Let a linear demand curve be

•At any point on the demand curve, the change in demand per unit change in the price

= âˆ†q/ âˆ†p =-b

•Price elasticity of demand for a good *e*_{D} = (âˆ†Q/Q)/ (âˆ†P/P)

•Hence, *e*_{D} =-b.p/q

•*Putting the value of q*

•*e*_{D} =-b.p/(*a – bp)*

•We know *e*_{D} =-b.p/(*a – bp)*

•*Thus the value of * *e*_{D} is different for different points at the liner demand curve

•*At p=0 * *e*_{D} =0

•*At q=0, e*_{D} =∞

•*At p= a/2b, e*_{D}=1

•*At any price greater than 0 and less than a/2b, e*_{D} is less than 1

•*At any price greater than than a/2b, e*_{D} is greater than 1

•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 *p*^{0}, the demand for the good is *q*^{0}.

•With a small change, the new price is *p*^{1}, and at that price, demand for the good is *q*^{1}.

•âˆ† *q *= *q*^{1}*q*^{0} = *CD *and

•âˆ† *p *= *p*^{1}*p*^{0} = *CE*

•*e*_{D} = (âˆ†q/q)/ (âˆ†p/p)

•= (âˆ†q/ âˆ†p)x(p/q)

•=(CD/CE)X(Op^{0}/Oq^{0})

•=ECD and Bp^{0}D are similar triangle

•Hence CD/CE=p^{0}D/p^{0}B

•But p^{0}D/p^{0}B = Oq^{0}/p^{0}B

•Hence *e*_{D} = (Oq^{0}/p^{0}B)x(Op^{0}/Oq^{0})

•=Op^{0} /p^{0}B

•Since Bp^{0}D, BOA and Dq^{0}A are similar

•*Hence, **e*_{D} = DA/DB

•*e*_{D} = 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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