The Federal Economy page two

After reading page one you should now be able to run a decent economy. But to truly get the best out of it, you'll need to spend a little more time on it and tax your natives in the best possible ways, don't build too many structures, terraform where useful and don't terraform useless planets, use your Race+ advantage and improve the right governments.


5. Formulas

The first step in optimising your economy is to have a clear understanding of the formulas involved, the factors influencing your economy and the consequences of your actions on it. Your economy will run by the following formulas, all taken from Eden Tan's famous infolist:

Taxes earned: (native population)*(taxrate)*(government factor)*0.001*2 (last factor *2 applies only to Feds)
          With the taxrate being a factor between 0 and 1 (40% tax is a factor of 0.4) and the following government factors:
          Anarchy:            20%
          Pre-tribal:          40%
          Early-tribal:        60%
          Tribal:                80%
          Feudal:             100%
          Monarchy:        120%
          Representative: 140%
          Participatory:    160%
          Unity:               180%

Native happiness change:
trunc (5 + government factor/40 - sqrt(number of natives / 1000000) -
                                            (mines+factories)/200 - taxrate * 0.85)
                                            with the same government factors as mentioned above

Native growth:
4 * sin(temp*pi/100) / (1 + taxrate/5)
                          Here the taxrate is the actual taxlevel: 30% taxes is 30.


6. Earning taxes

With double tax-earnings being one of your main advantages you can do without paying too much attention to taxing and still come up with enough money to keep you alive, but you'd be better off paying a lot of attention to this aspect and get the best out of your natives. Simply following the first formula above, there's nothing to it: you drop clans on a planet, you tax the natives and your clans collect taxes. How much they can collect at a certain taxlevel depends on the number of natives on the planet and their government factor. Unless you're playing with the Race+ addon you cannot influence the government factor, but it is pretty easy as a Fed to influence the number of natives. Two major ways are terraforming and taxing them through the so-called growth method (or ofcourse not taxing them at all).

6.1 Taxing your natives - different strategies
There are a couple of different ways to tax your natives. The most commonly known methods are the so-called growth method and the safetax-method. The difference between them is that the safetax-method taxes the natives every turn, and keeps their happiness at 70 points (the minimum at which the natives still grow). The growth-method taxes the natives very high every couple of turns, then waits for their happiness to reach 100 again and than yanks them for another round of taxing. The difference in the result of these methods derives from the 'native growth' formula: as you'll see the taxlevel is an influence on growth.
A simple glance at the formula will show us that the natives will grow at a percentage, calculated by a multiplying a factor for the temperature (we'll get to that later) by four and then dividing it by a taxrate-factor. So at 0% taxes the temperature-factor is divided by 1; at 7% taxes it's divided by 2 and at 39% taxes by 8.

Now, in short the safetax-method would tax the natives at 7% every turn, while the growth-method taxes at for example 35% at one turn and then a four turns at 0%. The net-result over five turns looks the same at first: 5*7% equals 35%, after all. But there's the catch: now in the sixth turn the growth-method implements another 35% taxround. But this time the number of natives has grown at a maximum level for four straight turns, instead of half the maximum level as with the safetax-method. Using this advantage the growth-method earns you more money. Or at least, that's what everybody says.

6.2 Comparing different policies
Ofcourse, some just don't believe anything no matter how many people say it's so, without seeing some actual proof. In this case one of those people is me, so I fired up a spreadsheet or two and started calculating. I've used the formulas as stated on top of this page, and created my own virtual natives. I think I've used the formulas in the correct order (growth occurs after happiness change, but to be sure I didn't make a mistake there I just kept happiness at 70 or higher) and have taken a few things into account. It is reported that above a population of approximately 6.5 million natives only grow half as fast. Furthermore, native population is limited by temperature. At 50 degrees the max. populations is 15.6 million, at 84 degrees it's 12 million. My testgrounds included:

And just for the heck of it I also tested a third strategy I call the half-tax strategy. Tax one turn at about 10%, so that happiness drops the same amount of points as it will grow at a turn of non-taxing, than don't tax for one turn so happiness reaches 100 again and tax again, and so on and so on.

6.3 Money, money, money
To keep this at least somewhat readable I won't bother you with the sheets of the different methods (twelve in total). In the online version of this guide you can download them here. We'll stick with the end-results here. The following is a table with the total taxes earned over 40 turns using the different methods under different circumstances. A few remarks beforehand: I manually set the (virtual) taxlevel each turn, mostly staying under the 5000 MC limit. In some occasions one percent higher taxes would earn more money, but would lift the total earned amount for that turn over 5000 MCs. So it is possible to squeeeze some extra bucks out of the growth-method.

  Low starting pop.

