How is Elasticity at point different from Elastic Demand Curve?

Question

Let's say I have an Elastic Demand Curve as shown below

Now, as this is Elastic Demand Curve (When % Change in Quantity Demanded > % Change in Price, the curve is said to Elastic Demand Curve ), Elasticty should always be > 1.

But, If I calculate using Geometric Method, Elasticity at point A is AM / AP. This will give Elasticty at A < 1

I just wanted to know as to why do we get Elasticty < 1 when it's Elastic Demand Curve.

Please enlighten me, as maybe I don't know the different between Elasticity at Point and the Elastic Cuver's Elasticty.

Answer 1

Point elasticity at price $P$ is defined as $\frac{P}{Q}\times \frac{dQ}{dP}$ (therefore it is usually a negative number, but the sign is often omitted). A straight line has a constant ratio $\frac{dQ}{dP}$ while $\frac{P}{Q}$ ranges from $0$ to $\infty$ (as you can see by moving $A$ on your plot). Hence, if a demand curve is a straight line with a negative slope the absolute value of its elasticity will range from $0$ to $\infty$. Moreover, any price elasticity of demand curve that can be represented as a straight line will have a region of elastic demand until the point where $\frac{Q}{P} = \frac{dQ}{dP}$, after which it will have inelastic demand.

With regards to the image you provided, maybe the notion of "elastic demand" is not used here to describe the whole curve, but to describe a particular region, namely a change from $P_1$ to $P_2$. Anyway, I agree that the image is confusing because it gives an impression that price elasticity depends on absolute value changes, which is not true, and it is hard to compare relative change of $P$ and $Q$ because they start from different absolute values and have different absolute changes.