Hyperbola Demand Curve - Unit Elasticity Everywhere

When we draw a rectangular hyperbola demand curve, it is not meant to reflect the usual elasticity pattern of a linear demand curve (elastic at the top, inelastic at the bottom). Instead, it is a special case constructed to illustrate unit elasticity (PED = 1) at every point.

Here’s why:

• The formula for PED is PED=% ΔQ/ % ΔP

• A rectangular hyperbola has the property that total revenue (P × Q) is constant at every point on the curve.

• Since revenue doesn’t change, the % change in Q is always exactly offset by the % change in P.

• That’s what makes PED = 1 all along the curve.

Now, about the “steeper at the top” issue:

• Visually, yes — the upper part of the hyperbola looks steeper. But slope and elasticity are not the same.

• Slope measures the change in Q for a change in P (ΔQ/ΔP).

• Elasticity measures the % change in Q for a % change in P (%ΔQ/%ΔP), multiplying by P/Q.

• On a rectangular hyperbola, even though the slope changes along the curve, the ratio P/Q changes in just the right way to keep PED = 1 everywhere.

• Left (Linear Demand Curve): Elastic at the top, unit elastic in the middle, inelastic at the bottom.

• Right (Rectangular Hyperbola): Looks steeper at the top and flatter at the bottom, but PED = 1 at every point because total revenue (P×Q) stays constant.

This is why economists use the hyperbola to illustrate unit elasticity specifically.