# why is this economics parabola sideways? switch x and y axis

Why is this "parabola" sideways?

Normally, f(x)=y, would be that x is graphed horizontally, and you would write that "wage rate is a function of hours worked", which is how I would normally think about wages and hours. However, this graph seems to read that the hours worked are a function of the rate.

Perhaps a graph of the wage itself against hours might be more useful.

Is there some point to graphing this "sideways"?

(Of course, it might not be a parabola, I'm just guessing.)

The wikipedia entry says it's "S-shaped", which I interpret to mean it goes up and down, maybe more like a sine-wave or something along those lines. But why sideways?

• It's definitely not a parabola. Parabolas have a very specific form and geometric interpretation. What is this graph representing? It tells me that for any given given number of hours worked, I can have 2 different wages. We need a little more info if you want a better answer. Commented Jan 6, 2014 at 23:48
• Also, typically in economic graphs, one doesn't interpret them as one the vertical axis exclusively depending on the horizontal, but instead simply a relationship between the two paramaters, so it shows that as one increases/decreases, the other changes according to the graph. Commented Jan 6, 2014 at 23:51
• en.wikipedia.org/wiki/Backward_bending_supply_curve_of_labour pardon, thought I included that but I forgot. @Jeremy that's what I'm asking, why do they do that? I thought it was a graph like you would see in h.s. algebra...? Commented Jan 6, 2014 at 23:55
• I think @Jeremy is arguing that choice of axis to which a DV is assigned doesn't necessarily matter in economic graphing. Maybe you should edit to ask why that is? Your premise is that it isn't the case, but that the rule is reversed from other fields' rules. Commented Jan 7, 2014 at 3:33

This is not a mathematics question but rather an economics question. It is tradition in economics to have in the Y-axis the independent variable and in the X-axis the dependent variable.

Here wage is the independent variable (set by market forces) and hours worked is the dependent variable (workers choose how much to work at the prevailing wages). It may not be realistic but this what the graph is suppose to depict.

The reason it bends backwards is that as wages become too high, workers prefer to work less and take more leisure time.

• It's curious, or notable, that you write that "it may not be realistic but that is what the graph is supposed to depict." Commented Jan 7, 2014 at 0:08
• It is not realistic because it ignores search frictions and it assumes the labor market is perfectly competitive. Still a good model for undergrad classes but search models give a better picture. Commented Jan 7, 2014 at 0:12

There are two different issues here:

1. Economists often reject the general convention of putting the independent variable (usually prices or wages) on the $x$-axis and the dependent variable on the $y$-axis. In doing so they follow Alfred Marshall, who was considering marginal costs and marginal utilities of additional goods at the time. So here, although hours worked is a function of wage rates, the curve is "sideways" because of economists' unconventional convention.

2. The curve does not a priori have a positive or negative slope. It will have a positive slope when higher hourly wage rates give you an incentive to work more hours, and a negative slope when the higher incomes associated with higher hourly wage rates mean you can afford to and want to take more leisure time. It may never change direction, or may change direction a number of times as the substitution effect and income effect interact.

• I'll check out Alfred Marshall, thanks for the link. I think this is about as far as this question goes -- I'll try to figure out their unconventional convention. It's just hard to read. Commented Jan 7, 2014 at 0:10

Please note that $$y=f(x)$$ meaning $$y$$ is a dependent variable and $$x$$ is an independent variable and this convention is always used. In economics traditionally for simplicity's sake we take $$p=f(qd)$$ or $$p=f(qs)$$ which is not correct. In economics the correct form i.e. $$qd,qs=f(p)$$ should be used.

Dr. M. Ahsanuddin

• Welcome to MSE. Please edit and use MathJax to properly format math expressions. This answer post of yours is currently under review and will likely be deleted via community votes if no improvement is made. Commented Feb 23, 2019 at 18:23