Lets start with a few assumptions:
1. Is this only about initial setup cost or also ongoing operational cost?
Assumption: Only initial cost
2. Is wifi only at street level or also inside the subway systems, at multiple floor levels of local government buildings, etc.?
Assumption: Street level only
3. What is the size of the city?
Assumption: A simple 50km by 50 km square city. So 2250 sq km.
4. What is the range of each router being installed?
Assumption: 100 sq meters
5. What is the max bandwidth supported by each router?
Assumption: 1 GBPS
6. Is this free wifi or paid wifi?
Assumption: Its FREE!
7. Maximum # of devices that will be using free wifi?
Assumption: (Population size) X (% of users who will choose to use free wifi vs their paid data plans) X Avg. number of devices per user. Lets assume population size is 5M. 90% choose to use the wifi and at an average there are 1.5 devices per user.
= 5M X 90% X 1.5 = 6.75M devices.
8. Any per device usage restrictions?
Assumption: Yes. 1 GB/device/day
9. Total bandwidth that needs to be supported daily?
Answer: Max # of devices X daily usage restriction = 6.75M GB/day
10. What is the cost of a single leaf node (router + wiring + labor )?
Assumption: router - $100, wiring - $50, labor - $200. Cost per node is 350$
11. Any booster nodes needs to mesh with the leaf nodes?
Assumption: 1 per 50 nodes. Cost: booster - $200, wiring - $50, labor - $300. Cost per booster node is $550.
12. Any sat link costs or underground cabling costs, to coonect this network to the internet?
Assumption: Use existing cable infrastructure. No extra cost.
13. Any other set up cost?
Based on a simple : (Max daily total bandwidth)/ (bandwidth per router per day), we can get an answer but that would be inaccurate since it doesnt take into account the sheer size of the city. Lets take the city size into account.
Few more assumptions:
14. Is the population evenly distributed?
Assumption: Yes. if no, then we need to go into max number of concurrent devices that can be supported per node and if the density of the population is higher than can be supported per node, we would need more node in certain areas vs others.
City size: 2250 sq. km.
Per node range: 100 sq meters.
Total number of nodes needed: 2250 sq. km / 100 sq. meters = 22.5M Nodes
Total number of booster nodes needed: 22.5M / 50 nodes = 450K booster nodes
Total cost of wifi set up is therefore: 350$ X 22.5M nodes + 550$ X 450K booster nodes = $7.875B + $247.5M = $8.1225B give or take a few hundred million :)