Why do economists break the standard math rules regarding the placement of independent and dependent variables?
First, I'm not sure they do. In microeconomics, changes in production capacity shift the supply curve and changes in tastes shift the demand curve. These are effectively quantity changes that subsequently affect prices. This makes quantity the independent variable and price the dependent variable. From this perspective, price should be on the vertical axis. If you insist that price determines quantity, but not the other way around, then you obviously don't understand the effect of weather on agricultural output.
Second, my guess is that economists measure so much stuff in terms of price, that it is convenient to always have price on the same axis. Would you really prefer price on the horizontal axis like this?
Price appears on lots of economics graphs. By always putting price on the vertical axis, economists don't have to repeatedly swap which axis is the price axis from one graph to another.
Update: I decided to ask "The Google." In an old post, here's what Harvard's Greg Mankiw had to say on the issue:
On the axis question: The instructor is right that, given the way we now teach supply and demand, it makes more sense to have price on the horizontal axis. The price is viewed as the variable that determines quantity supplied and quantity demanded, and we usually put the dependent variable (which here is quantity) on the vertical axis.In the same post, Mankiw also adds the input of Robert Barro:
So why is it switched? Here is a guess. The early economists may have been imagining that, in the very short run, a given quantity of goods was supplied to the market (an agricultural harvest, for example). The supply curve is then vertical, and the price adjusts to ensure that quantity demanded equals this exogenous quantity supplied. So, in this very short run, the price seems more like the dependent variable. Now, however, the choice of axes is based more on historical convention than logic.
I am not an historian of economic thought, so these answers may be off base.
As I recall, Hicks in Value and Capital thought in terms of demand price and supply price. The demand price is how much a person was willing to pay for an additional unit of goods (starting from some initial quantity, Q). The supply price is how much a producer would have to be paid to provide an additional unit of goods. This construction—which I think comes from Marshall—makes it natural to have P on the vertical axis and Q on the horizontal.And finally, Wikipedia points me to this from An Introduction to Positive Economics, 7th ed. by Richard G. Lipsey:
Readers trained in other disciplines often wonder why economists plot demand curves with price on the vertical axis. The normal convention is to put the independent variable on the X axis and the dependent variable on the Y axis. This convention calls for price to be plotted on the horizontal axis and quantity on the vertical axis.
The axis reversal — now enshrined by nearly a century of usage — arose as follows. The analysis of the competitive market that we use today stems from Leon Walras, in whose theory quantity was the dependent variable. Graphical analysis in economics, however, was popularized by Alfred Marshall, in whose theory price was the dependent variable. Economists continue to use Walras' theory and Marshall's graphical representation and thus draw the diagram with the independent and dependent variables reversed — to the everlasting confusion of readers trained in other disciplines. In virtually every other graph in economics the axes are labelled conventionally, with the dependent variable on the vertical axis.