# Why is price on the vertical axis and quantity on the horizontal axis?

In most of science, it is typical to have the independent variable on the horizontal axis and the dependent variable on the vertical axis.

But in economics, this is often (traditionally?) flipped around. As an economist (Greg Mankiw) writes:

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.

(To elaborate: Demand is typically taught as a function which takes as input prices and gives as output quantity demanded.)

Similarly,

• When drawing the supply and demand for loanable funds, the interest rate is on the vertical axis, while savings and investment are on the horizontal.
• When drawing the supply and demand for money, the interest rate is on the vertical axis and money supply and demand are on the horizontal.

It seems that it was Alfred Marshall who popularized this convention, though possibly he was merely following Cournot. What precisely is the correct historical account for why price is on the vertical axis and quantity on the horizontal? Why does economics deviate from the rest of science with respect to this particular convention? When did it happen?

• Could the down-voter and close-voters please explain what is wrong/bad/low quality about this question, so I can try to improve it? Thank you. – user67 Oct 30 '14 at 15:26
• See my related meta question: meta.hsm.stackexchange.com/questions/44/… – Tom Au Oct 30 '14 at 15:46
• I'm not the downvoter so I can't explain the downvote but as far as the close vote is concerned, i did vote to close this question as off-topic because I fail to see how this question relates to history of science (I'm not questioning the fact that econometrics is a science, more the "history" part that I don't see in your question). – plannapus Oct 30 '14 at 15:47
• The establishment of conventions are part of the history of science to me. – Franck Dernoncourt Oct 30 '14 at 18:16
• Absolutely, the establishment and practical application of conventions are indeed a major part of the history of science and maths. – user22 Oct 30 '14 at 19:14

We have price on the vertical axis because that's how Alfred Marshall (1890) drew his graphs in Principles of Economics. For better or worse, Principles was hugely influential. And so the present-day convention is Marshall's convention. As Humphrey (1992) writes:

The Marshallian cross diagram bears Marshall's name because he gave it its most complete, systematic, and persuasive statement, not because he was the first to invent it. His account was definitive, not pathbreaking. For this he received — and deserved — credit.



The above answer is not completely satisfactory. It merely pushes the question back one level: Why did Marshall put price on the vertical axis?

Short answer: Marshall first introduced a demand curve in 1879. There, he thought of quantity as the independent variable, with prices adjusting to clear the market. It was thus perfectly logical for him to have quantity on the horizontal axis.

Marshall (1879) was not the first to draw demand or supply curves. According to Humphrey, we have:

1. Augustin Cournot (1838). Price on horizontal axis.
2. Karl Rau (1841). Price on vertical axis.
3. Jules Dupuit (1844). Price on horizontal axis.
4. Hans von Mangoldt (1863). Price on vertical axis.
5. Fleeming Jenkin (1870). Price on horizontal axis.

1. William Stanley Jevons (1871, figure). Price on vertical axis.

Did any of the above influence Marshall?

Prior to his 1879 publication, Marshall may not have been aware of Rau or Mangoldt's work, who were less well-known. But Marshall was aware of Cournot, Dupuit, Jenkin, and Jevons's work (see e.g. Whitaker, 1975). But of these four, only Jevons had price on the vertical axis. Cournot, Dupuit, and Jenkin all had price on the horizontal axis.

Moreover, according to the man himself, Marshall's main influence was Cournot:

following the lead of Cournot I had anticipated all the central points of Jevons book and had in many respects gone beyond him,

my obligations are solely to Cournot; not to Fleeming Jenkin or Dupuit. (Quoted in Whitaker.)

But Cournot had price on the horizontal axis! I can find in Marshall's writings no explicit explanation for why he chose to deviate from Cournot, who was his greatest influence (at least in this matter).

However, when introducing for his very first demand curve (1879), he does write the following:

we may draw what may be called "the Demand curve," thus: Let $$M$$ be any point on $$Ox$$ (fig. 20), and let the price at which it is possible to dispose of $$OM_1$$ coals annually be estimated and found to be equal to $$ON_1$$.

That is, Marshall first takes the independent variable to be the quantity demanded (the $$OM_1$$ coals to be disposed of). Marshall's demand curve then tells us about the dependent variable, i.e. the price at which such coal can be disposed.

I thus conclude that Marshall thought of quantity as the independent variable, with prices adjusting to clear the market. It was thus perfectly sensible for him to put quantity on the horizontal axis and price on the vertical.

This way of thinking seems slightly unnatural to me (and many others). But perhaps this is only because we've been trained, since our first economics classes, to think of price as the independent variable.

Moreover, as some here have pointed out, it's not really all that absurd to think of quantity as the independent variable, as Marshall did.



P.S. There's also another cynical explanation I once came across: Marshall simply wanted to differentiate himself from Cournot et al. So he deliberately switched the axes. In my opinion this can plausibly serve as part of the explanation. After all, Marshall felt that he had done a lot of his own original work and was somewhat peeved that others, such as Jenkin, had anticipated his work (see e.g. Marshall's reaction to Jenkin's 1870 article, quoted in Whitaker, 1975).



## Supply and Demand Diagrams before Marshall (1879)

• Can I give you more than one upvote? – Aminadav Glickshtein May 31 '19 at 9:21
• @AminadavGlickshtein: What you can upvote are my YouTube videos: youtube.com/econcow. And of course, also subscribe. Thanks =D – user4795 Jun 27 '19 at 4:30

• When drawing supply and demand, price (which one might more naturally think of as being the independent variable) is on the vertical axis and quantity on the horizontal axis.

For elastic demand you are sometimes able to dictate the demand by the price. Normally though, the demand dictates the price. For (purely) inelastic demand, the price is entirely set by demand. So price is the dependent variable.

• When drawing the investment schedule, the interest rate is on the vertical axis and investment on the horizontal.

This is is basically a demand curve but its geared toward predicting rates rather than reporting rates at different investments.

• When drawing the money market (money supply and demand), the interest rate is on the vertical axis and money supply/demand on the horizontal.

As you said this is also a demand curve.

I think the confusion is because you usually see price as being the independent variable. The price isn't the independent variable because its on the x axis. The price is on the x axis because its the independent variable. As far as (basic) supply and demand go, the price is going to be set by demand.

Note, in my explanations I always said demand to keep it clean. You could switch it to Supply and it still makes sense (unless i made a mistake.)

• Having answered the question... Is the question off topic? – Carlos Bribiescas Oct 30 '14 at 15:54

This question cropped up on Economics.SE, where I posted this answer:

This objection never made too much sense to me. In the standard model of perfect competition, firms take the price as given and respond by choosing their quantity. So you have a model in which a bunch of actors choose quantity and the market price emerges as a consequence of all of those decisions. This makes it sound awfully like price is the "dependent" variable, which by convention is always placed on the vertical access.

Indeed, this seems to be how Alfred Marshall (who originated the modern form of the Demand-Supply diagram) thought about things. Here's a quote from An Introduction to Postitive Economics, Seventh ed. by Richard G. Lipsey (as quoted here):

"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."