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A propos Marshall's Ps and Qs, you may be interested in what Allyn Young 
said in his lectures at the LSE (as recorded by Nicholas Kaldor) in 1928, a 
few months before his untimely death. (See Journal of Economic Studies, 
Vol. 17, 3/4, 1990, pp.35-6.) 
 
"Demand price" is the price at which a specified quantity of goods will 
be taken off the market. The older economists in saying that "prices are 
determined by supply and demand" used common concepts they themselves did 
not scrutinise carefully. 
 
They had in mind that p=f(s.d.), more particularly, one aspect of it -- 
i.e., changes in supply and demand and what effect they have on price. 
J.S.Mill first attempted to give precision to the notion. "Price will 
always be, or tend to be, at that point where supply equals demand." 
There he considers price not so much as f(s.d.), but rather supply and 
demand as functions of price (s=f(p); d=f(p)). And this is more than 
changing the dependent and independent variable; IT IS NOT THE SAME 
STATEMENT. Taking Mill's tendency statement prima facie, it is a 
tautology; but it really implies a generalisation about the character of 
supply and demand functions. Marshall then used curves to give Mill's 
statement greater precision. (Cournot and Jenkin (first of all) had 
already used curves.) Cairnes, however, favoured the older conception of 
supply and demand varying and so affecting price. Regarding these curves, 
the negatively sloping demand curve is really a generalisation from the 
market. It is implicit, not explicit, in Mill. Notice that Marshall 
violated mathematical convention by using price as the independent 
variable and yet measured price vertically. Contrast Cournot's curves. 
 
On Marshall's curve, demand equals the amount that will be purchased at a 
given price, and really means hypothetical purchases. Movement up and 
down the curve does not mean a change in demand. While the older 
economists were talking about changes in demand, with Marshall this can 
only be shown by shifting the whole curve..." 
 
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