CCP|0|0|0|0|0|0|0|0|
|Popuaton<br>|OCA|-99.1|-96.7|-24.8|-24.2|-0.012|-0.012|-96.1|-93.8|
||OCP|-99.1|-96.7|-24.8|-24.2|-0.063|-0.062|-96.9|-94.5|

_Table 2: Household utility, aggregate land values and population variation (in %) compared to a no-flood situation depending on the location of flood prone areas and the severity of floods (damage inflicted to structures when a flood occurs) in the four polar settings of classic urban economics._ For closed cities, impacts from floods for household utility losses and aggregate land values compared to a ‘no-flood’ baseline are identical between CCA and CCP models when floods are homogenously distributed in the urban area (cities (a) to (d)).<sup>3</sup> And results for floods which are distributed in the city center or in the periphery are very similar in CCA and CCP models for utilities and aggregate land values (cities (e) to (h)). For open cities, the same conclusions hold between OCA and OCP models: identical impacts on land values and populations for cities (a) to (d) and very similar results for these same variables when floods are central or peripheral (cities (e) to (f)).

This suggests that the absentee landowner or public ownership of land assumption has limited impacts on our results. One small exception here consists of the results for aggregate land values in OCA and OCP models when floods are peripheral (cities (e) and (f)). Whereas the impacts of floods on aggregate land values are nearly non-existent in both cases, the sign of the change is different: negative, meaning aggregate land value destruction from floods in an OCA setting, positive, meaning aggregate land value creation in an OCP setting.

The difference in impacts from floods are much more significant between open or closed city models. First, because utility is fixed in open city models, populations decrease with floods, leading to much less severe competition for land and smaller aggregate land values. This is true even when floods are homogenously distributed (cities (a) to (d)) where no impacts are reported in closed cities. For these cities 1 ((a) to (d)), the loss of utility in closed cities is measured by , whereas the loss of population and aggregate land values is measured by in open cities. With both γγ aaββ and , is small ff ff CC = CC ff CC MM< 1 ββ< 1 MMββ

> 3 Note that this is distinct from saying that household utilities are identical in cities with Absentee Landowners or Public Ownership of land: they aren’t. But they are reduced in the same proportion when compared to their ‘noflood’ situations, which constitute distinct baselines in CCA and CCP models.

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