Multiplying and dividing both terms on the right-hand side of
Equation 8.1 by p · Q yields
Because dp and dQ are opposite in sign as we move along the
demand curve, dTE will have the same sign as the term in
brackets on the right-hand side that dominates—that is, on which
percentage change is largest.
A second way of arranging Equation 8.1 is to divide both sides
by dp to get
From the definition of point elasticity in note 7, however,
which we can substitute into Equation 8.2 to obtain
Because η is a negative number, the sign of the right-hand side of
Equation 8.4 is negative if the absolute value of η exceeds unity
dTE=[dpp +dQQ]⋅(p⋅Q)dTdpE =Q+p⋅ddQp[8.2]
Q⋅η=p⋅ddQp[8.3]
ddTpE =Q+Q⋅η=Q⋅( 1 +η)[8.4]