There's gonna be a lot of shorthand going on, so here's your cheat-sheet!
I won't pretend it's entirely orderly.

s = Seconds
w = Wood
S = Stone
i = Iron
B = Bazaar
aB = Additional Bazaar (beyond the 1st)
tc, Turn = Tax Cycle (time to complete one Tax cycle)
Wc = Wood Cycle
Sc = Stone Cycle
Ic = Iron Cycle
BWc = Bazaar's Wood cycle
BWc = Bazaar's Stone cycle
BWc = Bazaar's Iron cycle
T1E = Tier 1 Extractor Covered (Resource type inferred by context)
T2E = Tier 2 Extractor Covered (Resource type inferred by context)
EG = Excess Gold (Gold from Autoselling Resources)
NC = No Coverage (Bazaar is not in Range of any Extractors)
PP = Payoff Period (how long it takes the building's Gold Profit to reach it's Build Cost)
T2K = Tier 2 Keep

*The duration of a Tax Cycle starts at 24s and increases with each Keep upgrade, to a max of 34s at Keep T4, hence the tc ranges you will see following. Additionally:

• Tax Cycle: 24|28|30|34s
  
• Wood cycle: 49s
  
• Stone cycle: 65s
  
• Iron cycle: 91s

So, there's massive confusion about how the Bazaar works. This is not surprising, as it's very complicated. After extensive testing, I thought I'd share the details with everyone:

The gist is this: Bazaars have their own Resource Production and Storage, entirely separate from other all other Production and Storage.

The Bazaars will produce Wood, Stone, and Iron until their Storage is full. Afterward, any Resources they Produce will be automatically Sold for Gold ("Excess Gold").

Alternatively, you can Buy Resources from the Bazaar's Storage and use them. Why you have the right to sell a thing, but have to pay to use it is a mystery only the Devs can fathom.

The 1st Bazaar (and ONLY the 1st) gets a Standard amount of Resource Production, regardless of whether it's in range of any Quarries/Camps (hereafter: "Extractors"). Additionally, Bazaars, collectively, get a production boost from every Extractor that's in range (hereafter: "Covered Extractor") of a Bazaar; Gold Quarries excluded. This boost is completely unrelated to the Size or Production of the Extractors; it is determined by 3 factors: Number of Extractors Covered, Tier of Extractors Covered, and number of Bazaars in existence. It goes like this:

• Wood: +(55w for 1st B) + (5.5w per T1E) + (5.5w per T2E) | cycles every 180s
  
  • 1w/BWc = 0.27w/Wc: 1w/BWc / 180s/BWc * 49s/Wc
    
  • 1st B, NC produces equivalent of 15 w/Wc: (55w / 180s) * (49s / Wc)
• Stone: +(33S for 1st B) + (7.5S per T1E) + (12S per T2E) | cycles every 270s
  
  • 1S/BSc = 0.24S/Sc: 1S/BSc / 270s/BSc * 65s/Sc
    
  • 1st B, NC produces equivalent of 8 S/Sc: (33S / 270s) * (65s / Sc)
• Iron: +(22i for 1st B) + (5.5i per T1E) + (7i per T2E) | cycles every 360s
  
  • 1i/Bic = 0.25i/ic: 1i/Bic / 360s/Bic * 91s/ic
    
  • 1st B, NC produces equivalent of 5.6 i/Ic: (22i / 360s) * (91 / Ic)

Note that Tier 2 Mines get a bigger boost, but T2 Camps do not. This is likely a bug.
Also note that the 1st Bazaar gets outsized Iron production, providing the equivalent of an extra Mine, for a resource that you will almost certainly bottle-neck on between Waves 1-3.

Storage capacity goes as follows:

• Wood: 260 + 60/aB
  
  • 1st B, NC, time to fill, with T2K: 30.4 tc = 260w * (1Bwc / 55w) * 180s/Bwc * 1tc/28s
• Stone: 210 + 60/aB
  
  • 1st B, NC, time to fill, with T2K: 61.4 tc = 210w * (1Bwc / 33w) * 270s/Bwc * 1tc/28s
• Iron: 130 + 30/aB
  
  • 1st B, NC, time to fill, with T2K: 76.0 tc = 130w * (1Bwc / 22w) * 360s/Bwc * 1tc/28s

Now, I know what you're thinking: "Resources are great, but SHOW ME THE MONEY!"

