Hurricane. Here you'll get the raw numbers, so feel free to check them (and do further testing if you want to):
This is a scenario with one AI civ only. The monarchy price in paranthesis is when the Hanging Gardens is already built.
AI seller (minimum gold the AI accepts)
Chieftan: Currency 342, Monarchy 694 (684), Republic 794
Warlord: Currency 345, Monarchy 700(690), Republic 801
Regent: Currency 355, Monarchy 721(711), Republic 825
Monarch: Currency 402, Monarchy 815(803), Republic 934
Emperor: Currency 479, Monarchy 968(956), Republic 1112
Deity: Currency 654, Monarchy 1321(1308), Republic 1522
Human seller (maximum gold the AI will pay)
Chieftan: Curr 342, Mon 694, Rep 794, wine 300
Warlord: Curr 339, Mon 688, Rep 787, wine 298
Regent: Curr 329, Mon 668, Rep 764, wine 289
Monarch: Curr 359, Mon 726, Rep 833, wine 283
Emperor: Curr 383, Mon 773, Rep 887, wine 268
Deity: Curr 495, Mon 999, Rep 1152, wine 261
I also did a few tests where I changed the AI-AI trade bonus and got exactly the same numbers as above, and a few tests where I changed the AI cost factor and found the results completely consistent with my formula.
Ex: A deity game with AI cost factor increased from 0.6 to 1 would change the demand for republic from 1152 (794 / 0.6 * 1.15) to 913 (794 / 1.0 * 1.15).