Trade Equations

I have, potentially, my first game on Monday.  It's at a local gaming store, but since it's during the weekday, it should be relatively quiet.  Because of this, I have been frantically working at the trade tables to get them into a useable state - it also keeps me distracted from the schoolwork that needs to be done this weekend as well.

I was completing the second step in the process, aggregating all of my world's references into thematic groups with some rudimentary determination of goods that require no processing, when I ran into two problems.

Before I get into this, if you are not familiar with Alexis' trade tables, I suggest you fix that - the following discussion will make no sense if you don't.

The first problem was with the valuation of gold.  This is the first calculation on the sheet, and it's important because it determines the price, in copper pieces, of 1 reference's worth of goods.  For the sake of simplicity, I am calling that quantity a crop.  Right now, a resource's crop size is determined by dividing the global production of that resource by all of the references for it (on a global scale).

It struck me as a little odd that the gold crop had no direct bearing on the local value of gold.  Then I started digging a little further and it appeared that the price of gold would only fluctuate based upon .002*local/global, where local is the number of local references of gold and global is the total number of gold references.  This seemed strange to me, but I continued forward.

What convinced me that this was a problem, though, was the double-conversion to coinage seen whenever the price of a good was to be generated.  The formula for an arbitrary good looked something like this,

Where refVal is the value in copper pieces of 1 reference, calculated as above and production is the global quantity of a good produced.

This simplifies to

Which means that the local amount of a reference has no significant bearing upon its price.  Additionally, since refVal has already converted from oz. gold to copper coins, the additional coin conversion at the end of the equation is extraneous.

Which means that I needed a new way to value gold and a new way to assign a coin value to 1 unit of a resource.  I called in my roommate and we spent half the night yesterday/this morning fighting through this to find a solution.  And find one we did.

The challenge of this problem is that there are so few actual variables that depend upon location - every meaningful combination of them resulted in their cancellation, which defeated the purpose of the proposed improvement.  We eventually hit upon the idea of incorporating a new variable: the power of the market in question, determined by the sum of all the local references (i.e. all the references in the world altered by their distance from the market in question).  With this in hand, we returned to the problem.

For gold, we have

I'll walk you through this equation.  The product/global term gives us the crop size - how many units of a good are worth 1 reference.  We then multiply our crop size by the power of our market which tells us how many oz. of gold our economy is worth (since 1 reference is equal in value to any other reference, we have product/global*power value in our system as a whole).  We divide this number by how many references of gold we actually possess, local, and this gives us a ratio of the total value of our system in gold by how many references for gold we actually have.  We convert this to copper coins and are done.

Now to tackle valuing goods.  Working this morning, I constructed the following expression:

The first term calculates the value of the goods on hand in copper pieces.  The second term scales that price by how powerful our market is and how abundant the resource is - a resource with fewer references will have a higher price than one with many, and a more powerful market (drawing more things from more places) will command lower prices overall.

Alexis' explanations of his own steps are as good, if not better than mine.  But the units of all of these expressions work out, and now each good's price is influenced by the market's power and the global and local reference values, increasing site-specific prices.

Of course, due to the probabilistic process through which I generated my references, I may have some correcting to do (I needed to add a bunch of iron references, for example), and that may necessitate either adding more references or modifying the production totals in order for the economy to work in the way that I need, but I am much happier with these expressions.

Also, as a side note, VLOOKUP is a godsend in this work.  No more hunting for appropriate references!