You can edit your tax rate in the Keep.
Your Gold income depends on your tax rate (which can varry from 0% to 100%) and your Population (grown with Homes). Raising the tax rate decreases Happiness, which can lead to a drop in Population.You can also gain extra gold by attacking other players and Goblin Camps.
Tax is defined as how much you charge your population for living in your city. The higher the tax rate, the more gold income you will receive dependent on the size of your population. Happiness is what defines how happy your population is with your current tax. If you set your tax too high, the population will become unhappy and will begin to leave your city over time resulting in you getting negative Idle Population. Having negative idle population results in your inability to train troops. If you set your tax low, more of the population will be happy and willing to work and fight for you.
The formula for Happiness/Tax is as follows:
In the beginning, it is recommended setting tax to 50% and then leaving it completely alone. It starts off as being set to 10%, but 50% is optimal for what new players need to get their city under way. You will get a lot of your beginning gold from following the Quests system too. When your Beginner's Protection is about to expire, reduce tax rate. From then on you will want to leave Tax set to as close to zero as possible to maximize your population and free up more Troops for training. Leave tax set to a very small number (usually lower than 5% but this could be greater depending on the size of your population) just so you have enough gold income to cover your upkeep (if you have heroes assigned to tasks in your Great Hall).
(Provided courtesy of FinrodFelagund of the HouseOfFinarfin)
To: Those who wish to maximize their Gold Production
My dear comrades in arms; by now you must have read the "Tax Rate & Happiness" section of the wikia in which it states that: Happiness = 100 - Tax Rate %. And that Happiness * Population Limit = Population (For Example: 98% Happiness * 49,500 Population Limit = 48,510 Population). Your Gold grows at a rate of: Population * Tax Rate % (For Example: 48,510 Population * 2% Tax Rate = 970 Gold per hour).
So, if your tax rate is 50%, from the examples above, your current Population would be 24,750 and your Gold Rate would be 12,375gph (gold per hour). Over 10 hours, this would be 123,750 Gold, or 25% of your Population Limit which would seem to be the best you could hope for...
However, since loss of population is not instantaneous, you can nearly DOUBLE THAT RATE! The rate of population change is 1% per 6 minutes, and gold collection is also every 6 minutes (1/10th of your hourly gold rate). Using the example above (and releasing all heroes from their positions) it would take 12 minutes to elevate the current Population to the Population Limit after setting my Tax Rate to 0%. Once I have the maximum amount of Population possible, I start a 10 hour cycle...
You will need to keep close track of time to accomplish the maximum amount of return. For the first 5 hours, I set my Tax Rate to 100%. After the first 6 minutes, I collect 4,950 Gold. After the next 6 minutes, I collect 4,900 Gold. After the next 6 minutes, I collect 4,851 Gold and so on. After 5 hours, my Population will be 24,750, and I will have collected 184,375 GOLD! I've already collected 49% more gold than a static 50% Tax Rate and am 82% of the way toward my goal.
After reaching a reduction of my Population to 50% of Population Limit, I need to "grow back" my population. If you have the time and the patience, you can lower your tax rate 1% every 6 minutes after collecting your gold starting at 49%. So, your gold collected at 5 hours and 6 minutes would be 49% * 24750 / 10 = 1,212. Your gold collected at 5 hours and 12 minutes would be 48% * 25245 / 10 = 1,211, and so on. If you change your Tax Rate persistently at 6 minute intervals after collecting your gold, you will have collected 39,997 Gold during the 5 hour "grow back" stage, totaling 224,372 Gold collected over the 10 hour period. That's 46% of your Population Limit!
If you are not that patient to monitor your tax rate every 6 minutes, you can change your Tax Rate by 5% in 30 minute intervals to net just over a 44% return on your Population Limit. (221,069 Gold over 10 hours instead of 224,372 Gold over 10 hours). And if you can only monitor your Tax Rate every 5 hours, setting your tax rate to 1% for the last 5 hours will net you a meager 37.6% return over the 10 hours (which is still better than the 25% we started with above!)
So, in conclusion, don't forget that "Time" is also a resource that you can manage!
Your faithful servant,
PS: If you found this information to be useful, please don't attack me ;-)