Monday, April 8, 2013

The Supply Side of Economics

If you can only handle Excel math, you might want to invest in big girl panties.

where G sub i is not equal to 0
First some notation. Lower case letters refer to local conditions and upper case refer to global conditions. So g is the local cost of a good and b is the good's base value (a fixed value). "g sub s" (lordy blogger hates math notation) would be the local supply coefficient and "g sub d" would be the local demand coefficient.

The first equation shows the general idea behind setting a price. The price is derived from the base value and then is decreased by higher supply and increased by higher demand. Nothing too ground breaking here.

Don't get too tripped up on the terms supply and demand and think this is modern economic theory here. You can instead think of "supply" as factors that reduce the price of a good and "demand" as factors that increases its price.

Supply is universally defined in the second equation. The supply coefficient is the product of a sequence of Global value of a good in a particular Center of Trade (COT) divided by the base value. This term is then taken to a root power of i + 2. i = 0 is defined as the COT in which the province resides. As i increments, it draws the COT value of neighboring COTs.

If you are still awake, we are basically saying that the supply decreases price in a root manner. So in order to drop the price in half, the supply would have to be 4 times the base value. To drop the price by one third, there would have to be a supply of 8 times the base value. And so on.

We do a product of a sequence so that farther COTs have a diminishing effect. Once you get one COT away, the sequence evaluates a cubic root. So to drop the price in half as a result of a distant COT, the trade value there would have to be 8 times the base value.

No chance you are still awake. But maybe a pretty picture will help. Here is a screenshot from EU3 illustrating a system of COTs.

Each colored region represents a COT and all the provinces that trade into it. Lets assume we are in Austria's COT Wien at "i = 0". COTs at "i = 1" include the Ottoman COT in Thrace, the Venetian COT in Venice, the north German COT in Hamburg, and the Polish COT in Danzig. "i = 2" COTs would be located in France, Genoa, Moscow, etc. So the supply of goods flows in from around the world, having a smaller impact as the distance traveled increases.

Nifty part is that the COTs in colonial powers such as Spain include their territories in the New World so colonial goods are also factored in.

That's it for considering supply for now. Go wipe up the drool from your keyboard. Tackling "demand" will be much more daunting.

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