Let’s say we want to build a small playing area in a fantasy/medieval setting.  We have some basic assumptions we want to start with, based on the preceding sections:

• The society is of a typical pre-industrial early steel type, relying on labor for cultivation
• The society uses horses for draft, transport and war
• Humans are a powerful minority, and are under constant threat of raids by humanoids
• There is relative equality between the sexes, and women can perform traditionally male roles
• Magic is a known technology, but not earth-shakingly powerful or common

From these basic axioms, we can make some immediate assumptions about the society.  They subsist largely on wheat or something like wheat, to encourage the domestication and use of horses.  However, they need to have had sufficient leisure time to develop magic, and don’t have a huge population to contribute to this, so their food gathering has to be more efficient than the historical norm.  Food production is also assisted by the fact that peasant women work the fields alongside the men.  Because they are under constant threat of incursion from humanoids, it behooves them to keep their zone of control as small as they can, reducing the availability of farmland, and requiring even more efficient food technology.

This leads us to some other conclusions:

• The primary crop of the society is a strain of efficient wheat that requires less acreage per bushel of yield
• Magic probably started as a means of increasing food production, and is therefore somewhat systemized so the harvest doesn’t hinge on whether or not an appropriate wild talent happens to manifest itself in an "inborn" mage
• The more equitable division of labor between men and women means that hedge magic is also used to assist in childbirth and growing to adulthood without mishap, stabilizing the population without dedicating all available women to reproduction
• Because of the importance of hedge magic to prevent starvation and promote safe childbirth, and the rarity of mages, magic users are particularly important, and therefore socially well-off
• Since food yields are more efficient, the leisure time of the population is increased, allowing for enough "surplus" people to research things like magic
• The excess population allotment also contributes to a larger standing army, a better military tradition, and the possibility of freelance adventurers (i.e. the player characters)
• Because of the large military and the importance of iron in warfare, even if iron is readily available to pre-water pump mining techniques, most of it will be going into military applications
• The use of horses as a military tool, combined with a strong military tradition, means that the primary weapon of infantry would be the spear in formation, and possibly the pike if lances and/or heavy horse are used heavily
• Assuming the humanoids are prototypical bronzeworking hunter/gatherer types with a high breeding rate and a rapacious need for foraging, the amount of "civilized" land needs to be considerably less than the "wilderness."

Now let’s make up some numbers that apply to our superwheat and farming techniques.  Assume that the intervention of the agro-mages eliminates the need for a field rotation system, so all farmland is being planted on for every harvest.  This is an increase of 50% yield as compared to a 3-field system.  Now assume that superwheat is exceptionally hardy and high in grain yield, say yielding 9 bushels per acre per harvest as opposed to normal wheat, which yields 8 bushels.  This is a cumulative 12.5% increase.  Therefore, our square mile of superwheat agriculture will have an annual yield 170% as great as a standard wheat field.  It may take extra people to harvest this much grain, so let’s say the field requires about 140% the manpower of a standard wheat field.  Furthermore, because the field is being worked by women, the amount of grain required to feed non-producing dependent peasants is reduced as well, say from 3 dependents per farmer to 2.  This can get complex, so to simplify the issue we just fudge and say the increased working peasant population translates into a surplus bonus of 5%, taking into account the fact that women will still be taking time off to bear children, and the increased need for food (and availability of it in the field) while they are pregnant.

Thus, one square mile of superwheat requires about 90 peasant farmers, who produce a staggering 27% surplus, or enough to support roughly 24 nonfarmers.  This is a fantastic advantage, almost on the level of corn production, but it allows for advanced horse domestication.

So now let’s figure out how many of these nonfarmers we will need to establish all the trades and practices we want.  We can fudge the mundane professions a bit (merchant, village blacksmith, farrier, etc.), but we want to have a reasonable figure that allows for the study of a systemized magical practice, which is crucial for food production.  Let’s assume that our system is aimed at a mage percentage of player character adventurers of about 10%.  The percentage of mages in the overall PC/NPC population of non-peasants will be considerably smaller.  If the standing army and levies combines comprises 10% of your total population, and you figure mages on the whole are about 1/4 as likely to show up in the overall population as they do as player characters, then your total number of mages is about 1/4 of 1% of your populace.  Figure that you need roughly 5 NPC mages as instructors who maintain the tradition, and about 20 NPC working student-mages who travel around performing civic duties such as lie detection, criminal tracking, healing, and most importantly crop control.  With a base figure of only 25 mages, your overall working population must therefore be no less than 10,000.  Increase this to about 12,000 to allow for the large number of adventurers that will be running around, and multiply the peasants by 3 to reflect dependents.  This is a very large city-state for this level of technology, but thanks to superwheat, it only requires about 110 square miles of arable farmland.  This would be a circle of nothing but farmland in a radius of 6 miles from the capitol, but figure that you need a certain amount of living, industrial, grazing, and forested space… the holdings could more logically be said to extend for up to about 10 miles from the city center, with markets placed in strategic areas to facilitate food distribution and trade.  The extra people who are freed from farming can increase the size of the dedicated standing army, but more people will want to use their leisure time for other pursuits, so let’s say the army comprises about 30% of the nonfarmer populace.

So now we know the following about the makeup of our theoretical fantasy kingdom:

• Population 31,800
• Working peasant population 9900
• Nonworking peasant population 19800
• Non-peasant population 2100
• Average distance from border to border approx. 20 miles
• NPC mages about 25
• Standing army 630
• Possible levies 700

This is a manageable area for the army and militia to cover and defend, assuming all your enemies and rival city-states follow these rules.  However, the numbers still seem pretty small to the 20th-century mind.  If you feel the need to get ridiculous with your population assessments, allow the agricultural mages to double the food yield with magical soil refreshment, allowing for two harvests per year.  Figure this increases the required workers per acre by about 50% due to the additional toil, and keep the size of the holding the same (110 square miles of farmland).  One square mile of superwheat now requires 135 peasants, with an amazing 62% surplus.  The massive number of non-peasants will primarily want to better their lot through mercantilism, study, or government (and extra government is most certainly required with this population density), so figure 20% of nonfarmers are enlisted in the standing army.  We now extrapolate the following figures:

• Population 53,700
• Working peasant population 14,850
• Nonworking peasant population 29,700
• Non-peasant population 9150
• Average distance from border to border approx. 20 miles
• NPC mages about 50
• Standing army 1830
• Possible levies 1040

This seems about right for our high fantasy setting, and we only had to use a minimum of black box assumptions to get there.  However, our population density is now up to about 170 per square mile on average.  Middle ages England had a counted population of only 30 per square mile, but early census takers did not count dependents, i.e. a farming family of 4 with one working farmer counted as one person.  Still, 170 per square mile is considerably high for this level of civil engineering, and the area of greatest density (the capitol city) is going to be ridden with pestilence.  Black boxes in the form of clerical healings and disease control can help control the sense of filth that a good and accurate middle ages city should convey, but don’t go crazy.  Disease was an important form of population control, and should not be ignored in the background of your campaign world.