I would like to compare building Infrastructure regularly and by using twice or even triple ic. Let us assume that manpower and ic are not limited and that any excessive ic is used for consumer goods. The money/icd ratio remains constant. There is no progress in technology. There is no change in ministers, national ideas and sliders and there is no peacetime modifier. Those conditions will essentialy never be met but they allow an easy comparision and donnot detract much from truth.
Building Infrastructure costs 2 ic over 120 days, uses 0.5 manpower and gives 5% per unit. Some terrains increase building time, gearing bonus decreases it and so do 2 sliders and 2 national ideas. Those modifiers are relevant for the question whether to build infra or not. They are not relevant for the question whether to use accelerated production for it because the time advantage of accelerated production is proportional to building time. Let this modifier be called tm, time modifier. There is also an effect of manpower being consumed earlier if the next unit starts production earlier. We will ignore it. Than there remains the price of additional icd invested by accelerated production. This is (4 x 120 / sqrt(2) - 2 x 120 ) x tm x icd or (6 x 120 / sqrt(3) - 4 x 120 / sqrt(2)) x tm x icd. After a unit is finished there is the need to repair infra and additionaly the provincial effeciency is needed to increase to the new maximum. Both processes are finished fast and more importantly they are the same. They donnot depend on acceleration and can therefore be ignored. What leaves is an advantage in time. This is (120 - 120 / sqrt(2)) tm x d or (120 / sqrt(2) - 120 / sqrt(3)) tm x d. This time needs to be multiplied with the number of infra units left(later called size). During this time the output of ic, the 4 resources and the 3 resource plants will be increased. Let us ignore plants for energy, oil and rares. Than the advantage is size x 0.015 x (factories x (1 + 0.01 factories) x effective ic modifier x (1 - civil expenses ratio + 2 energy x trade ratio / money modifier + 1 metal x trade ratio / money modifier + 0.5 rares x trade ratio / money modifier) + (1 + 0.01 factories) x resource modifier x ( base energy x trade ratio + base metal x trade ratio + base oil x trade ratio + base rares x trade ratio) / money modifier) x (120 - 120 / sqrt(2)) tm x d for double acceleration. Civil expenses ratio is the ratio of ic that is needed for consumer goods to fund increased civil expenses due to an increase of effective ic by 1. trade ratio is the trade ratio to money you get(or have to pay) for this change in tradeable resources. money modifier is the amount of money you get per 1 icd put into consumergoods. resource modifier is the modifier for resources by machine tools techs and ministers. Since effective ic and days are calculated as integers there is quite some rounding error but that will reduce when building long lines of infra. After all this we get that the following inequation must be true for double acceleration to increase the money stockpile in the end:
size x 0.015 x (factories x (1 + 0.01 factories) x effective ic modifier x (1 - civil expenses ratio + 2 energy x trade ratio / money modifier + 1 metal x trade ratio / money modifier + 0.5 rares x trade ratio / money modifier) + (1 + 0.01 factories) x resource modifier x ( base energy x trade ratio + base metal x trade ratio + base oil x trade ratio + base rares x trade ratio) / money modifier) x (1 - 1 / sqrt(2)) / ( 2 x sqrt(2) - 2 ) > 1
In most cases the delta in resources is small compared to the money value of increased ic. So lets assume the delta resources may be zero, that addional resources are exactly consumed by addional effective ic. Lets assume that civil expenses ratio is 0.2 at war and that effective ic modifier is 1.25. Than things get relativly easy.
size x (factories x (1 + 0.01 factories) > 188.562 for double acceleration or size x (factories x (1 + 0.01 factories) > 326.598 for triple acceleration. If 20 units or 100% infra are left size is 20. Than (factories x (1 + 0.01 factories) would need to be 9.4281 for double acceleration or 16.3299 for triple acceleration.
Edit: corrected a factor of 2
Building Infrastructure costs 2 ic over 120 days, uses 0.5 manpower and gives 5% per unit. Some terrains increase building time, gearing bonus decreases it and so do 2 sliders and 2 national ideas. Those modifiers are relevant for the question whether to build infra or not. They are not relevant for the question whether to use accelerated production for it because the time advantage of accelerated production is proportional to building time. Let this modifier be called tm, time modifier. There is also an effect of manpower being consumed earlier if the next unit starts production earlier. We will ignore it. Than there remains the price of additional icd invested by accelerated production. This is (4 x 120 / sqrt(2) - 2 x 120 ) x tm x icd or (6 x 120 / sqrt(3) - 4 x 120 / sqrt(2)) x tm x icd. After a unit is finished there is the need to repair infra and additionaly the provincial effeciency is needed to increase to the new maximum. Both processes are finished fast and more importantly they are the same. They donnot depend on acceleration and can therefore be ignored. What leaves is an advantage in time. This is (120 - 120 / sqrt(2)) tm x d or (120 / sqrt(2) - 120 / sqrt(3)) tm x d. This time needs to be multiplied with the number of infra units left(later called size). During this time the output of ic, the 4 resources and the 3 resource plants will be increased. Let us ignore plants for energy, oil and rares. Than the advantage is size x 0.015 x (factories x (1 + 0.01 factories) x effective ic modifier x (1 - civil expenses ratio + 2 energy x trade ratio / money modifier + 1 metal x trade ratio / money modifier + 0.5 rares x trade ratio / money modifier) + (1 + 0.01 factories) x resource modifier x ( base energy x trade ratio + base metal x trade ratio + base oil x trade ratio + base rares x trade ratio) / money modifier) x (120 - 120 / sqrt(2)) tm x d for double acceleration. Civil expenses ratio is the ratio of ic that is needed for consumer goods to fund increased civil expenses due to an increase of effective ic by 1. trade ratio is the trade ratio to money you get(or have to pay) for this change in tradeable resources. money modifier is the amount of money you get per 1 icd put into consumergoods. resource modifier is the modifier for resources by machine tools techs and ministers. Since effective ic and days are calculated as integers there is quite some rounding error but that will reduce when building long lines of infra. After all this we get that the following inequation must be true for double acceleration to increase the money stockpile in the end:
size x 0.015 x (factories x (1 + 0.01 factories) x effective ic modifier x (1 - civil expenses ratio + 2 energy x trade ratio / money modifier + 1 metal x trade ratio / money modifier + 0.5 rares x trade ratio / money modifier) + (1 + 0.01 factories) x resource modifier x ( base energy x trade ratio + base metal x trade ratio + base oil x trade ratio + base rares x trade ratio) / money modifier) x (1 - 1 / sqrt(2)) / ( 2 x sqrt(2) - 2 ) > 1
In most cases the delta in resources is small compared to the money value of increased ic. So lets assume the delta resources may be zero, that addional resources are exactly consumed by addional effective ic. Lets assume that civil expenses ratio is 0.2 at war and that effective ic modifier is 1.25. Than things get relativly easy.
size x (factories x (1 + 0.01 factories) > 188.562 for double acceleration or size x (factories x (1 + 0.01 factories) > 326.598 for triple acceleration. If 20 units or 100% infra are left size is 20. Than (factories x (1 + 0.01 factories) would need to be 9.4281 for double acceleration or 16.3299 for triple acceleration.
Edit: corrected a factor of 2
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