Part 35: Economic Breakdown 2
It's been quiet. Time for an update!Non-Farm economic buildings - What are my returns?
Welcome back to the second bonus economic update of my Rise of the Samurai LP. In this update I will be discussing all the economic buildings that are not part of the farming food chain (The pastures chain, despite providing some wealth, is a building chain that is a capacity increase, not an economic building) and the nature of their benefits to your economy.
Economic buildings consist of three types, food providing (Global growth buildings), local wealth (town growth and town wealth boosts) and trade buildings (Closely related to the second category).
Food providing buildings (The most common being farms) are those which increase your global food supply, providing additional wealth growth to every province you control and so require a different approach to measure the economic effectiveness of them. This methodology is covered in the sister post to this, Empire size and food growth - What are my returns? I posted earlier in the thread. Farms were covered extensively in that, the only other building chain that produces food is the Granary chain, which will be covered in this post.
Local Wealth buildings are the most common economic building in Shogun 2: Rise of the Samurai, providing either a boost to the base wealth of the province, a boost to the wealth growth of the province, increasing the tax rate of the province or some combination of the previous.
Trade buildings provide not only base wealth or wealth growth, but also produce trade goods. Trade goods are sold to other clans through Trade Agreements, proportional to the size of the clan you are trading with. Any trade goods not sold in this way are instead locally consumed at half their value. While this makes them very similar to the Local Wealth buildings, they can not be included in the same category as external situations (War declaration, clan elimination, cancelled agreements) impact their level of profitability and so they must be assessed in a different way.
Some buildings can be upgraded into two possible chains, only those which are economic will be considered in this update (Examples of buildings that will not be considered are Military Ports, Pastures, Trails or Fletchers)
As we are interested in what each individual building gets us, we look only at the difference between two buildings in the upgrade chain to determine our returns. As Trade Buildings are province specialities and are always present in the province, only their upgrades will be looked at in this update.
As in my previous economic post, the values are calculated by:
quote:
The amount of income added to your empire on a given turn from the upgrade is calculated as:
(Building Wealth bonus+(Building growth bonus x Turns since built)+(Food Bonus x Empire Size x Turns Since Built)) x Tax Rate
For the mathematically inclined, it would look like this:
(a+(b+(f*e))x)t
Where a is building wealth, b is building growth, f is the food bonus, e is empire size, t is the tax rate and x is the number of turns since construction.
Since each building adds only a single food and no additional town growth, we simplify it to:
(a+ex)t
Which can also be represented as:
at+etx
This is not the whole story however, as the tax rate can vary from province to province. Instead, we elect to have 2 tax rates, one for the local province and one for the empire. While all the local bonuses are affected by the (usually higher) local tax rate, your empire wide tax rate (which is what generates wealth from your empire growth) is likely to be significantly lower and is inversely impacted as your empire increases in size. Indeed, as your empire grows, your administrative cost will increase, reducing your empire tax rate from it's base of 30%.
We will call the empire tax rate m and now our formula looks like this:
at+emx
However, we are interested not in the income added on a single turn, but instead the total income that upgrade has given us up until our selected point. To find that, we must integrate our above formulae with respect to the turn.
This gives us the following result:
atx+(emx^2)/2 + c
Where c is a constant. As we will only be taking the integral between two values of x (0 and turns since upgrade), the value of c will cancel out. In addition, at x=0, the result is 0 and so we will just calculate for x is turns since upgrade to get our result.
This is no longer entirely accurate, as the buildings that do not produce food have a simplified integral that looks like:
atx+(btx^2)/2 + c
Where b represents the town growth generated by the building. If the building produces both food and growth, the integral would look like:
atx+((bt+em)x^2)/2 + c
Of the four locally produced trade goods, they have the following value:
Silk - 18, Iron - 22, Crafts - 40, Wood - 20
Now that we have determined our methodology for calculating the benefits of the building upgrades, we need to identify what benefits are provided by an individual building.