  High starting pop.

temp=50

temp=84

temp=50

temp=84

growth-tax

14673

13292

52896

47792

half-tax

15135

11658

37301

33087

safe-tax

15541

13516

44246

43744


As you'll see, for a low starting population the differences aren't that impressive. What's surprising is that the safetax-method actually earns more money than the growth-method. The difference however is negligable: a maximum of 900 MCs over 40 turns. So, since it doesn't seem to matter which method you use on low populations from this point of view it's time to take a look at the long-term strategy: the big bucks can be earned from large populations, and to get to a large populations non-taxing (only a valid option if you're really swimming in money) or the growth-method are the best ways.
Now, at a high starting population things become more interesting. I've read somewhere (I think it was in the newsgroup) that using the growth-method on high populations isn't worth the trouble because of the halved growth. But from the looks of things it's defenitely worth the trouble. The major reason for the success of the growth-tax method with high populations is that the natives will reach their maximum population faster that way, and once that's happened you don't have to worry about keeping them happy anymore. Just tax them straight down to 40 happiness points, which means taxing them high for a turn or three. That's where you make the extra bucks.

6.4 Differences other than money
Since the benefits of the growth-tas method moneywise aren't that impressive on low populations, let's just have a look at the growth results. As stated, using this method your natives grow faster, but just how much faster do they grow? The number of natives in millions we've ended up with after using the above described taxing methods for 40 turns (as above, a low population is 2 million and a high population 9 million) are as follows:

  Low starting pop.

  High starting pop.

temp=50

temp=84

temp=50

temp=84

growth-tax

7.04

3.87

15.6(T33)

12(T36)

half-tax

5.17

3.28

15.6(T40)

11.7

safe-tax

4.01

2.78

13.6

10.9

Clearly, using the growth-method you'll end up with substantially more natives. Big deal, you say. Well, yes! As seen above, once your population hase grown to a nice large amount, the bucks really begin to fly in. And what if your natives are Bovinoids? Each turn, the difference in number of natives for both method grows. So each turn, the growth-method would give you more "extra" natives and thus more extra supplies. A comparison:

Difference in natives: comparing safetax with growth-tax.

Starting population 2 million, government monarchy, temp 50.

Turn

growth-tax

safetax

difference

Difference in supplies

1

2,00

2,00

0,00

0

2

2,08

2,08

0,00

0

3

2,09

2,09

0,00

0

4

2,17

2,12

0,05

5

5

2,26

2,16

0,10

10

6

2,35

2,20

0,15

15

7

2,44

2,23

0,21

21

8

2,54

2,27

0,27

27

9

2,64

2,31

0,34

34

10

2,66

2,35

0,31

31

11

2,76

2,38

0,38

38

12

2,87

2,42

0,45

45

13

2,99

2,47

0,52

52

14

3,11

2,51

0,59

59

15

3,23

2,56

0,67

67

16

3,36

2,61

0,76

76

17

3,49

2,65

0,84

84

18

3,51

2,70

0,81

81

19

3,65

2,75

0,90

90

20

3,80

2,80

1,00

100

21

3,95

2,85

1,10

110

22

4,11

2,90

1,20

120

23

4,27

2,96

1,32

132

24

4,44

3,01

1,43

143

25

4,62

3,06

1,56

156

26

4,64

3,12

1,52

152

27

4,83

3,18

1,65

165

28

5,02

3,23

1,79

179

29

5,22

3,29

1,93

193

30

5,43

3,35

2,08

208

31

5,65

3,41

2,23

223

32

5,87

3,48

2,40

240

33

6,11

3,54

2,57

257

34

6,14

3,60

2,53

253

35

6,38

3,67

2,71

271

36

6,51

3,74

2,77

277

37

6,64

3,80

2,84

284

38

6,77

3,87

2,90

290

39

6,91

3,94

2,96

296

40

7,04

4,01

3,03

303

Total:                5086

So by simply using the growth-method on your Bovinoids, you've just earned yourself 5086 extra supplies over a course of 40 turns. And putting those extra supplies through a Merlin would have earned you 1695 minerals. Now, considering a base and a new Merlin together will cost you a grand total of 1871 minerals, you'll see you've just about earned yourself quite a substantial amount of extra resources. And that is just for a low starting population.
Comparing both methods for a high starting population of nine million cows, we find a difference of 6299 supplies over 40 turns. This ofcourse equals 2100 minerals, or put into perspective: a starbase, a Merlin and the minerals for a Diplomacy or two Kittyhawk hulls.

6.5 Some final words on taxing
Apart from all the above mentioned, the way in which you tax a certain planet depends entirely on the situation. How long you expect to own the planet and profit from it's natives is a big influence. The growth-method din't really pay off in 30 turns, for example (Before calculating the differences for both methods over 40 turns I did it for 30 turns). The amount of clans you can put on a planet should also influence your tax-strategy. There's not much use for the growth-method when you only have 100 clans on a planet. Sure, using the growth-method allows the natives to grow faster before your ship with colonists arrives, but then again so will not taxing them at all. If it's a planet you expect to lose to your enemy in the near future, just tax the natives into a civil war and make the planet useless to him.
As for my calculations, I have yet to make them for longer periods of time, and have yet to make them for Avians and have a look at the situation with Insects (not only do they produce double taxes, they also grow faster on hot planets). If someone discovers a mistake in the formulas I've used or the conclusions I've drawn from all this, please don't hesitate to let me know.

I'm currently working on page 3 of the Federal economy: the influence of the number of structures you build on a planet, the benefits of terraforming and the true profit of the HUD-mission from raceplus.


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