Question

A consumer buys 80 units of a good at a price of rupees 5 per unit. Suppose price elasticity of demand is -2 at what price will he buy 64 units?

Answer 1

$\bold {Answer}$

$Price = 4.50 \space rupees \space per \space unit$

$\bold {Solution}$

$PED = \dfrac {\%∆ \space Quantity}{\%∆ \space Price}$

$\% ∆ \space Quantity = \dfrac {80-64}{80}×100\%$

$=\dfrac {16}{80}×100\%$

$\bold {= 20\%}$

Let $x$ be the price when $Q= 64 \space units$

$\%∆\space Price = \dfrac {x -5}{5}×100\%$

$\bold {= 20(x-5)\%}$

Therefore, $-2 = \dfrac {20\%}{20(x-5)\%}$

$=> -2(x-5) = 1$

$=> -2x + 10 = 1$

$=> -2x = 1-10$

$-2 x = -9$

Dividing both sides by $-2$ gives:

$\bold {x = 4.50}$

Therefore, when the consumer buy 64 units, the price is 4.50 rupees per unit.