code:
Food Producing:
Food Stores 2000 +0 wealth +5 town growth +1 food
Granary 3000 +0 wealth +5 town growth +1 food
Grain Warehouse 7500 +200 wealth +15 town growth +1 food
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 2000 50 47 44 42 40 38 36 35 34
Granary 3000 62 57 54 51 49 46 44 43 41
Grain Warehouse 7500 55 49 44 41 38 35 33 31 29
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 4000 71 66 62 59 56 53 51 49 48
Granary 6000 87 81 76 72 68 65 63 60 58
Grain Warehouse 15000 81 73 66 61 57 53 50 48 45
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 6000 87 81 76 72 68 65 63 60 58
Granary 9000 107 99 93 88 84 80 77 74 71
Grain Warehouse 22500 102 91 83 77 72 67 64 60 58
Time to Break Even - 5 provinces : Empire tax Rate : 27%
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 2000 42 40 38 36 35 34 33 32 31
Granary 3000 51 49 46 44 43 41 40 39 38
Grain Warehouse 7500 51 46 42 39 36 34 32 30 29
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 4000 59 56 53 51 49 48 46 45 43
Granary 6000 72 68 65 63 60 58 56 55 53
Grain Warehouse 15000 75 68 63 58 54 51 49 46 44
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 6000 72 68 65 63 60 58 56 55 53
Granary 9000 88 84 80 77 74 71 69 67 65
Grain Warehouse 22500 93 85 79 73 69 65 61 58 56
Time to Break Even - 10 provinces : Empire tax Rate : 24%
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 2000 35 34 33 32 31 30 29 28 28
Granary 3000 43 41 40 39 37 36 35 35 34
Grain Warehouse 7500 46 42 39 37 34 32 31 29 28
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 4000 49 47 46 44 43 42 41 40 39
Granary 6000 60 58 56 54 53 51 50 49 48
Grain Warehouse 15000 68 63 58 55 51 49 46 44 42
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 6000 60 58 56 54 53 51 50 49 48
Granary 9000 73 71 68 66 64 63 61 60 58
Grain Warehouse 22500 85 78 73 69 65 61 59 56 54
Time to Break Even - 15 provinces : Empire tax Rate : 21%
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 2000 32 31 30 29 28 28 27 27 26
Granary 3000 39 37 36 35 35 34 33 32 32
Grain Warehouse 7500 44 40 38 35 33 31 30 28 27
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 4000 44 43 42 41 40 39 38 37 37
Granary 6000 54 53 51 50 49 48 47 46 45
Grain Warehouse 15000 64 60 56 53 50 47 45 43 41
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 6000 54 53 51 50 49 48 47 46 45
Granary 9000 66 64 63 61 60 58 57 56 55
Grain Warehouse 22500 80 74 70 66 62 59 57 54 52
Time to Break Even - 20 provinces : Empire tax Rate : 19%
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 2000 29 29 28 27 27 26 26 25 25
Granary 3000 36 35 34 33 33 32 31 31 30
Grain Warehouse 7500 42 39 36 34 32 31 29 28 27
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 4000 41 40 39 38 38 37 36 35 35
Granary 6000 50 49 48 47 46 45 44 43 43
Grain Warehouse 15000 61 57 54 51 48 46 44 42 40
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Food Stores 6000 50 49 48 47 46 45 44 43 43
Granary 9000 62 60 59 57 56 55 54 53 52
Grain Warehouse 22500 76 71 67 64 61 58 55 53 51
code:
Local Wealth:
Clan Estate 700 +0 wealth +0 town growth +5% tax
Shinden 1520 +0 wealth +0 town growth +5% tax
Mandokoro 3600 +0 wealth +0 town growth +5% tax
Clan Palace 6800 +0 wealth +0 town growth +5% tax -20% admin cost
Barter Exchange 800 +200 wealth +5 town growth
Market 1800 +300 wealth +0 town growth
Goods Exchange 3300 +300 wealth +0 town growth
Merchant Guild 7600 +700 wealth +5 town growth
Harbour 900 +100 wealth +2 town growth +1 trade route +80 export value
Trading Port 2530 +200 wealth +7 town growth +1 trade route +80 export value
code:
10% Admin/20% Admin/40% Admin
Province Wealth: 1000 1500 2000 2500 3000 3500
Clan Estate 700 15/18/23 11/12/16 8/9/12 7/7/10 6/6/8 5/5/7
Shinden 1520 34/38/51 23/26/34 17/19/26 14/16/21 12/13/17 10/11/15
Mandokoro 3600 80/90/120 54/60/80 40/45/60 32/36/48 27/30/40 23/26/35
Taira Palace* 6800 152/170/227 101/114/152 76/85/114 61/68/91 51/57/76 44/49/65
Base Income Percentage: Income / (100 - Admin Cost)
= 14000 / 60
= 233.33 Koku per percentage
Percentage reduction in Admin Cost: Base Admin Cost * Admin Reduction%
= 40 * 20%
= 8%
Koku gained: Percentage * Koku per percent
= 8% * 233.33
= 1866.64 Koku per turn
Which in this case, just by itself it would pay for the Palace in 3 turns even without the tax boost provided by the palace, an absolutely amazing economic deal!
