A Taylor approximation would indeed be much quicker in most computing applications. However, the stated two-term Taylor approximations of the functions do a very poor job of estimating the original formula - I don't know what the designers originally intended for that function, however it is clear that they did NOT intend the function to closely follow any of the exponential functions I posted (by the end of any game the approximation would be off by many orders of magnitude). Hence the reason for my edit in my previous post on the subject.
A quadratic function can never approximate an exponential function well. The exponential function will always outgrow the quadratic function after a while, so I'm not surprised that such an approximation would be poor. But I don't know what people at Firaxis know about this.
That sounds reasonable - why not give it a try? I, for one, have no idea what inflation rates would be balanced at what settings at what point in the game.
Phew, creating my own formula for inflation. But I dislike the very notion of the inflation game mechanic.
The inflation game mechanic is there to have some meaningful cost level in the late game. Now that could be achieved in many ways. Before civ4, it was achieved by making some buildings have an upkeep cost. This was removed in civ4 in order to streamline the game, simplify it. Now, I don't mind removing pollution and replacing it with health or removing city rebellions in unhappy cities and replacing them with the new unhappiness system where unhappy citizens don't work. But removing building upkeep and replacing them with the system of city upkeep + inflation. Mwah.
City upkeep is good, it stops (or at least slows) the Rapid Expansion Strategy. It is good that it is hard to maintain a large empire with a primitive civilization. But after some technological developments, it starts to become meaningless. In the real world, modern cities do become more expensive and not because of some game turn number, but because you have to maintain more things. So I would just reintroduce building maintenance for the more modern buildings. That could go from 1 gpt for an observatory to 3 gpt for a factory.
Actually, that is what they did when they introduced corporations. Corporations are actually a type of buildings that requires maintenance. It does more than that as you can spread it to foreign empires and its maintenance is dependent on the number of resources used and it has a special headquarters, but in its basis it is a building that gives you something and requires a certain maintenance cost.
Other ways to increase late game costs:
Make the maintenance for more modern units higher than for ancient units. Knights and macemen and such could cost 2 gold per turn. Musketmen, grenadiers and cavalry 3 gold per turn. Infantry, sam infantry 4 gold per turn. Airplanes and mechanized units 6 gold per turn.
Probably a bit over the top. Yeah, these numbers should be a bit lower, but you get the idea.
I like to decide myself that I invest in something that increases my maintenance. I don't like it when my maintenance increases because I clicked next turn while nothing changed in my empire except the game turn number.
If you really think that it is best to create some abstract multiplier for the costs, then it should be dependent on the level of technological development. The technological development is a more accurate measure to see how profitable your cities are. Not perfect, but better than the turn number.
For instance, lets say that each age has 10 technologies (yes way off, just an example)
Ancient inflation: 0
Classical inflation: 0 + 1 per classical technology
Medieval inflation: 10 + 2 per medieval technology
Renaissance inflation: 30 + 3 per renaissance technology
Industrial inflation: 60 + 3 per industrial technology
Modern inflation: 90 + 1 per modern technology
Future inflation: 100
This is probably also not a perfect curve, but I must say that the profitability of my cities starts to increase greatly during the medieval and renaissance age because of the availability of buildings and the growth of cottages. Because of some superior civics, it continues to steadily grow in the industrial age. There's not a lot of improvement left in the modern age, so that's why inflation shouldn't grow that hard anymore in that age. The future age doesn't add anything anymore.
But I prefer the costs for buildings and units method. That way, you can see what you're paying for and you can decide whether you want that building/unit for that extra upkeep cost.
(That's a criticism of Firaxis' choice of implementation, and not your commendable attempt at improving it, just so you know.)
No wonder people are making a big deal out of it.
inflation, at least 2/3 was from corporations.
