Thursday, February 10, 2011

Why do economists put price on the vertical axis?

I see over on Paul Krugman's blog that several readers are complaining about the drawing of supply and demand curves. According to them, it is wrong to put price on the vertical axis and quantity on the horizontal axis, as economists typically do:

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.

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.
In the same post, Mankiw also adds the input of Robert Barro:
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.


  1. Yes, quantity determines price. Those leftists who want to deny that quantity determines price are presumably implying that all-powerful corporate entities can dictate price with impunity (witness how Bush-Cheney-Haliburton-Big Oil was blamed for rising gas prices). Their perverted conspiracy theory of powerful "big business" fits directly with their denial of market equilibrium and their demonization of those who produce and sell in order to provide us with a higher standard of living.

  2. What a jerky reply.  That's not helpful at all.  I don't know what you do all day that makes you have leftists on the mind, but the convention for placement of dependent variable on the vertical axis is absolutely standard for scientists.

  3. price is not deliberately changed in the real world. changes in demand and/or supply determine changes in price. sellers resist raising prices until it is no longer possible to continue to absorb higher costs. the myth of prices being "deliberately changed" is part of the anti-capitalist propaganda that is used by the intellectuals to attack the producers.

  4. Fundamental physical properties include distance, time and mass.  Volume is distance cubed.  Quantity of something is essentially mass or volume times density.  Price is not a fundamental quantity.  There are other fundamental quantities, such as electrical charge.  Indeed, the usage of electricity is based on a derived quantity of kilowatt hours which is joules times time, essentially total energy.

    Economics is a study of the distribution of scarce resources.  Resources is the available quantity of stuff.  The way the demand curve reads is "given this quantity of stuff, this is the price the average buyer is willing to pay." The way the supply curve reads is, "given this quantity of stuff, this is the price that the supplier must charge."

    Price is a psychological value that human being assign to a thing.  It
    is an individual assessment of what something means to them. It is, in
    essence, a feeling.  Science doesn't take feelings as fundamental

  5.  What have 'leftists' to do with graphing conventions in economics?

  6. Leftists are the source of numerous dangerous myths that poison economics and introduce deceptions into all of the social sciences. 

    Here's just a few from the previous year

    "Eternal vigilance is the price of liberty—power is ever stealing from the many to the few…. The hand entrusted with power becomes … the necessary enemy of the people. Only by continual oversight can the democrat in office be prevented from hardening into a despot: only by unintermitted Agitation can a people be kept sufficiently awake to principle not to let liberty be smothered in material prosperity."

  7.  So economists all over the world put price on the vertical axis of graphs because ideological leftists made them do it. Is that what you mean? No, I think I am misunderstanding you. I think you mean that ideological leftists deceived all of the other economists into putting price on the vertical axis of their graphs, presumably so that they might be confused and make dangerous policy decisions because they could no longer tell the difference between independent and dependent variables...because of this clever deception. So, the solution ought to be to inform the major non-leftist economists that they have been deceived by their colleagues. You should start a petition. I imagine that professional economists all over the world would be relieved and delighted to learn about this outrageous conspiracy. You could start by writing to the federal government and they could disseminate the information from there to the universities. Thank God David that you have discovered this just in time. We could save the country. All we need to do is show those poor, center-leaning and right-leaning fools that they have just mixed up the axes in their graphs. That's why everything went wrong. Those leftists will stop at nothing!

  8. as above, more important than the graphing conventions are the philosophical implications of seeing price as the independent (rather than dependent) variable. When price is seen as a variable that can be manipulated, rather than as the result of sovereign consumers in a broadly dispersed marketplace, such a myth is shamelessly used by leftists in order to promote intrusive and destructive government (and central bank) intervention in the market economy.

    "What vitiates entirely the socialists economic critique of capitalism is their failure to grasp the sovereignty of the consumers in the market economy. " (Ludwig von Mises, Liberty and Propserity) 

  9. One place where the problem becomes very obvious is hours worked for wage rates. This become a back-bending curve, which violates the laws of calculus functions. (No two output Y for any given input X)

  10. this is the stupidest post i've ever seen - price is more often the independent variable than quantity. picking on a few analogies in which the inverse is true does not make your point valid. also, the time/price graph is completely absurd. that is in no way similar to this situation and in that case time would obviously be the independent variable as it always is.

  11. Here is my take on this question:

    Neither price nor quantity is mathematically an "independent variable" since there are valid supply and demand graphs which fail both the vertical and horizontal line test. I like to think P should go on the Y axis to remind readers that it's NOT dependent. In any event, there aren't many good answers to this question on the internet, because I think not many people have thought about supply and demand in a causal way. Many Econ 101 teachers teach their students that prices cause quantities and leave it at that, but as you say, it's not that simple.

  12. Well done! I am so glad I've read your comment . It makes so much sense. I wish you were my econ tutor !!

  13. It is really tricky which one to follow: standard or conventional one. As we may have a general view that a graph is based on data that are mathematical presentations. so, it could be more logical to sketch a graph based on what is in practice in the domains of science and mathematics. Being a B.Sc.(Maths) and M.Ed.(English), i find an independent variable presented on x-axis more logical and clearer rather than sticking to what way Marshall began the graph.

    Today, there was a monthly test of the economics paper in class 12 at my college. In course of invigilating, I had a look at the graph and went through some explanations. I got confused at why the students had selected y-axis for the price of commodity whereas according to their interpretation price was an independent variable - the higher the price, the lower the demand. I also went through their text book and found the same. On several websites including Wikipedia, price has been explained as an independent variable, but it has been placed on the y-axis. I don't suppose it is wise to bear it simply saying that it is conventional. it is more confusing than conventional, since a graph represents a good description. If explained on the standard basis, it is sure to get misinterpreted. for example, look at the graph of demand relationship and your standard interpretation goes like this: If the demand of a commodity increases, its price decreases! How ridiculous!