Note that the same mathematics can be used to calculate the value of the Administrative Cost reducing arts (Direct Land Tax and Police Office). Note that all reductions to the Administrative Cost are additive and apply to the base Administrative Cost of your empire. Having both arts would reduce your administrative cost by 40%. This means that the maths is a little more complicated if you want to find out the value of the second reducing art, but your base rate can be easily derived by: Current Admin Rate / (100% - Admin Reduction%)
This will only impact your amount of admin cost reduction, the calculation for koku per percent remains calculated in exactly the same way.
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Barter Exchange 800 17 14 12 11 9 9 8 7 7
Market 1800 30 24 20 18 15 14 12 11 10
Goods Exchange 3300 55 44 37 32 28 25 22 20 19
Merchant Guild 7600 47 39 33 29 25 23 21 19 18
Harbour* 900 34 29 25 22 19 18 16 15 14
Trading Port* 2530 38 33 29 26 23 21 19 18 17
Time to Double
code:
10% Admin/20% Admin/40% Admin
Province Wealth: 1000 1500 2000 2500 3000 3500
Clan Estate 1400 32/35/47 21/24/32 16/18/24 13/14/19 11/12/16 9/10/14
Shinden 3040 68/76/102 46/51/68 34/38/51 28/31/41 23/26/34 20/22/29
Mandokoro 7200 160/180/240 107/120/160 80/90/120 64/72/96 54/60/80 46/52/69
Taira Palace* 13600 303/340/454 202/227/303 152/170/227 121/136/182 101/114/152 87/98/130
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Barter Exchange 1600 30 25 22 19 17 15 14 13 12
Market 3600 60 48 40 35 30 27 24 22 20
Goods Exchange 6600 110 88 74 63 55 49 44 40 37
Merchant Guild 15200 84 70 60 53 47 42 39 36 33
Harbour 1800 58 49 43 38 34 31 29 26 25
Trading Port 5060 62 53 47 42 38 35 33 31 29
code:
10% Admin/20% Admin/40% Admin
Province Wealth: 1000 1500 2000 2500 3000 3500
Clan Estate 2100 47/53/70 32/35/47 24/27/35 19/21/28 16/18/24 14/15/20
Shinden 4560 102/114/152 68/76/102 51/57/76 41/46/61 34/38/51 29/33/44
Mandokoro 10800 240/270/360 160/180/240 120/135/180 96/108/144 80/90/120 69/78/103
Taira Palace* 20400 454/510/680 303/340/454 227/255/340 182/204/272 152/170/227 130/146/195
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Barter Exchange 2400 40 34 30 26 24 22 20 18 17
Market 5400 90 72 60 52 45 40 36 33 30
Goods Exchange 9900 165 132 110 95 83 74 66 60 55
Merchant Guild 22800 116 97 84 74 66 60 55 51 47
Harbour 2700 77 66 58 52 47 43 39 37 34
Trading Port 7590 80 69 62 56 51 47 44 41 38
code:
Trade Building:
Silk Spinner 2050 +200 wealth +0 town growth +10 silk
Master Silk Spinner 3800 +200 wealth +0 town growth +10 silk
Lumberyard 1350 +160 wealth +0 town growth +10 wood
