Question

Explain the geometric method of measuring price elasticity of supply. Use Diagram.

Answer 1

The geometric method measures elasticity at a given point on the supply curve and is also
known as ‘Arc method’ or Point method’.

At point ‘A’, the price is OP and the quantity supplied is OQ. When the price rises to OP1,
quantity supplied also raise to OQ1. The supply curve is extended beyond the Y-axis, so
that it meets the extended X-axis at point ‘L’ now, at point A, an elasticity of supply is equal to:

`E_S = (ΔQ)/(ΔP) xx P/Q`

Given

`ΔQ = QQ_1;ΔP = PP_1; P = 0  P and Q = OQ`

Substituting these values in the formula, we get

`E_S = ("QQ"_1)/(PP_1) xx (OP)/(OP)`

QQ1 = AC;PP1 = BC and OP = AQ.

Substituting these values in the above equation, we get

`E_S = (AC)/(BC) xx (AQ)/(OQ)`

Now, ΔBAC and ΔALQ are similar triangles on account of AAA property.

The ratio of their sides will be equal. It implies that

`(AC)/(BC) = (LQ)/(AQ)`

Substituting the value, we get :

`E_S = (LQ)/(AQ) xx (AQ)/(OQ)`  or

`E_S = (LQ)/(OQ) = "Intercept on X-axis"/"Quantity Supplied at that price"`

Three different cases of Geometric Method

1) Highly Elastic Supply (E_s > 1)

A supply curve, which passes through the Y-axis and meets the extended X-axis at some point (say, L in Figure) , then supply is highly elastic. In

Elasticity of supply `(E_S) = (LQ)/(OQ)` and LQ > OQ

Since LQ > OQ, the elasticity of supply at point A > 1 (E_s >1).

2) Unitary Elastic Supply (E_s =1)

If the straight line supply curve passes through the origin, then the elasticity of supply will be equal to one `E_S = (OQ)/(OQ) = 1`

Hence, the supply is unitary elastic.

3) Less Elastic Supply `(E_S > 1)`

If a supply curve meets the x-axis at some point say L, then supply is less elastic.

`E_S = (LQ)/(OQ)` and  LQ < OQ.

Hence, supply is less elastic `E_S < 1`