A consumer buys a certain quantity of a good at a price of $R s . 10$ per unit. When price falls to $R s . 8$ per unit, she buys $40$ per cent quantity. Calculate price elasticity of demand.

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Solution

Suppose the consumer initially buys $100$ units of the good.
New quantity $= 100 + 40$ per cent of $100 = 140$
$P = R s . 10; P_{1} = R s . 9; △ P = P_{1} - P = R s . 8 - R s . 10 = (-) R s . 2$
$Q = 100 u n i t s; Q_{1} = 140 u n i t s; △ Q = Q_{1} - Q = (140 - 100) u n i t s = 40 u n i t s$
Price elasticity of demand $(E_{d}) = (-) \frac{P}{Q} \times \frac{△ Q}{△ P}$
$= (-) \frac{10}{100} \times \frac{40}{- 2} = 2$
Percentage change in price $= \frac{△ P}{P} \times 100$
$= \frac{8 - 10}{10} \times 100 = \frac{- 2}{10} \times 100 = (-) 20 %$
Price elasticity of demand $(E_{d}) = (-) \frac{Percentage change in quantity demanded}{Percentage change in price}$
$= (-) \frac{40 %}{(-) 20 %} = 2$
Price elasticity of demand $= 2$ .

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A consumer buys a certain quantity of a good at a price of Rs.10 per unit. When price falls to Rs.8 per unit, she buys 40 per cent quantity. Calculate price elasticity of demand.

A consumer buys a certain quantity of a good at a price of $R s . 10$ per unit. When price falls to $R s . 8$ per unit, she buys $40$ per cent quantity. Calculate price elasticity of demand.