Price Elasticity of Demand for Positive Price Increases What does it mean when the price elasticity of demand  %Qd/%P is greater than one?  Typically I hear that it means the demand is elastic since if, say, the price decreases by 1% the demand for the good increases by more than 1%.  But what happens if %P is +1% and %Qd still increases by more?  Sure, this is elastic, but does it give us any more information?  I can't see why %Qd/%P > 1 makes sense in this case.
Except of the purely descriptive aspect, "elastic demand", or more accurately, regions of the demand schedule where demand elasticity with respect to price is higher than unity, in absolute terms, is linked to the basic monopoly theory, since the monopolist maximizes profits at a point of the demand schedule where "demand is elastic".

Define the demand point-elasticity with respect to price as

$$\eta = \frac {\partial Q }{ \partial P}\cdot \frac {P}{Q} \Rightarrow \frac {\partial Q }{ \partial P} = \eta \cdot \frac {Q}{P} \tag{1}$$

Note that algebraically, the elasticity is a negative number, with the sign indicating the direction of influence, since $\partial Q / \partial P &lt;0$.

The profit function of a monopolist is

$$\pi = P\cdot Q(P) - C(Q(P)) \tag{2}$$

The first-order condition for a maximum with respect to price is

$$\frac {\partial \pi}{\partial P} = 0 \Rightarrow Q + P\frac {\partial Q }{ \partial P} - MC\cdot \frac {\partial Q }{ \partial P} = 0 \tag{3}$$

Inserting $(1)$ into $(3)$ we have

$$Q + P\cdot \eta \cdot \frac {Q}{P} - MC\cdot \eta \cdot \frac {Q}{P} = 0$$

$$\Rightarrow 1 + \eta - \eta \cdot \frac {MC}{P} =0$$

$$\Rightarrow - \eta \cdot \frac {MC}{P} = -\eta -1 $$

$$\Rightarrow  |\eta| \cdot \frac {MC}{P} = |\eta| -1$$

$$\Rightarrow P^* =  \frac {|\eta|}{|\eta|-1} MC \tag{4}$$

$(4)$ is essentially an implicit relation since $\eta$ is a function of price also, but it provides a specific insight: Since we naturally expect that price will be positive, we see that we must have $|\eta| &gt;1$: the price will necessarily be set at a level where "demand is elastic", i.e. at a point on the demand schedule where the point price elasticity of demand is higher than unity, in absolute terms.