Question

When the price of a doll is Rs. 4 per doll, a doll maker supplies 8 dolls per day. If the price rises to Rs. 5 per doll, he is willing to supply 10 dolls per day. Calculate the price elasticity of supply of dolls.

Answer 1

Hint:
Here, we need to find the price elasticity of the supply of dolls. Price elasticity of supply is the proportionate change in quantity supplied of a product caused by a change in the price of the product. We will calculate the percentage change in quantity supplied by dividing the change in quantity supplied by the original quantity supplied and multiply it by 100. Similarly, we will calculate the percentage change in price. Finally, we will divide the percentage change in quantity supplied by the percentage change in price to get the price elasticity of supply.
Formula Used: We will use the formula of the price elasticity of supply, \[{\text{Price Elasticity of Supply = }}\dfrac{{{\text{Percentage change in Quantity supplied}}}}{{{\text{Percentage change in Price}}}}\].

Complete step by step solution:
First, we will calculate the change in quantity supplied and the percentage change in quantity supplied.
We can find the change in quantity supplied by subtracting the old quantity supplied from the new quantity supplied.
Thus, we get
Change in Quantity supplied \[ = 10 - 8 = 2\] dolls
We can find the percentage change in quantity supplied by dividing the change in quantity supplied by the original quantity supplied and multiply it by 100.
Therefore, we get
\[{\text{Percentage change in Quantity supplied}} = \dfrac{2}{8} \times 100\]
Simplifying the expression, we get
\[ \Rightarrow {\text{Percentage change in Quantity supplied}} = 25\% \]
Now, we will calculate the change in price and the percentage change in price.
We can find the change in price by subtracting the old price from the new price.
Thus, we get
Change in Price \[ = 5 - 4 = {\text{Rs}}{\text{. 1}}\]
We can find the percentage change in price by dividing the change in price by original price and multiply it by 100.
Therefore, we get
\[{\text{Percentage change in Price}} = \dfrac{1}{4} \times 100\]
Simplifying the expression, we get
\[ \Rightarrow {\text{Percentage change in Price}} = 25\% \]
Finally, we will calculate the price elasticity of supply of dolls.
The price elasticity of supply is given by the formula\[{\text{Price Elasticity of Supply = }}\dfrac{{{\text{Percentage change in Quantity supplied}}}}{{{\text{Percentage change in Price}}}}\].
Substituting the percentage change in quantity supplied as \[25\% \] and percentage change in price as \[25\% \] in the formula, we get
\[{\text{Price Elasticity of Supply = }}\dfrac{{25\% }}{{25\% }} = 1\]

Therefore, the price elasticity of supply of dolls is 1. This means that the supply of dolls is unitary elastic.

Note:
We can also calculate the price elasticity of supply using the formula \[{\text{Price Elasticity of Supply = }}\dfrac{{\Delta Q}}{{\Delta P}} \times \dfrac{P}{Q}\], where \[Q\] is the original quantity supplied, \[P\] is the original price, \[\Delta Q\] is the change in quantity supplied, and \[\Delta P\] is the change in price.
We can find the change in quantity supplied by subtracting the old quantity supplied from the new quantity supplied.
Thus, we get
Change in Quantity supplied \[ = 10 - 8 = 2\] dolls
We can find the change in price by subtracting the old price from the new price.
Thus, we get
Change in Price \[ = 5 - 4 = {\text{Rs}}{\text{. 1}}\]
Now, substituting \[Q = 8\], \[\Delta Q = 2\], \[P = {\text{Rs}}{\text{. 4}}\], and \[\Delta P = {\text{Rs}}{\text{. 1}}\] in the formula, we get
\[{\text{Price Elasticity of Supply = }}\dfrac{2}{1} \times \dfrac{4}{8}\]
Simplifying the expression, we get
\[{\text{Price Elasticity of Supply}} = 1\]
\[\therefore\] The price elasticity of supply of dolls is 1.