Saw Mills 2000 +170 wealth +0 town growth +10 wood
Small Iron Mine 1400 +150 wealth +0 town growth +10 iron
Iron Mine 2400 +150 wealth +0 town growth +10 iron
Washi Mills 1350 +150 wealth +0 town growth +15 crafts
Lacquerware Works 3750 +300 wealth +0 town growth +25 crafts
Gold Lodes 2400 +500 wealth +0 town growth
Gold Mine 5000 +500 wealth +0 town growth
Time to Break Even
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Silk Spinner 2050 10/16 9/15 9/14 9/13 8/13 8/12 8/11 8/11 7/10
Master Silk Spinner 3800 18/30 17/28 16/26 16/24 15/23 15/22 14/20 14/19 13/19
Lumberyard 1350 6/11 6/10 6/10 6/9 6/9 5/8 5/8 5/8 5/7
Saw Mills 2000 9/15 9/15 8/14 8/13 8/12 8/12 8/11 7/11 7/10
Small Iron Mine 1400 6/10 6/10 6/10 6/9 5/9 5/8 5/8 5/8 5/7
Iron Mine 2400 10/18 10/17 10/16 9/15 9/15 9/14 9/13 8/13 8/12
Washi Mills 1350 3/5 3/4 3/4 3/4 3/4 3/4 2/4 2/4 2/4
Lacquerware Works 3750 4/7 4/7 4/7 4/7 4/7 4/6 4/6 4/6 4/6
Gold Lodes 2400 24 20 16 14 12 11 10 9 8
Gold Mine 5000 50 40 34 29 25 23 20 19 17
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Silk Spinner 4100 19/32 18/30 18/28 17/26 16/25 16/23 15/22 15/21 14/20
Master Silk Spinner 7600 35/59 34/55 32/51 31/48 30/45 29/43 28/40 27/38 26/37
Lumberyard 2700 12/21 12/20 11/19 11/18 11/17 10/16 10/15 10/15 10/14
Saw Mills 4000 18/30 17/29 16/27 16/26 15/24 15/23 15/22 14/21 14/20
Small Iron Mine 2800 12/20 11/19 11/19 11/18 10/17 10/16 10/16 10/15 10/14
Iron Mine 4800 20/35 19/33 19/31 18/30 18/29 17/28 17/26 16/25 16/24
Washi Mills 2700 5/9 5/8 5/8 5/8 5/8 5/8 4/8 4/8 4/7
Lacquerware Works 7500 8/12 7/14 7/13 7/13 7/13 7/12 7/12 7/12 7/12
Gold Lodes 4800 48 39 32 28 24 22 20 18 16
Gold Mine 10000 100 80 67 58 50 45 40 37 34
code:
Province Tax Rate: 20% 25% 30% 35% 40% 45% 50% 55% 60%
Silk Spinner 6150 28/48 27/44 26/41 25/39 24/37 23/35 22/33 22/31 21/30
Master Silk Spinner 11400 52/88 50/82 48/76 46/72 44/68 43/64 41/60 40/57 38/55
Lumberyard 4050 18/31 17/29 17/28 16/26 16/25 15/24 15/23 15/22 14/21
Saw Mills 6000 26/45 25/43 24/40 24/38 23/36 22/34 22/33 21/32 20/30
Small Iron Mine 4200 17/30 17/29 16/28 16/26 15/25 15/24 15/23 14/22 14/21
Iron Mine 7200 29/52 28/49 28/47 27/45 26/43 26/41 25/39 24/38 24/36
Washi Mills 4050 7/13 7/12 7/12 7/12 7/12 7/12 6/11 6/11 6/11
Lacquerware Works 11250 11/21 11/20 11/20 11/19 11/19 10/18 10/18 10/17 10/17
Gold Lodes 7200 72 58 48 42 36 32 29 27 24
Gold Mine 15000 150 120 100 86 75 67 60 55 50
Coming up next, the third and final post in our economic analysis: How to build the perfect province
Where I will answer the all important question "These numbers are great and all Shalcar, but how do I actually use them?"