Skip to content

Price or Quantity on the X Axis?

March 22, 2013

There is a small debate over whether price or quantity should go on the x axis of the supply and demand graph. Historically, quantity has gone on the x axis, since that’s how Alfred Marshall, an early pioneer of supply and demand analysis, drew it.

what-is-supply-and-demand

The convention in mathmatics is to put the independent variable on the x axis and the dependent variable on the y. When you have variables in causal relationships, the variable on the x axis causes the variable on the y axis. Neither price nor quantity satisfy these criteria. Prices do not cause quantities, nor do quantities cause prices. Both are jointly determined by the supply and demand curves. The domain of the function is the two curves, the range is the Cartesian coordinate which corresponds to a price and a quantity.

In Mathese:
f(supply, demand) = (P,Q)

The Vertical Line Test
Demand curves are almost always downward sloping, but supply curves are all over the map. As a function can only have one output for each distinct input, the vertical line test helps to determine which variable is the domain of a function and which is the range.

Both of these supply curves are valid according to economic theory:
vertical line supply
Note: “Backward bending” supply curves occur in labor markets when, at high wages, people may decide to work less and enjoy more leisure time.

Conclusion
Price should remain on the vertical axis, not because it is the dependent variable, but because it may be mistaken for the independent variable. No one thinks that quantities are causal, but some people do mistakenly think that prices are. Putting P on the vertical axis is a subtle reminder that prices don’t cause things.

Further reading:
A bit of history on the subject from the Richmond Fed.

Advertisements
3 Comments leave one →
  1. Tom permalink
    December 21, 2013 10:35 pm

    “Neither price nor quantity satisfy these criteria. Prices do not cause quantities, nor do quantities cause prices. Both are jointly determined by the supply and demand curves. The domain of the function is the two curves, the range is the Cartesian coordinate which corresponds to a price and a quantity.

    In Mathese:
    f(supply, demand) = (P,Q)”

    This should be in every economics text; maybe authors assume this is common sense, but I never assumed that they might be implying this.
    That explanation cleared up so much confusion in explaining equilibrium shifts; thank you!

    • December 22, 2013 11:54 am

      Glad to be of assistance! The reason I wrote this article is because of the confusion in many intro econ texts.

  2. devesh shobhasaria permalink
    February 5, 2016 12:26 pm

    Ok according to you if independent variable should be on x axis then tell me that how should we prepare diagram according to LAW OF DEMAND in which

    price increase then demand decrease

    Price decrease then demand increase

    Here price is independent and qty is dependent

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: