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My goal is to try to make a population size algorithm. What I learned is that a simple equation can do that (I have to look it up to give you it) year by year. One of the variables in that equation is Fertility Rate and that's where the problem is.

There are 3 things that determine Fertility rate:
1. Children Survival rate
2. GDP per Capita
3. How Developed the Area is which breaks down into:

  • Health
  • Education
  • Living standards

The first is easy to figure the things that affect that.
The third is likewise pretty easy to figure out, and I'm pretty sure there is a site that states it for the research...

So that leaves GDP... In the modern world we can just measure through jobs, but in the past, I'm completely stymied (First time I've ever gotten to use that word ^.^) I have no clue how to go about determining GDP for Hunter-Gatherer, Nomadic, bronze-age, medieval age civilizations... I mean, what qualifies as GDP and how do you determine it? Should farmland for yourself/family be considered part of GDP? Should a buffalo that you hunted and are eating that day be considered?

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    $\begingroup$ Fertility rate is the number of live births per woman (or, more usually, number of live births for 100,000 women) of reproductive age. Nothing to do with children survival rate, which, together with fertility rate, is a factor in calculating the rate of natural population increase. The link between fertility rate and GDP per capita is not straighforward and most likely not applicable at all before the 19th century. $\endgroup$ – AlexP Jan 20 '17 at 6:02
  • $\begingroup$ You missing what I'm saying... Fertility Rate is what you say, but the things I'm talking about a been shown to effect Fertility rate and that is what I'm looking for... Also, I know this might have very low overall effect, but still it's nice to have the variance. $\endgroup$ – Durakken Jan 20 '17 at 6:24
  • $\begingroup$ "Have been show to affect" does not mean that we can compute fertility rate from those inputs. $\endgroup$ – AlexP Jan 20 '17 at 6:30
  • $\begingroup$ @AlexP Yes and no... It actually means that there are correlations between the 4 numbers. The numbers correlate with each and you should get roughly the same answer using each of them. Using 3 to come up with the 4th is just a way to create variances in that 4th number rather than they numbers are exactly equivalent. $\endgroup$ – Durakken Jan 20 '17 at 6:35
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You need an index. A good index is something that is a substitute good, so that it can be compared. In modern world it is cash, because you can exchange it to anything. In your case it could be salt, bone, fur, tools... GDP answers to a question: "If you would exchange all of your goods produced, during a time interval, to the index for a current market price, how much would you get?"

GDP is a measure of productivity. A higher GDP means ability to produce more or higher quality goods. It's an abstraction for modern world, in your case GDP may not make sense, because the food has a great value already for a survival. GDP would fluctuate a lot. Maybe carrying capacity https://en.wikipedia.org/wiki/Carrying_capacity might make more sense.

EDIT: An example:

Population consumes 90 buffalos per year for food
Index is salt

Year 1:
100 buffalos hunted
after consumption 10 buffalo meat to sell
=> willing to sell for some amount of salt, because the meat would anyway rot
market value of a buffalo meat 1kg salt
GDP = 100kg of salt

Year 2:
80 buffalos hunted
for consumption 10 buffalo meat to buy 
<= willing to use infinite amount of salt to not starve
market value of a buffalo meat 10kg salt
GDP = 800kg of salt

Less buffalos hunted, but they are much more valuable on second year, leads to 8 times higher GDP. On first year there was a surplus, but on a second because of the deficit the GDP is higher. GDP does not reflect what you are looking for.

EDIT 2: https://en.wikipedia.org/wiki/Purchasing_power_parity That may help in a way. It would lead to right valuation in the example, but there is still the problem that it would remove the value of other goods. The main point is that survival leverages the value of goods disproportionately.

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There is a floor of private consumption of sufficient low quality food to prevent starvation, and minimal clothing and shelter for the environment (the less hostile the environment is the lower this threshold is since clothing and shelter are less necessary and easily available food and water may require little work to produce). This is going to be true for every society no matter how it goes about securing these things. From there, think about long lasting tangible personal property and structures and food reserves.

