Elasticity on One Demand Curve (No Hand-Waving)

Real example: weekend concert tickets. Demand curve: Q = 100 - 2P.

Step 1: Same demand line, different places

Pick 3 points on the same line:

PointPrice PQuantity QElasticity |E| = 2 × (P/Q)Type
Top area40202 × (40/20) = 4.0Elastic
Middle25502 × (25/50) = 1.0Unit elastic
Bottom area10802 × (10/80) = 0.25Inelastic

Why it changes: slope stays the same, but P/Q changes a lot by location.

Step 2: Demand curve with the 3 points

Quantity (Q) Price (P) 20 50 80 40 25 10 Demand A: |E|=4 B: |E|=1 C: |E|=0.25

A (top): elastic. B (middle): unit. C (bottom): inelastic.

Step 3: What does the graph of E look like?

Here is elasticity magnitude as quantity changes on this same demand curve.

Quantity (Q) |E| 1 2 4 20 50 80 unit elastic line Q=20, |E|=4 Q=50, |E|=1 Q=80, |E|=0.25

As quantity gets larger (moving down the demand curve), elasticity falls.

Midpoint method in one sentence

Use the average of old and new values as the base, so elasticity is the same whether you move forward or backward between two points.

For this demand curve from P=40 to P=20, Q goes 20 to 60:

%ΔQ = (60-20)/40 = 100%, %ΔP = (20-40)/30 = -66.7%, so |E| = 1.5.