Questions: Adam Incorporated makes specialized garden figurines. Its monthly total is 760 when it charges 20 for each figurine. One month, the firm tried lowering its price to 19, and its total sales revenue that month dropped to 760. On the basis of this data. What is the price elasticity of demand for Adam Incorporated's product? Note: Round your answer to 2 decimal places.

Adam Incorporated makes specialized garden figurines. Its monthly total is 760 when it charges 20 for each figurine. One month, the firm tried lowering its price to 19, and its total sales revenue that month dropped to 760. On the basis of this data. What is the price elasticity of demand for Adam Incorporated's product? Note: Round your answer to 2 decimal places.
Transcript text: Adam Incorporated. makes specialized garden figurines. Its monthly tot is $\$ 760$ when it charges $\$ 20$ for each figurine One month, the firm tried lowering its price to $\$ 19$, and its total sales rever mat month dropped to $\$ 760$. On the basis of this data. What is the price elasticity of demand for Adam Incorporated's product? Note: Round your answer to 2 decimal places. \[ \epsilon= \]
failed

Solution

failed
failed

To calculate the price elasticity of demand, we use the formula:

\[ \epsilon = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}} \]

First, we need to determine the percentage change in price and the percentage change in quantity demanded.

  1. Calculate the percentage change in price:

    The original price is \$20, and the new price is \$19. The change in price is:

    \[ \Delta P = 19 - 20 = -1 \]

    The percentage change in price is:

    \[ \%\ \text{change in price} = \frac{\Delta P}{\text{original price}} \times 100 = \frac{-1}{20} \times 100 = -5\% \]

  2. Calculate the percentage change in quantity demanded:

    The total revenue remains the same at \$760, even after the price change. This implies that the quantity demanded must have increased to offset the decrease in price.

    Let \( Q_1 \) be the original quantity demanded at \$20, and \( Q_2 \) be the new quantity demanded at \$19.

    \[ 20 \times Q_1 = 760 \quad \Rightarrow \quad Q_1 = \frac{760}{20} = 38 \]

    \[ 19 \times Q_2 = 760 \quad \Rightarrow \quad Q_2 = \frac{760}{19} \approx 40 \]

    The change in quantity demanded is:

    \[ \Delta Q = Q_2 - Q_1 = 40 - 38 = 2 \]

    The percentage change in quantity demanded is:

    \[ \%\ \text{change in quantity demanded} = \frac{\Delta Q}{Q_1} \times 100 = \frac{2}{38} \times 100 \approx 5.26\% \]

  3. Calculate the price elasticity of demand:

    \[ \epsilon = \frac{5.26\%}{-5\%} \approx -1.05 \]

The price elasticity of demand for Adam Incorporated's product is approximately \(-1.05\). This indicates that the demand is elastic, as the absolute value of elasticity is greater than 1.

Was this solution helpful?
failed
Unhelpful
failed
Helpful