The first thing to notice about faucet/drain economies is that there are actually three things going on in them. There's wealth (in the two forms of items and money) that enters the game through the "faucet" of mission payouts and currency loot drops; there's wealth exiting the economy through the "drain" (item destruction and things like taxes and service fees); and there's wealth circulating in the game among players (people exchanging money and items).
What's important to see here is that only the faucet and drain matter when considering whether inflation is occurring inside the game world. Money and goods circulating among players do not contribute to inflation -- in fact, the more of this that happens, the better for everyone in the game it is.
To understand how the faucets and drains determine inflation, we first need to agree on what "inflation" really is. According to economists, inflation is the condition that occurs when the price of a broad array of standard goods rises over time relative to the perceived usefulness of those goods. Note that term "broad array" -- it means you can't just look at the price of swords only, or at the prices of very rare items, to know whether inflation is occurring. You have to consider the average price of several different kinds of readily available goods. If that average price goes up meaningfully over an extended period of time, then you've got inflation, but not otherwise.
And just to make life more entertaining, there's not just one kind of inflation -- there are at least three.
Standard inflation is the kind most of us think of; this is where a bunch of money enters an economy while the number and quality of goods produced remain relatively constant. In standard inflation, the value of an individual unit of currency decreases over time for most available goods. If 10 dollars today is worth half of what it was yesterday, then an item whose absolute value was generally agreed to be 100 dollars yesterday will cost you 200 dollars today.
Demand-pull inflation is the next type. Suppose you have a fixed amount of money circulating in your economy. Now, slowly cut back on the kinds and numbers of goods being created in that economy, or add a lot of new people to the economy without also increasing production. Over time, prices will generally increase as people consider goods to be worth more (i.e., as demand increases because supply is not keeping up with purchasing power). As prices rise for the same goods over time, an individual unit of currency is worth less and less... and that's demand-pull inflation. (This is something that can happen in a MMOG if crafters are widely supplanted by loot drops for high-end objects, or if you irritate your crafters so thoroughly that they quit your game and aren't replaced by new crafters.)
Finally, cost-push inflation is what you get when the costs to produce goods rise generally. This kind of price increase is usually caused by things like increased wage costs (as through "minimum wage" increases or hikes in corporate taxation) that are passed on to consumers. In games that don't support corporations or that don't have corporate taxes applied by the system, this type of inflation generally doesn't happen. But it can happen if crafting requires natural resources, and the developers cut back sharply on the amount or quality of those resources.
The most common type of inflation in MMOGs is standard inflation. It shows up when the amount of money being created in the game by players (doing whatever the game allows them to do to make money -- usually running quests) exceeds the amount of money exiting the economy in the form of taxes and fees. This can happen if taxes and fees aren't set high enough to match the amount of money players are creating.
This can also happen when there's a currency dupe exploit. If when these happen they aren't corrected by changing the code (to stop the exploit) and removing the money very quickly (so that innocent players don't exchange valuable goods for "dirty" money), a game economy can inflate badly, possibly to the point of ruining the game. So tools for tracking the creation, circulation, and destruction of money in the economy are crucial.
Finally, not every MMOG winds up dealing with inflation. Another potential problem for MMOG economies is deflation (sometimes called "mudflation"). This occurs when valuable objects enter the game world and never leave while the money supply remains relatively constant.
Mudflation tends to happen in particular as developers create high-level content. If powerful items can be obtained more than once and/or can be transferred to other players, then over time the price of low-level or average items of the same type will decline as more of the high-end items enter the general economy and trickle down to younger characters.
Note that a major secondary effect of mudflation is to make many quests and mobs irrelevant. When everyone can afford to buy very good items, there's no need to loot mobs or do quests that yield less valuable items. For a developer, this decreases the value of time spent developing low- to mid-level quest and mob content because now users are able to complete this content more easily than expected.
Various efforts have been made to combat mudflation. The concept of "soulbinding" -- setting the "no-drop" and "no-trade" flags on items -- is only partly to counter twinking; its primary purpose is to prevent valuable items from entering the general economy. Decay and damage effects also help reduce mudflation, though not as effectively as soulbinding.
The main reason that both inflation and deflation are bad news for a MMOG is because they alter the difficulty balance of the game, especially for new players. Because new players have less money than established players, the value of their money is significantly greater. So if new players are unable to buy standard items because of inflation, the starting game will feel too hard. If they are able to buy more items and more powerful items than the designers intended for them to be able to own (due to deflation), their starting gameplay experience can be too easy.
In both cases, these first impressions of a game can be the difference between a long-term subscriber and someone who goes elsewhere to find a game that isn't too easy or too hard.
Designing systems to effectively monitor and manage the economy is non-optional for a large gameworld.