Question

What will be the effect of 10 percent rise in price of a good on its demand if price elasticity of demand is $(A)$$0$
$(B)$$ - 1$ $(C)$\[ - 2\]

Answer 1

Hint: The percentage change in the ordered quantity of a product or service by the percentage change in the price. Be using a specific formula for calculating the price elasticity of quality demanded. The equation of an inverse demand, or price equation, and its price as a function of the sum ordered.

Formula used:
Formula for elasticity demand,
${E_d} = \dfrac{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded}}}}{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{demanded}}}}$
Where,
${E_d}$ is the Elasticity demand
According to that,
${\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded = }}{{\text{E}}_{\text{d}}}{{ \times percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{demanded}}$

Complete step-by-step answer:
To find
Elasticity demand ${E_d}$ is $\left( a \right)\,0,\left( b \right)\, - 1,\,\left( c \right)\, - 2$
And percentage change in price is $10\% $
$\left( A \right)$ Given that,
${E_d} = 0$, ${\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\, = 10$
Substituting the given formula,
${E_d} = \dfrac{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded}}}}{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{demanded}}}}$
We know that,
$0 = \dfrac{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded}}}}{{{\text{10}}}}$
Rearranging the equation is
${\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded = }}{{\text{E}}_{{d}}}{{ \times percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{demanded}}$
\[{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{{demanded = 0 \times 10}}\]
Therefore,
The percentage change in quantity demanded is $0$.
$\left( B \right)$ Given that,
$\Rightarrow$ ${E_d} = - 1$,${\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{ = 10}}$
Substituting the given formula,
We know that,
$\Rightarrow$ ${{\text{E}}_{\text{d}}}{\text{ = }}\dfrac{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded}}}}{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{demanded}}}}$
Substituting the given value,
${\text{ - 1 = }}\dfrac{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded}}}}{{{\text{10}}}}$
Rearranging the above equation,
${\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded = }}{{\text{E}}_{\text{d}}}{{ \times percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{demanded}}$
$\Rightarrow$\[{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{{demanded = - 1 \times 10}}\]
Therefore, the percentage change in quantity demanded is $ - 10$
$\left( C \right)$ Given that,
$\Rightarrow$ ${E_d} = - 2$, ${\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{ = 10}}$
Substituting the given formula,
We know that,
${{\text{E}}_{\text{d}}}{\text{ = }}\dfrac{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded}}}}{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{demanded}}}}$
We know that,
${\text{ - 2 = }}\dfrac{{{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded}}}}{{{\text{10}}}}$
Rearranging the equation is
${\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{\text{demanded = }}{{\text{E}}_{{d}}}{{ \times percentage}}\,{\text{change}}\,{\text{in}}\,{\text{price}}\,{\text{demanded}}$
Substituting the above value,
$\Rightarrow$\[{\text{percentage}}\,{\text{change}}\,{\text{in}}\,{\text{quantity}}\,{{demanded = - 2 \times 10}}\]
On simplifying an equation,
Therefore,
The percentage change in quantity demanded is $ - 20$.

Note: If the percentage change in the required quantities is smaller than the percentage change in price, consider the demand is not very sensitive to price changes. When the change in demand is seen to be comparatively higher relative to the change in price and price elasticity. The rate at which demand increases or decreases with the resulting change in price was price elasticity.