Another way to think about it is to look at what percentage of the population is engaged in food production. In the poorest society, 100% of the labor force spends all of its time feeding itself with no resources to support anyone doing anything else. (Within those societies, the percentage of the population in the food producing labor force as opposed to caring for and being children and dependents, and the number of calories per person per day can be good proxies for per capita GDP.)

As of 1800, in the United States, 1,405,000 people out of a labor force of 1,900,000 were engaged in direct food production. So, the standard of living that could be supported was about 35% higher than one in which everyone was engaged in direct food production.

Right now, about 2% of the labor force of the United States is engaged in food production, while the other 98% of the labor force is free to do other things, so the standard of living that can be supported is about 5000% higher than one in which everyone is engaged in food production.

The percentage of people engaged in direct food production has declined almost every single decade from 1800 to the present.

This isn't a perfect measure (e.g. it doesn't distinguish between different levels of productivity of non-agricultural workers), but it is a good starting benchmark that can be estimated from information that isn't completely impossible to obtain, and can be used as a staring point. Figure out how many people who rulers, scribes, entertainers, priests, soldiers, craftsmen, bankers, traders, etc. and use those estimates to figure out what percentage of the population was engaged in direct food production. Then convert that to a percentage and multiply by a base number for minimum subsistence.

For much of early history, society was largely Malthusian. Per capita GDP was kept fairly constant and any excess resources were used to increase population until the theoretical floor of private consumption was reached.

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Should farmland for yourself/family be considered part of GDP?

No, GDP is Gross Domestic Production. Land is wealth, not production. Plowing the land or planting crops would be part of GDP. The land itself is not. You could calculate Owners' Equivalent Rent and include it that way. But it might be simpler just to neglect land altogether.

Should a buffalo that you hunted and are eating that day be considered?

Yes, although it usually isn't in current statistics.

The larger problem is that GDP statistics are meaningless without accurate prices. But if there are no transactions because everyone consumes only what they produce, there are no meaningful prices.

I would consider using a GDP value of zero and seeing what happens. Presumably you're also going to be using low values for health, education, and living standards.

I'm not sure that GDP is the best measure to use with a hunter gatherer society. Fertility is more likely to be affected by more direct measures like quantity and regularity of food. The formula most likely uses GDP as a proxy for that and other measures.

The primary reason to use GDP modernly is that it is commonly calculated. But in your societies, it wouldn't be. It might be easier to find a different formula than to approximate a GDP value.

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Well, google says that the following equation is used to calculate the GDP:

GDP = C + I + G + (X - M)

or

GDP = private consumption + gross investment + government investment + government spending + (exports - imports).

this can be simplified at times depending on what you are going for, for example, if you want to calculate for hunter-gatherers decide on a monetary value for things like meat, furs, wood, tools, etc etc.

Then, selecting a number for the starting population, calculate what they would use themselves (say one family uses 80% of what they gather and hunt, add the two values and multiply by .8), what they would use for the community (the .2 not used by the families) government investment might, in this case, relate to trades with other tribes(exports-imports) as well as what tribe leaders might give to families in need etc, etc, and then because of the more simplistic government they might have, assign government spending a value of 0.

So starting out this is going to be hard for you because you have to select how many people there are and then calculate families, average income per family based on the values to materials you assigned and so on, but if you keep this information after you calculate it, it's scalable and you can reuse it.

So I hope this helped :) Good luck.

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  • $\begingroup$ I know this... My issues is in figuring out how to get the numbers for C + I + G + (X - M). I'm so lost with regard to that ^.^ $\endgroup$ – Durakken Jan 20 '17 at 6:26
  • $\begingroup$ @Durakken don't forget to include the sex industry in the "private consumption" term. Ooops, without contraceptives, this is a factor that's going to mess up not only the GDP, but also the number of born children. $\endgroup$ – Adrian Colomitchi Jan 20 '17 at 8:18

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