Again, Excess Gold is the Gold you get from the Bazaar automatically Selling a Resource, when that Resource's Bazaar storage is full, and the Bazaar's production bar for that Resource ticks over. I did some tests... a lot of tests. It was very confusing for a while, particularly since I started out testing the wrong way around, as it turns out, but I eventually pieced it together.

Because the 1st Bazaar has Standard Resource Production, it also has a Standard profit, of Excess Gold, for Selling those Resources (once full). This is broken down for each Resource. Also similarly, that profit increases as you Cover more of that Resource's Extractors with Bazaars, and as the Tier of those Extractors increases (latter excepting Wood). Production goes up, profit goes up. Makes sense.

What's strange about Excess Gold is that it also increases just from building more Bazaars, completely separate from any Resource Production increase. i.e., like the Standard Resource Production of the 1st Bazaar, every Bazaar comes with a Standard Profit when Resources are automatically Sold. Like I said - complicated. Let's break it down with the maths:

Wood | cycles every 180s = 3mins = 0.47 Full Days = 7.5 to 5.3 tc

• EG: (84g for 1st B) + (54g per additional B) + (6.2|6.15g per B per T1E|T2E)
  
  • = 84g + (54g * aB) + (6.2w * B * T1E) + (6.2w * B * T2E)
• EG to g/tc Conversion: (EG / 180s) * ([24s to 34s] / tc)
  
• g/B/tc per T1|T2 Wood Camp: 0.83|0.83 to 1.2|1.2
  
• 1st B, NC produces 11.2 to 15.9 g/tc: (84g / 180s) * ([24s to 34s] / tc)

Stone | cycles every 270s = 4.5 mins = 0.7 Full Days = 11.3 to 7.9 tc

• EG: (76g for 1st B) + (65g per additional B) + (15.2|24.8g per B per T1E|T2E)
  
  • = 76g + (65g * aB) + (15.2g * B * T1E) + (24.8g * B * T2E)
• EG to g/tc Conversion: (EG / 270s) * ([24s to 34s] / tc) = g/tc
  
• g/B/tc per T1|T2 Stone Mine: 1.4|2.2 to 1.9|3.1
  
• 1st B, NC produces 6.8 to 9.6 g/tc: (76g / 270s) * ([24s to 34s] / tc)

Iron | cycles every 360s = 6 mins = 0.94 Full Days = 15 to 10.6 tc

• EG: (90.5g for 1st B) + (86.5g per additional B) + (22|27.8g per B per T1E|T2E)
  
  • = 90.5g + (86.5g * aB) + (22g * B * T1E) + (27.8g * B * T2E)
• EG to g/tc Conversion: (EG / 360s) * ([24s to 34s] / tc) = g/tc
  
• g/B/tc per T1|T2 Iron Mine: 1.5|1.9 to 2.1|2.6
  
• 1st B, NC produces 6 to 8.5 g/tc: (90.5g / 360s) * ([24s to 34s] / tc)

It's a lot, I know, so let's do an example!

Let's try an example, with 4 Bazaars covering an optimistic array of Extractors
e.g. 4 Bs, Covering 2 T1 Wood, 1 T1 Stone, 3 T2 Stone, 2 T1 Iron, gets:

Total Production: 18.0 w/Wc | 18.4 S/Sc | 8.3 i/Ic

• 66 Wood/BWc: 55w + (5.5w/We * 2We) + (5.5w/We * 0We)
  
• 76.5 Stone/BSc: 33S + (7.5S/Se * 1Se) + (12S/Se * 3Se)
  
• 33 Iron/BIc: 22i + (5.5i/Ie * 2Ie) + (7i/Ie * 0Ie)

Total Profit: 130g to 185g / tc: ([295g/180s] + [629g/270s] + [526g/360s]) * ([24s to 34s]/tc)

• 295 EG from Wood: 84g + (54g/B * 3B) + (6.2g/We/B * 4B * 2We) + (6.2g/we/B * 4B * 0We)
  
• 629 EG from Stone: 76g + (65g/B * 3B) + (15.2g/Se/B * 4B * 1Se) + (24.8g/Se/B * 4B * 3Se)
  
• 526 EG from Iron: 90.5g + (86.5g/B * 3B) + (22g/Ie/B * 4B * 2Ie) + (27.8g/Ie/B * 4B * 0Ie)

The game's Income Tooltip may lead you to believe otherwise, but this is another dirty troll by our devious Dev overlords; do not be fooled! The Earnings Tooltip shows Excess Gold for just the Resources that are full (in the Bazaar) and ignores the difference in cycle rates between the Bazaar and Taxes, which is huge. It does the same for Gold Mines, which also cycle slower than Taxes (0.38 Gold Cycles per Tax Cycle). Bear in mind that the Income above is ONCE FULL. It takes quite a while to fill Bazaar Storage, especially for Iron, and they earn nothing until full, so the actual Payoff Period is VERY long.

