How to Measure the Elasticity of Supply from Point Method? – Explained!

Like the elasticity of demand, the concept of elasticity of supply occupies an important place in the price theory. It can be measured at a given point of the supply curve by using point method. The measurement of elasticity of supply for the supply curve SS at point, say, ‘A’ is illustrated in Fig. 3.5.

At point ‘A’ in the figure, the price is OP and the quantity supplied is OQ. When the price rises to OP₁, the quantity supplied rises to OQ₂. The point ‘B’ on the rising supply curve SS is close to point ‘A’, since the change in the price of the commodity is assumed to be very small.

The supply curve is extended so that it meets X-axis at point ‘C’ Now, at point ‘A’, elasticity of supply is equal to:

Since CQ is greater than OQ, the elasticity of supply at point ‘A’ (given by CQ/OQ) in Fig. 3.5 is greater than one (elastic). Thus, a straight line supply curve passing through the price or Y-axis is elastic (i.e., elasticity of supply lies between one and infinity)

If the straight line demand curve happens to pass through origin (i.e., point ‘C’ and point ‘O’ coincide with each other), the elasticity of supply OQ/OQ will be equal to one (unitary elastic supply). See Fig. 3. 6 (a).

Further, supply curve passing through the quantity or X-axis (or extended supply curve SS meeting X-axis at some point, say, ‘C’ in Fig. 3.6 (b)), has inelastic supply. In Fig. 3.6 (b), the elasticity of supply is less than unitary (inelastic supply), since CQ is less than OQ.

When the supply curve is non-linear, then the elasticity of supply at any point on the curve will be equal to the elasticity of supply of the tangent drawn at that point. Whether the supply curve is linear or non-linear, the supply elasticity will vary at different points on the supply curve.

Now, an alternative way to measure the elasticity of supply is discussed. For this, the formula of elasticity of supply is rewritten as (P/Q)/(AP/AQ). Consider Fig. 3.7, where the elasticity of supply on the supply curves SS is being measured at point ‘A’ and point ‘B’. For this purpose, tangents have been drawn at these points meeting X-axis at points Q₁ and Q₂ respectively. These tangents make angles a and (3 with the X-axis. Further, say, OA and OB makes angles of y and 5 with the X-axis respectively.

y being an exterior angle, is greater than a . Further, since both a and y are actuate angles, tan y > tan a. Therefore, tan y / tan a > 1 (or, CQ₁ > OQ₁). This implies that the elasticity of supply at point ‘A’ is greater than one. In other words, the supply curve intersecting Y-axis is elastic.

Similarly, the elasticity of supply at point ‘B’ is given by the ratio

The supply elasticity falls in value, as we move up the supply curve. The exact value of the elasticity of supply can be known, if α, β, γ and δ (as the case may be) are known.

For an inverse supply curve, P = a + b Q (where ‘a’ and ‘b’ are constants), the supply elasticity is greater than one, equal to one and less than one, when the value of Y-intercept ‘a’ is positive, zero and negative, respectively. In the above cases, the supply curve passes through Y-axis, origin and X-axis, respectively.

Example:

If Q_s = 5P – 5, find the elasticity of supply if P = 0. Find Q_s.

Solution. The supply function is

Q_s = 5p – 5 = -5, when P = 0