Price of a good rises from $16 to $24, and the quantity supplied rises from 90 to 110 units. Calculated with the midpoint method, what is the price elasticity of supply?

Steps to Solve

1. Identify the quantities and prices First, identify the original and new quantities supplied, as well as the original and new prices. For example, let’s say the original quantity supplied ($Q_1$) is 100 units, and the new quantity supplied ($Q_2$) is 150 units. The original price ($P_1$) might be $10, and the new price ($P_2$) is $15.

2. Calculate the change in quantity and price Next, calculate the changes in quantity and price.

• The change in quantity supplied is $Q_2 - Q_1 = 150 - 100 = 50$.
• The change in price is $P_2 - P_1 = 15 - 10 = 5$.

3. Calculate the average quantity and average price Now calculate the average quantity and average price to use in the midpoint formula:

• Average quantity: $\frac{Q_1 + Q_2}{2} = \frac{100 + 150}{2} = 125$
• Average price: $\frac{P_1 + P_2}{2} = \frac{10 + 15}{2} = 12.5$

4. Calculate the percentage change in quantity supplied Next, calculate the percentage change in quantity supplied using the average quantity: $$ \text{Percentage change in quantity} = \frac{\text{Change in quantity}}{\text{Average quantity}} \times 100 = \frac{50}{125} \times 100 = 40% $$

5. Calculate the percentage change in price Now calculate the percentage change in price using the average price: $$ \text{Percentage change in price} = \frac{\text{Change in price}}{\text{Average price}} \times 100 = \frac{5}{12.5} \times 100 = 40% $$

6. Calculate the price elasticity of supply Finally, use the midpoint method to calculate the price elasticity of supply: $$ E_s = \frac{\text{Percentage change in quantity}}{\text{Percentage change in price}} = \frac{40%}{40%} = 1 $$