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

Q.2. Attempt the following:

(a) Price of a commodity falls from ₹4 to ₹3 per unit. As result total expenditure on it rise from ₹200 to ₹300. Find out price elasticity of demand by percentage method.

(b) As a result of a 5 per cent fall in the price of a good, its demand rises by 12 per cent. Find out price elasticity of demand and say whether demand is elastic or inelastic and why?

(c) Price of good rises by 10%. As a result, its demand falls from 16 units to 12 units. Find out the price elasticity of demand.

(d) The price of a commodity fell from

₹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: \(Q+\Delta Q=40=80\)

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