# Chapter – 2: Elasticity of Demand – II (Numericals)

### ₹10 to ₹5 and its coefficient of price elasticity of demand is 2. How much quantity will be demanded at the changed price where the original quantity demanded is 40?

Ans. (a)

Price Total Expenditure Demand
₹ 4
₹ 200
₹ 50
₹ 3
₹ 300
₹ 100

Percentage method of price Elasticity

$${e_{d\,}} = \frac{{{\rm{Percentage}}\,{\rm{change}}\,{\rm{in}}\,{\rm{demand}}}}{{{\rm{Percentage}}\,{\rm{change}}\,{\rm{in}}\,{\rm{price}}}}$$

$$= \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} = \frac{50}{1} \times \frac{4}{50} = 4$$

$$\begin{array}{l}\left( b \right)\,\,\,{e_{d\,}} = \frac{{{\rm{Percentage}}\,{\rm{change}}\,{\rm{in}}\,{\rm{demand}}}}{{{\rm{Percentage}}\,{\rm{change}}\,{\rm{in}}\,{\rm{price}}}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{12}}{5}\end{array}$$

= 2.4, i.e. more than unity or more elastic

$$\left( c \right)\,\,\,{e_{d\,}} = \frac{{{\rm{Percentage}}\,{\rm{change}}\,{\rm{in}}\,{\rm{demand}}}}{{{\rm{Percentage}}\,{\rm{change}}\,{\rm{in}}\,{\rm{price}}}}$$

$$= \frac{\frac{\Delta Q}{Q}\times 100}{10} = \frac{\frac{4}{16}\times 100}{10}=2.5$$

(d) $${e_d} = \frac{{\Delta Q}}{{\Delta P}} \times \frac{P}{Q}$$

$$= \frac{x}{5} \times \frac{10}{40}= 2$$

$$= \frac{x}{20}=2$$ or $$x=40$$

$$\therefore$$ Quantity demanded will be: $$Q+\Delta Q=40=80$$