[Mkguild] A question of money exchange

[Alex Green]

This is an interesting problem, and as such, I have spent more time than I
probably should have thinking about it.

The first issue is the manufacture of the links.  At first glance, it seems
like it would be difficult to come up with a way to quickly and accurately
mass produce enough of these links to be useful for currency.  However,
after thinking about this for a while, I came up with a relatively simple
solution.  The pure metals in their proper proportions would be melted down
and mixed together to form an alloyed metal.  This metal would then be
drawn into a wire of the right thickness.  It would be rough cut to length
and then trimmed down till the weight matches that of a standard link of
that alloy.  It would then be formed into a the shape of a link and
soldered shut around previous lengths to make a chain.  The excess
trimmings would be melted down into the next batch of the same alloy.

So now that we know how these links are going to be manufactured, we need
to figure out what proportions of metal to make the alloys out of to ensure
the links have the right value.  As Chris and Charles have already stated,
that's best determined by weight, and here in lies the next problem; you've
specified these links by their spatial dimensions giving us links of
constant volume, not weight.  Fortunately, a ring like what you've
specified is a torus, and it's rather trivial to find the volume of a
torus.  Simple that is provided you know calculus, which I'm assuming the
people in the universe Metamor do not.  I'm just going to assume through
trial and error or coincidence that they came up with a standard size of
link that matches the dimensions you've specified.  That leaves each link a
volume of 0.206 cubic inches.  Now we can relate the volume of the links to
the weight of precious metals given the densities of the metals.  The
following are the densities of the possible component metals given in troy
ounce per cubic inch.

Gold 10.2 t.oz/in^3
Silver 5.527 t.oz/in^3
Copper 4.721 t.oz/in^3
Tin 3.851 t.oz/in^3

Now we still need to know the relative cost of each metal so we can
determine the composition of each link, and we also need the composition of
each Metamorian coin to figure out the exchange rate.  Fortunately, the
Wiki has a table <http://mkworld.wikidot.com/writers-guidelines#toc12> that
specifies the weight and composition of each Metamorian coin and its
approximate buying power in US dollars.  Unfortunately, that table is very,
very wrong.  First off, the approximate buying power of the Copper Penny,
the Silver, and the Bronze Crescent don't line up with the previously
stated definitions of their value.  The correct value for buying power
should be $0.60, $3.00, and $6.00 respectively.  With those fixed we can
now solve for the approximate value of the metals in US dollars per troy
ounce (I'm assuming troy ounce because that's the proper US customary unit
for precious metals).  Now we run into another much bigger problem.  The
values start off reasonably enough.  Gold is worth $585.66 per troy oz.
Silver is worth $37.82 per troy oz. Then we get to copper.  In order to
make the values given in the chart work, Copper must have a value of
-$40.43 per troy oz.  That's right; copper has a negative value, a very
large negative value, as in, if you ended up with an ounce of copper in
your possession, just by throwing it away you gain more value than if you
picked up an ounce of silver.  This is clearly an enormous problem.

I'm currently trying to figure out a way to rectify this.  It would be best
to define the relative values of each metal first and then derive coin
composition from there.  Historically, from the 15th to the 19th century
the ratio of the price of silver to gold was fairly constant at 15:1.  That
closely matches the ratio derived from the table so that's a good place to
start.  The value of copper has fluctuated a lot throughout history mostly
based on its utility.  The ratio of the value of copper to silver has
fluctuated wildly being any where from 10:1 to 350:1.  Currently it is
about 120:1.  Around the middle ages it was about 300:1.  However, the
value of silver compared to gold has dropped significantly since then so
that ratio makes more sense.  If we assume the approximate buying power of
gold has stayed constant a 300:1 ratio of copper to silver and a 15:1 ratio
of silver to gold gives us a ratio of copper to gold of 4500:1.  compared
to the current ratio of 5344:1, this makes copper worth a little bit more
in Metamor than it is today.  The value of tin would be closely related to
copper thanks to it's primary use in the making of bronze.  Let's give in a
ratio of 2700:1 which makes tin worth about half of what it is now.

If we continue to assume that gold has an approximate buying power in
Metamor similar to what it does on modern day Earth we can give dollar
values to precious metals in Metamor and use the approximate buying power
of Metamor coins to determine their composition.  Gold is about $1350/t
oz., so that leaves us with the following prices for Metamorian metals:

Gold $1350/t oz
Silver $90/t oz
Copper $0.30/t oz
Tin $0.50/t oz

Now we have enough information to work out the composition of our various
currency; however I'm too busy at the moment to do that right now, so I'll
try to work those out and post them later tonight.
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