Given a collection of goods you can choose any one you like as money, and use that as a token of exchange. This is useful because it allows people to trade unequal-value lumps of "stuff" by making up the difference with money. To be suitable as money, a good should be finely divisible, durable, relatively useless, but valuable. At various historical times and places different goods have been used as money. We are most familiar with precious metals, but a very important example is salt as money (whence comes the word salary). There is a technical term for a good used as money and that is Numeraire. Whether some qualitative relation is independent of an arbitrary change of numeraire is an importan sanity check.

In a way it doesn't matter whether you have the gold standard or fiat money: there is still "differential inflation". What happens with fiat money is that it can be created at will, so in a way there is no tradeoff between it and other goods, and so it cannot be used to price other things. The only way you can make fiat money useful is by controlling the creation of money, and that's what the [central] banking system is about.

You may remember that I once cooked an example called "gold for soybeans" where I showed that, if you are sitting at a point of the Production Possibility Frontier of Gold and Soybeans, the slope of the normal direction is the relative price of the two, and the intercepts of the tangent line with the axes are the GDP expressed in units of gold or of soybeans. Assuming that the PPF is convex (mild assumption) you get that moving along the PPF will increase one of the GDP values but decrease the other. This fails the change-of-numeraire sanity check. But if you can move the PPF outwards you can increase the GDP regardless of which numeraire you're using.

Arrgh! I'm rambling again.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman