Microeconomics,, 16th Canadian Edition

Walras did not use graphical representation. Had he done so, he
would surely have placed p (his independent variable) on the
horizontal axis.
Marshall’s work influenced later generations of economists, in
particular because he was the great popularizer of graphical
analysis in economics. Today, we use his graphs, even for
Walras’s analysis. The axis reversal is thus one of those historical
accidents that seem odd to people who did not live through the
“perfectly natural” sequence of steps that produced it.
7. The definition in the text uses finite changes and is called arc
elasticity because it is being computed across an arc of the
demand curve. The parallel definition using derivatives is

and is called point elasticity.
8. The propositions in the text are proved as follows. Letting TE
stand for total expenditure, we can write

It follows that the change in total expenditure is

d(p)=s(p)

η= ddQp ⋅ Qp

TE=p⋅Q

dTE=Q⋅dp+p⋅dQ

[8.1]