Introductory Economics

Introduction

Percentage method:

Point elasticity of demand:
Price elasticity is the proportionate change in quantity demanded to the proportionate change in price.

In the figure below, when price falls from OP to OP1, quantity demanded rises from OQ to OQ1.This change in price by PP1 causes change in quantity demanded by QQ1. Substituting these in equation (i) above, we get,

Ep = QQ1 / PP1 X OP/ OQ
Since in figure below QQ1= MR1 and PP1 = RM and OP =QR

Therefore Ep = MR1/RM X QR/OQ --------------- (ii)
Now take triangles RMR1 and RQT
MR1R = QRT (Corresponding s )
RMR1 = RQT (right s)

MRR1 = RQT (Common s )
Therefore triangles RMR1 and RQT are similar; a property of similar triangles is that their corresponding sides are proportional to each other. From this it follows that:

MR1/RM =QT/QR
Writing QT/QR in place of MR1/RM in equation (ii) we get

Ep = QT/QR X QR/OQ
= QT/OQ
Now, in triangle OT1T QT is parallel to OT1, therefore,

QT/OQ =RT/RT1

Ep =QT/OQ = RT/RT1

Hence from above it is found that price elasticity at point R on the straight line demand curve T1T is
= RT/RT1 = Lower segment/Upper segment

If the point R exactly lies in the middle of the demand curve (as shown in figure below)

the elasticity at this point will be equal to one. If the point lies above the middle point R say S then elasticity at this point will be ST/ RT1 i.e. more than one. Similarly if this point lies below the middle point R then it will be less than one. At point T it will be zero and at point T1 it will be infinity.

• If the demand curve is non linear as shown in the figure below then elasticity at a point R ins measure by drawing a tangent line to the given point R It is equal to RT/T1R.

Arc Elasticity Method :

• When the price change is somewhat large or we want to measure elasticity over an arc of the demand curve rather than on a specific point, then the measure is called Arc elasticity method. Say we are interested to measure elasticity of demand between points A and B as shown in the figure below on the demand curve DD. For such cases concept of Arc elasticity is used in which we use the average of two prices i.e. original as well subsequent and average of two quantities i. e. original as well as subsequent. Thus the formula for elasticity is as given below.

Revenue Method:

• Price elasticity of demand can also be measured with the help of average and marginal revenue curves with the following formula.

Ep = A/ A-M where A= average revenue, M=marginal revenue

• In the figure below, revenue is shown on Y-axis and quantity on X-axis AB is the average revenue curve or demand cure and AN marginal revenue curve At point P elasticity of demand is calculated as

Ed = Lower portion/ upper portion or PB/PA
ΔPMB and ΔAEP are similar, so ratio of their sides is also equal
Ed = PB/PA =PM/AE -------------- (i)

ΔAET and ΔTPL are congruent triangles, so PL=AE. By substituting PL in place of AE in equation (i)
Ed = PM/Pl
Because PL = PM- LM , hence
Ed = PM/ PM-LM , where
PM =AR and LM =MR, so Ed = A/A-M So if the value of Ed is one it means elasticity is unitary, if it is more than one, then elasticity is more than one and if less than one then less than unitary.