To determine the type of demand for Sam's pizzas, we need to calculate the price elasticity of demand. The price elasticity of demand measures how much the quantity demanded of a good responds to a change in price.
Let's go through the steps:
1. Calculate the percentage change in price:
- The initial price of the pizza is [tex]$6.
- The new price of the pizza is $[/tex]5.
- The percentage change in price is given by the formula:
[tex]\[
\text{Percentage Change in Price} = \frac{\text{New Price} - \text{Initial Price}}{\text{Initial Price}} \times 100
\][/tex]
Plugging in the values:
[tex]\[
\text{Percentage Change in Price} = \frac{5 - 6}{6} \times 100 = -16.67\%
\][/tex]
2. Calculate the percentage change in quantity demanded:
- The initial sales are 400 pizzas.
- The new sales are 600 pizzas.
- The percentage change in quantity demanded is given by the formula:
[tex]\[
\text{Percentage Change in Quantity Demanded} = \frac{\text{New Sales} - \text{Initial Sales}}{\text{Initial Sales}} \times 100
\][/tex]
Plugging in the values:
[tex]\[
\text{Percentage Change in Quantity Demanded} = \frac{600 - 400}{400} \times 100 = 50\%
\][/tex]
3. Calculate the price elasticity of demand:
- Price elasticity of demand is calculated using the formula:
[tex]\[
\text{Elasticity} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}
\][/tex]
Plugging in the values:
[tex]\[
\text{Elasticity} = \frac{50\%}{-16.67\%} \approx -3.00
\][/tex]
The negative sign indicates that the relationship between price and quantity demanded is inverse, which is usually the case for demand.
4. Interpret the elasticity:
- If the absolute value of elasticity is equal to 1, the demand is unit elastic.
- If the absolute value of elasticity is less than 1, the demand is inelastic.
- If the absolute value of elasticity is greater than 1, the demand is elastic.
In this case, the elasticity is approximately -3.00 in absolute terms, which is greater than 1.
Therefore, the demand for Sam's pizzas in this range is c. elastic.
