Explain the geometric method of measuring price elasticity of demand.
Draw a downward sloping straight line demand curve touching both the axes. Mark price elasticity at different points of this demand curve.

What is elasticity of demand on the mid-point of a straight line moving down from left to right?

Solution

Elasticity on a straight line (linear) demand curve. Another method of measuring price elasticity of demand is geometric method which is used when elasticity is to be measured at different points on the straight line demand curve. This method involves the following steps as shown in the following Fig. 2.29.

(i) Straight line demand curve is first extended to both sides to join Y-axis at E and X-axis at D in Fig. 2.29.

Fig. 2.29

(ii) Take mid-point of straight line demand curve (say, point B) which divides the demand curve into two equal portions — upper portion (say, BE) and lower portion (say, BD). Point A is located in the upper portion and point C in the lower portion.

(iii) Elasticity at any point on straight line demand curve is worked out by dividing lower portion of the demand curve with upper portion of the demand curve. Thus:
$eD space at space point space straight B space equals space fraction numerator BD space left parenthesis Lower space segment right parenthesis over denominator BE space left parenthesis Upper space segment right parenthesis end fraction equals 1$ because B is the mid-point.
(Alternatively elasticity of demand on the mid-point of a straight line moving from left to right is 1 or unit elastic.)
$eD space at space point space straight A space equals AD over AE left parenthesis It space is space greater than 1 comma space because space AD thin space is space greater space than space AE right parenthesis eD space at space point space straight C equals CD over CE left parenthesis It space is space less than 1 comma space since space CD space is space smaller space than space CE right parenthesis eD space at space point space straight D space equals space Zero eD space at space point space straight E space equals space infinity space left parenthesis Infinity right parenthesis.$