Solid numbers on manufactories and inflation
Taken from this thread:
OK, I've had enough of the fumbling around, I'm going to advance the analysuis that Peter Ebbesen started.
One month of having the slider to the right gives you .083% inflation.
Assuming you start at zero inflation, incurring an inflation rate of x% causes your purchasing power to be penalized by a factor of x/(1+x). So, for example, a 10% inflation rate reduces your purchasing power by 9.1%. If your inflation is greater than zero, this formula overestimates the impact of inflation. For back-of-the-envelope calculations, you can ignore the denominator for small amounts of inflation (just say rhat the penalty for 10% inflation is 10%), athough this further overestimates the effects of inflation.
So the purchasing power penalty proportion (PPPP
) of minting n ducats is
n/(1200M+n)
where M is monthly income.
The actual yearly penalty, IN DUCATS, for minting n ducats, is:
((12M+Y)n)/(1200M + n)
where Y is the yearly income.
OK, so that's the inflation side of things. Now, a manufactory will get you 66 ducats a year in investment and income if in the wrong province, and 72 in the right province. Add the inflation penalty and it becomes 66*1200M/(1200M+n) or 72*1200M/(1200M+n)
SO... say a manufactory costs n ducats. Minting coin to build a manufactory in the wrong province will produce a net profit when,
66*1200M > n(12M + Y)
and replace the 66 with a 72 for the right province. Now, let k be the fraction of your income that comes from annual (census) taxes. Multiplying out and grouping terms as best I can gives:
6600/n > 1/(1-k) for the wrong province, and
7200/n > 1/(1-k) for the right province.
The yearly profit a manufactory will give you is:
(??*1200M - (12Mn/(1-k)))/(1200M+n)
(Where ?? is 66 or 72 depending on manufatory location). Which means you will break even from building the manufactory in:
n*(1200+(n/M))/(??*1200 - 12n/(1-k)) years
Example: If we say that 20% of your taxes come from census taxes, then minting coin to build a manufactory on the right province is profitable as long as the manufactory costs less than 5760. If you're talking about the wrong province, the break-even point is 5280. So unless you have something better to be doing with that money, making a manufactory is nearly always worth it.
For any reasonably large monthly income, a manufactory built in the right province for 1000 ducats will pay itself back in 20 years or so, after adjusting for inflation.
A few comments on this analysis:
In terms of eventual profitability, only the percentage of your income that comes from yearly census taxes matters. Your actual income is irrelevant. This is a fairly counter-intuitive result. The bottom line here is that if your income is very small, you will incur huge inflation to build the manufactory, but the manufactory income will be massive compared to the rest of your income.
In practice, since it takes a long time to pay back the manufactory income, you shouldn't mint coin to put in the manufactory until you have enough income to do it quickly.
This analysis ignores the peripheral benefits of manufactories. The 1% efficiency bonuses of refineries and goods manufactories make them extrodinarily profitable for large empires. And there are numerous other benefits (manpower, population, revoltrisk) that can't be easily quantified, but should be considered.
FINALLY: note the following dirty little inequality:
??/1.15 > 10.4M/(1-k)
That's the profitability inequality for going bankrupt to build a (1000 ducat) manufactory. The breakeven monthly income (for 20% census taxes) to build a wrong-province manufactory is 4.5 or so. So unless you're poor AND devoid of expansion opportunities, you probably shouldn't go bankrupt to build a manufactory.
Taken from this thread:
OK, I've had enough of the fumbling around, I'm going to advance the analysuis that Peter Ebbesen started.
One month of having the slider to the right gives you .083% inflation.
Assuming you start at zero inflation, incurring an inflation rate of x% causes your purchasing power to be penalized by a factor of x/(1+x). So, for example, a 10% inflation rate reduces your purchasing power by 9.1%. If your inflation is greater than zero, this formula overestimates the impact of inflation. For back-of-the-envelope calculations, you can ignore the denominator for small amounts of inflation (just say rhat the penalty for 10% inflation is 10%), athough this further overestimates the effects of inflation.
So the purchasing power penalty proportion (PPPP
) of minting n ducats isn/(1200M+n)
where M is monthly income.
The actual yearly penalty, IN DUCATS, for minting n ducats, is:
((12M+Y)n)/(1200M + n)
where Y is the yearly income.
OK, so that's the inflation side of things. Now, a manufactory will get you 66 ducats a year in investment and income if in the wrong province, and 72 in the right province. Add the inflation penalty and it becomes 66*1200M/(1200M+n) or 72*1200M/(1200M+n)
SO... say a manufactory costs n ducats. Minting coin to build a manufactory in the wrong province will produce a net profit when,
66*1200M > n(12M + Y)
and replace the 66 with a 72 for the right province. Now, let k be the fraction of your income that comes from annual (census) taxes. Multiplying out and grouping terms as best I can gives:
6600/n > 1/(1-k) for the wrong province, and
7200/n > 1/(1-k) for the right province.
The yearly profit a manufactory will give you is:
(??*1200M - (12Mn/(1-k)))/(1200M+n)
(Where ?? is 66 or 72 depending on manufatory location). Which means you will break even from building the manufactory in:
n*(1200+(n/M))/(??*1200 - 12n/(1-k)) years
Example: If we say that 20% of your taxes come from census taxes, then minting coin to build a manufactory on the right province is profitable as long as the manufactory costs less than 5760. If you're talking about the wrong province, the break-even point is 5280. So unless you have something better to be doing with that money, making a manufactory is nearly always worth it.
For any reasonably large monthly income, a manufactory built in the right province for 1000 ducats will pay itself back in 20 years or so, after adjusting for inflation.
A few comments on this analysis:
In terms of eventual profitability, only the percentage of your income that comes from yearly census taxes matters. Your actual income is irrelevant. This is a fairly counter-intuitive result. The bottom line here is that if your income is very small, you will incur huge inflation to build the manufactory, but the manufactory income will be massive compared to the rest of your income.
In practice, since it takes a long time to pay back the manufactory income, you shouldn't mint coin to put in the manufactory until you have enough income to do it quickly.
This analysis ignores the peripheral benefits of manufactories. The 1% efficiency bonuses of refineries and goods manufactories make them extrodinarily profitable for large empires. And there are numerous other benefits (manpower, population, revoltrisk) that can't be easily quantified, but should be considered.
FINALLY: note the following dirty little inequality:
??/1.15 > 10.4M/(1-k)
That's the profitability inequality for going bankrupt to build a (1000 ducat) manufactory. The breakeven monthly income (for 20% census taxes) to build a wrong-province manufactory is 4.5 or so. So unless you're poor AND devoid of expansion opportunities, you probably shouldn't go bankrupt to build a manufactory.
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