"Usually they draw it as a slightly bowed line on a Cartesian coordinate system, with S and D as the axes. You've seen it before. I have another question for these supposedly mathematically rigorous Economists. If the grid has supply on one axis and demand on the other, and the little curve is supposedly a line representing the function which is the relation between supply and demand, then how the @#!* does that chart tell us something about price? PRICE ISN'T ON THE AXES! It's not PART OF THE GRAPH AT ALL!"
Wait, am I the only one that has looked at an S/D graph today? S and D are not labels for the axes. They are the actual curves on the graph. The axes are labeled with P (Price) and Q (Quantity). At equilibrium, S and D should intersect at a given P/Q relationship to give you the market quanity supplied and the market price. This may be one of your fundamental errors. This may be the trouble you are having interpreting the graph.
Yes, I've seen those supply-demand graphs, too. You make an important point. But my misgiving still addresses them -- if the axes are Price and Quantity, then we still don't know jack sh*t about Supply or Demand, except as implied by Quantity (which, itself, could have relationship to S and D by inverse, direct, or any other relation).
We need a picture or two ...
Despite being a person about to finish up his Econ degree, I'm having a real hard time understanding what you're talking about, but I'll take a stab at it. Supply and Demand are not some quantifiable numbers, they are functions, relationships between quantity and price. At price P, suppliers supply quantity Q. At price P, demanders buy quantity Q. At competitive equilibrium, suppliers and demanders can agree on a quantity and price.
DON'T CONFUSE QUANTITY AND SUPPLY. They are two very different things. For example, if quantity supplied goes up and price goes up, then demand increased, supply need not even have changed.
As for your complaint about the fundamental principles of Microeconomics not working in practice, it all depends on how complicated you want the model to get. If supply goes up and price goes up, something else was going on to make it so---everything else was NOT equal, end of discussion. There are so many interrelationships and externalities that the Supply and Demand model they teach in Introduction to Microeconomics is not going to get you the whole picture, but it gets the basic concepts across. In reality, while you can take more and more pieces of the puzzle into consideration, nothing can be perfectly modeled, there are just too many factors to consider, but the underlying concepts are nonetheless valid.
For example, Econ 101 almost always assumes perfect competition, no transaction costs, no barriers to entry, etc. – does this ever happen in reality? No, Econ 101 models a fantasy world. But the basic principles are the same, and in many situations the assumptions are immaterial enough that the model is a good approximation for reality.
They’re not lying to you, they just start out with an easy fantasy world so your head doesn’t explode, and then reduce away the assumptions until you come closer to reality.
By the way, I’ve never seen Supply and Demand as axes, as this would make zero sense whatsoever, are you sure you’re interpreting the graphs right?