4B Total PP (if all simultaneously built, and T3 Keep): 66tc = 5.2 Full Days = 40tc + 26tc

• Turns to fill Wood: 40tc = 440w * (1Bwc / 66w) * 180s/Bwc * 1tc/30s
  
• Turns to fill Stone: 45.9tc = 390s * (1Bsc / 76.5s) * 270s/Bsc * 1tc/30s
  
• Turns to fill Iron: 80tc = 220i * (1Bic / 33i) * 360s/Bic * 1tc/30s
  
• Wood EG until Stone Fills: 290g = (45.9tc–40tc) * (295g/180s) * (30s/tc)
  
• Wood+Stone EG/tc: 119g/tc = [(295g/180s) + (629g/270s)] * (30s/tc)
  
• Remaining Turns to Payoff: 26tc = (850g*4 – 290g) / 119g/tc

It's about the same for a No-Coverage single Bazaar:
1B Total PP: 66.4tc = 4.9 Full Days = 61.4tc + 5tc

• wEG until Stone Fills: 405g = (61.4tc–30.4tc) * (84g/180s) * (28s/tc)
  
• w+sEG until Iron Fills: 307g = (76tc-61.4tc) * [(84g/180s) + (76g/270s)] * (28s/tc)
  
• w+s+iEG: 28g/tc = [(84g/180s) + (76g/270s) + (90.5g/360s)] * (28s/tc)
  
• Remaining Turns to Payoff: 5tc = (850g – 405g – 307g) / 28g/tc

For reference:

• A fully loaded Treasury gets about 450g/tc, PP 4.4tc.
  
• A great T2 Gold Mine (1 Store) is also 1.2kg/Gc * 0.38Gc/tc = 456g/tc, PP 3.5tc.
  
• A T3 House, with 38-Food T3 Farms, is 40g/tc - (16f/38f) * 40g/tc = 23g/tc, PP 31tc.
  
• 1st Bazaar, NC, ONCE FULL, gets 24g to 34g / tc, PP 35 to 25 tc.

To make those PPs more useful, here's how long it takes for the 4 Bazaars to not only pay for themselves but also make up all the lead a T3 House gets from its shorter PP; i.e. how long the game must go on before the Bazaars were a more profitable investment:

• T3 House headstart: 812g = (40g/tc – (16f/38f)*40g/tc) * (66tc – 31tc) = 23.2g/tc * 35tc
  
• Total Turns for 4B to overtake: 74.5tc = 5.8 Full Days = 66tc + [812g / (119g/tc – 23.2g/tc)]

You may get more benefit to your economy from buying the Stone/Iron, when you need it to continue building out Houses/Treasuries/Farms/Etc., but there's no easy way to test this.

Bazaars are a decent option for Gold Income, if you are at the point of using T3 Farms and have at least 6 Days left (but Treasuries and Gold Mines are way better). They serve as backup Storage, which can save you on a DN. But, most of all, the 1st Bazaar is a valuable avenue for getting Iron early on, particularly if you get stiffed on Iron Veins, as the 1st Bazaar produces the equivalent of 5.6 Iron Income, which is pretty darn good! You'll have to buy the Iron, of course, but it'll be worth it when you have plenty of Gold looking for a good time but Iron is playing wet blanket on your dreams. Grab a Bazaar after DN1 and use it to help you get your first Treasury before DN2.

The next 3 Bazaars can boost your Stone/Iron production a bit, if necessary, and provide decent Gold Income, but they're not nearly as much of a priority as the 1st. Finally, if you aren't Buying the Resources, let the Bazaar do the Selling on its own. For whatever reason, Manual Selling gives way worse profit. The Devs don't think much of your haggling skills.

• Cost per Unit to Buy w | s | i : 10g | 25g | 50g
  
• Profit per Unit to Manually Sell: 1g | 2.5g | 4g
  
• Profit per Unit to Automatically Sell: 4.5g | 8.2g | 15.9g

Hope that clears it all up! Drop questions in the comments if ya got 'um!

• Unfinished Bazaars contribute to the Bazaars' independent Excess Gold
  
• Unfinished Bazaars can not Store Resources
  
• Unfinished Extractors do not contribute to Bazaars in any way