#
The equation of the demand curve is given by D(*p*) = 25 – 2*p*. Calculate price elasticity of demand at price 5.

OR

In India, despite the rise in price of cigarettes due to the rise in taxes imposed by the government, the fall in the demand of cigarettes is not significant. Explain using the concept of elasticity of demand.

Dear Student,

$Wehavethedemandcurve:D\left(p\right)=25-2p\phantom{\rule{0ex}{0ex}}Now,elasticityofdemand={e}_{d}=\frac{\u2206Q}{\u2206P}\times \frac{P}{Q},wherePispriceandQisquantity.\phantom{\rule{0ex}{0ex}}Here,P=p,andQ=D\left(p\right).Also,\frac{\u2206Q}{\u2206P}isthefirst-orderderivativeofQwithrespecttoP.Thus,here,\frac{\u2206Q}{\u2206P}=D\text{'}\left(p\right).\phantom{\rule{0ex}{0ex}}DifferentiatingD\left(p\right)withrespecttop,weget\phantom{\rule{0ex}{0ex}}D\text{'}\left(p\right)=-2\phantom{\rule{0ex}{0ex}}Also,atp=Rs.5,D\left(5\right)=25-2\left(5\right)=25-10=15units\phantom{\rule{0ex}{0ex}}\therefore Elasticityofdemand={e}_{d}=D\text{'}\left(p\right)\times \frac{p}{D\left(p\right)}=-2\times \frac{5}{15}=\left(-\right)\frac{2}{3}=\left(-\right)0.67$

$Wehavethedemandcurve:D\left(p\right)=25-2p\phantom{\rule{0ex}{0ex}}Now,elasticityofdemand={e}_{d}=\frac{\u2206Q}{\u2206P}\times \frac{P}{Q},wherePispriceandQisquantity.\phantom{\rule{0ex}{0ex}}Here,P=p,andQ=D\left(p\right).Also,\frac{\u2206Q}{\u2206P}isthefirst-orderderivativeofQwithrespecttoP.Thus,here,\frac{\u2206Q}{\u2206P}=D\text{'}\left(p\right).\phantom{\rule{0ex}{0ex}}DifferentiatingD\left(p\right)withrespecttop,weget\phantom{\rule{0ex}{0ex}}D\text{'}\left(p\right)=-2\phantom{\rule{0ex}{0ex}}Also,atp=Rs.5,D\left(5\right)=25-2\left(5\right)=25-10=15units\phantom{\rule{0ex}{0ex}}\therefore Elasticityofdemand={e}_{d}=D\text{'}\left(p\right)\times \frac{p}{D\left(p\right)}=-2\times \frac{5}{15}=\left(-\right)\frac{2}{3}=\left(-\right)0.67$

OR

Cigarettes are habit forming goods, and those addicted to it aren't able to stop its consumption despite a rise in its prices. In other words, when a tax is levied on a good which is a habit forming good such as cigarettes or drugs, even though there is an increase in its prices, its quantity demanded doesn't fall significantly. This is because cigarettes and other habit forming goods have inelastic demand - when their price rises by 1%, their quantity demanded falls by much less than 1%.

**
**