Right, Barkely, I had written exactly the same thing. So I won't repeat 
it. I will try to add to it.

In these days of mathematical economics, it is important to keep in mind 
that, IN ECONOMICS, both price and quantity are dependent variables. 
Every teacher who tries to make the demand-supply construct meaningful 
in the classroom knows that both of these variables are determined by 
interacting entrepreneurs (Marshall's undertakers). Marshall must have 
recognized this and he must have wanted to represent this, since as 
practically everyone knows, his main aim was to depict reality. It has 
been a while since I read Marshall and I did not directly look this up. 
But is it not true that his discussions that accompany his diagrams take 
account of both the price setting and quantity determining process? 
Stated differently, what I am saying is that Marshall used the diagrams 
as a teaching tool, not as part of an effort to build an airtight 
mathematical economics, like some of the math econ textbooks. The 
correct answer to the question asked by Steve's student is that 
economists use the diagram for a different purpose than mathematics.

Yet the question remains concerning why this purpose cannot be achieved 
by a diagram that has quantity on the vertical axis.

Now the interesting problem that arises in telling stories to fit the 
demand-supply framework is that quantity refers only to a specific good, 
A. That is all that it can represent. The same is true of the demand 
prices of the consumer. These are the consumer demand prices of A. 
Supply prices, however, if properly understood, represent more than the 
supply prices of A. They represent the entrepreneur role's accounting of 
the demands for all goods and of the profitability of employing the 
factors of production in other uses besides A. Marshall was no expert in 
representing scarcity in the large, as evidenced by the real cost 
doctrine that was refuted by the Austrians (specifically by Bohm 
Bawerk). However, he certainly appreciated that the cost of producing 
more of A is the sacrifice of the benefits that could be obtained if the 
factors of production were used in their next best alternative use. 
Thus, the supply curve represents a whole lot more than the numbers in a 
chart representing the supply schedule for A.

Still, the question remains concerning why this fact (opportunity cost 
as calculated by the entrepreneur role) cannot be represented by a 
diagram that has quantity on the vertical axis.

Which takes me back to my original remarks, which I will embellish.

Quantity, something that can be counted on a preschoolers table, 
"belongs" on the horizontal axis. The eyes of the counter projects 
quantity from objects on the table out through window into the horizon 
over the ocean toward the setting sun.  This is a horizontal projection. 
Value (costs and benefits), an abstract concept that cannot be counted, 
belongs on the vertical axis. The complex economic calculation that is 
necessary to identify the supply prices also belongs on the vertical 
axis. The ponderer of these "ideas"  projects upward towards a distant 
star in the evening. And as the head tilts back, the eyes roll and the 
brain starts to work at more than mere counting.


On 2/5/2011 1:56 PM, Rosser, John Barkley - rosserjb wrote:
> Avi,
>       Thanks for the info on Gordon's view.  However, even if he is right about Marshall's motivation, this does not make much sense to me.  CS and PS are areas in P-Q space, and it does not matter
> a whit which one is on which axis for making such a measurement.  I would think that someone as mathematically sophisticated as Marshall would understand this.
> Barkley
> ________________________________________
> From: Societies for the History of Economics [[log in to unmask]] on behalf of Avi J. Cohen [[log in to unmask]]
> Sent: Saturday, February 05, 2011 9:55 AM
> To: [log in to unmask]
> Subject: [SHOE] why Marshall transposed the axes
>
> Barkley,
>
> Forgive my delay, but I only receive the SHOE list in digest form, once a day.
>
> The main reason is that Marshall privileged the geometric analysis and measurement of consumer and producer surplus, in order to asses welfare effects.
>
> Here are key summary quotes from Gordon:
>
> Main reason "why Marshall adopted the price-function form was that he wished to interpret the price consumers are willing to pay as a measurement of utility and the price producers are willing to accept as a commensurable measurement of real (disutility) cost of production. In order to understand Marshall's diagrammatic practice we must pay attention to his normative welfare economics" (32)
>
>
> "Why did Marshall transpose Cournot's axes? The answer, in my view, lies in Marshall's early, and continuing, interest in consumer and producer surplus, that is, in what we today call 'normative welfare economics,' as one of the main objects of economic analysis. There is no substantive difference, as such, in labeling coordinate axes one way or the other, but Marshall, in my opinion, put quantity on the abcissa and price on the ordinate because in doing the analysis of 'maximum satisfaction' this would be in accord with the mathematical convention of using the abcissa for the independent, and the ordinate for the dependent, variables."  (35)
>
> Conclusion
>
> "A demand (supply) curve can be read two ways: as a statement of the quantities consumers (producers) will buy (sell) at different prices, or as a statement of the prices consumers (producers) are willing to pay (accept) for different quantities. According to the first reading, mathematical convention requires that quantity be treated as the dependent variable and price as the independent variable, and diagrammed accordingly, but the second reading requires the opposite treatment. In this paper I have shown that Marshall interpreted demand (supply) functions in the second of these two ways from his earliest work in economic theory, and have argued that his treatment was, from the beginning and throughout his subsequent work, motivated by his desire to use price as a money measurement of benefits and costs in order to construct a theory of surplus serviceable for welfare economics. Thus, Marshall's diagrammatic practice was neither idiosyncratic nor mistaken, when viewed in terms of what he regarded to be the main purpose of economic theory."  (43-4)
>
>
> The article is very rich, and I encourage you to look at it. I have a pdf of the article, which I am happy to send to anyone who emails me (SHOE does not accept attachments). The digital version of EEJ does not go back to 1982.
>
> Best,
>
> Avi
>
>
> From: "Rosser, John Barkley - rosserjb"<[log in to unmask]<mailto:[log in to unmask]>>
> Date: February 4, 2011 9:32:17 AM EST
> Subject: Re: why Marshall transposed the axes
>
> Avi,
>       For those without quick access to this article, what is Gordon's answer roughly, please?
> Barkley
> ________________________________
> From: Societies for the History of Economics [[log in to unmask]] on behalf of Avi J. Cohen [[log in to unmask]]
> Sent: Friday, February 04, 2011 8:07 AM
> To: [log in to unmask]<mailto:[log in to unmask]>
> Subject: [SHOE] why Marshall transposed the axes
>
> Steve,
>
> See Scott Gordon, "Why Marshall Transposed the Axes"  Eastern Economic Journal 8 (1) Jan 1982: 31-45
>
> Best,
>
> Avi
>
>

-- 
Pat Gunning
Professor of Economics
Melbourne, Florida
http://www.nomadpress.com/gunning/welcome.htm