Summary of Section 5.5 from Text web site:
http://www.zweigmedia.com/ThirdEdSite/Calcsumm5.html
Elasticity of Demand

The elasticity of demand, E, is the percentage rate of decrease of demand per percentage increase in price. We obtain it from the demand equation according to the following formula:

 E = - dq dp . p q .

where the demand equation expresses demand, q, as a function of unit price, p. We say that the demand is elastic if E > 1, the demand is inelastic if E < 1, and the demand has unit elasticity if E = 1.

To find the unit price that maximizes revenue, we express E as a function of p, set E = 1, and then solve for p.

Example

Suppose that the demand equation is q = 20,000 - 2p. Then

 E = - (- 2) p 20,000- 2p = p 10,000- p

If p = 2,000, then E = 1/4, and demand is inelastic at this price.

If p = 8,000, then E = 4, and demand is elastic at this price.

If p = 5,000, then E = 1, and the demand has unit elasticity at this price.

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Addendum for connection of E=1 to maximum  revenues. [M. Flashman]

Proposition:
If p is the unit price that maximizes revenue and E is the elasticity of demand at that price,  then E = 1.

Proof:
Let R be the revenues. Then R = q*p .  To find the maximum for R we maust have that dR/dp = 0
If p is the unit price that maximizes revenue then  dR/dp = q*dp/dp + p *dq/dp q + p * dq/dp = 0.
So   dq/dp = -q/p  and thus E = -p/q * dq/dp = 1.