Economics (NCERT) Notes → Class XII

2.13 Elasticity Demand Curve

Elasticity along a Linear Demand Curve
 

Let a linear demand curve be
q = a – bp.
•At any point on the demand curve, the change in demand per unit change in the price
= ∆q/ ∆p =-b
•Price elasticity of demand for a good eD = (∆Q/Q)/ (∆P/P)
•Hence, eD =-b.p/q
Putting the value of q
eD =-b.p/(a – bp)
•We know eD =-b.p/(a – bp)
Thus the value of  eD is different for different points at the liner demand curve
At p=0  eD =0
At q=0, eD =
At p= a/2b, eD=1
At any price greater than 0 and less than a/2b, eD is less than 1
At any price greater than than a/2b, eD is greater than 1
 
Geometric Measure of Elasticity along a Linear Demand Curve
 

•The elasticity of demand at any point on a straight line demand curve is given by the ratio of the lower segment and the upper segment of the demand curve at that point.
•Suppose at price p0, the demand for the good is q0.
•With a small change, the new price is p1, and at that price, demand for the good is q1.
     •∆ q = q1q0 = CD and
     •∆ p = p1p0 = CE
eD = (∆q/q)/ (∆p/p)
     •= (∆q/ ∆p)x(p/q)
     •=(CD/CE)X(Op0/Oq0)
     •=ECD and Bp0D are similar triangle
     •Hence CD/CE=p0D/p0B
     •But p0D/p0B = Oq0/p0B
•Hence eD = (Oq0/p0B)x(Op0/Oq0)
•=Op0 /p0B
•Since Bp0D, BOA and Dq0A are similar
Hence, eD = DA/DB
eD = DA/DB
•Elasticity is 0 at the point where the demand curve meets the horizontal axis
•It is ∞  at the point where the demand curve meets the vertical axis.
•At the midpoint of the demand curve (a/2b), the elasticity is 1,
•At any point to the left of the midpoint, it is greater than 1
•At any point to the right, it is less than 1



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