I've been working on my algorithms to generate
trade networks and manufactured goods. Although probably several years out of date now,
Tao's Trade System
remains required reading for anyone wanting to do something similar.
This iteration was a muchneeded rework of the way a lot of the prices were
generated. I had gone through Alexis' work linked above and simplified it to
my needs. He is using references based in the real world, whereas I am trying
to generate from scratch.
I found that of all the equations, the final price of an object simplified to
just a few variables. The first is the local value of a unit (oz) of gold (in
cp, all prices are expressed in cp and can then be abstracted back up to sp or
gp as needed). I'll call this $g$. To find this number, we need the local
availability $g_\ell$ and the total availability $g_t$. $g_t$ is the total
number of references reachable from the point in question. This is easy to do
with network algorithms. Local availability is a weighted distance calculation
over all locations $i$ reachable from $\ell$: \[g_\ell = \sum_i
\frac{g_i}{\textrm{dist}\left(\ell, i\right) + 1}\] By this calculation, if
$i$ has 2 gold references, but is 4 days away, it contributes $\frac{2}{4+1} =
0.4$ references to $g_\ell$.
Right now, I am treating each hex as a node in the graph, but if there is no
defined settlement there, all its resources are given to the closest city hex
for pricing purposes.
We need a rarity factor $r$ that scales with the size of the network. As the
network grows larger, a smaller $r$ is needed to balance things out. I'm
trying this out for now: \[r = \frac{1}{n}\] where $n$ is the number of nodes
in the network.
The last two constants are the number of gold pieces per oz ($p =
\frac{1\textrm{ gp}}{0.48\textrm{ oz}}$) and ratio of cp to gp ($c =
\frac{100}{1}$). These are easy to change. A halfounce gold piece is somewhat
hefty; many coins in history would have been much smaller amounts. Gold is
valuable enough that a small bit is worth a lot, and hence a great deal of
value can be expressed in quite tiny coins. I like the idea of a gp being a
weightier coin. I also try to base the sizes of my coins on current analogs
that I can actually show to my players.

A thousand of these is no joke

So the final equation comes together: \[g = \left(r \cdot \frac{g_t}{g_\ell} +
1\right) \cdot p \cdot c \]
For an individual resource $q$, the equation is similar. First, we have to
define the base cost $b$ of a unit of $q$. I found that this was the most
important factor; it essentially represents the ideal economy where everything
is in perfect supply. Whether a boardfoot of wood is defined as 1 cp or 18 cp
will have approximately a 18x effect on the final price of wood no matter
where you are in the world. This becomes the key object of research
when sketching out the system. It is then an easy matter to determine how many
units of $q$ are equivalent to one reference of gold (assuming a gold ref =
1500 oz): \[\mathit{ref}_q = \frac{b}{\mathit{ref}_g = 1500\textrm{ oz}}\]
We obtain the rarity $r_q$ in a similar way as above with gold, using the
distance weighted availability. The final price (in cp) of an item at location
$\ell$ is then: \[\$_q = \frac{g}{\mathit{ref}_q} \cdot \left(r \cdot
\frac{q_t}{q_\ell} + 1\right) \mathit{ref}_g\]
There are some other ways to view this equation. It can simplify again to: \[\$_q = \frac{g}{b} \cdot \left(r \cdot \frac{q_t}{q_\ell} + 1\right)\]
The next step is to determine the availability of labor references. I haven't
quite decided how to assign these so I'll save that for a future post. We
obtain the available references by once again iterating on the network:
\[L_\ell = \sum_i \frac{L_i}{\textrm{dist}\left(\ell, i\right) + 1}\]
The cost of a material $m$ at a given stage (eg, hematite $\to$ iron ore) is
then the cost of the raw materials (the unit cost $\$_m$ times the number of
units $n_m$) plus the labor cost, which is raw material cost divided by the
labor references: \[\$_m = \$_q \cdot n_m + \frac{\$_q \cdot
n_m}{\mathit{ref}_L}\]
This step is repeated for each stage of the process, which can be quite
complex. I developed a JSON schema to represent each manufactured material. To
raise an auroch from a calf to weaned, you require the following.
{
"item": "auroch (weaned)",
"unit": "hd",
"stage": 1,
"tech": 7,
"weight": 200,
"recipe": {
"materials": {
"auroch (calf)": 1,
"min": [
{
"maize": 483,
"oats": 483,
"barley": 483,
"cassava": 483,
"rice": 483,
"wheat": 483
}
]
},
"labor": "herdsman"
}
}
Our raw materials are 1 auroch calf + whichever is cheaper between 483 lbs
of feed, plus the labor of a herdsman. As long as every manufactured item "downstream" exists, this "item" will be available for purchase.