3.  (9)  Suppose a pizzeria, appropriately named, “MPA = Master’s of Pizza Administration” (which has unfortunately occasionally been confused with the “Master’s of Propane Administration”) sells 500 cheese pizzas when the price is $10/pizza, and 1,100 cheese pizzas when the price is $8/pizza 
a.  (3) Use these figures to calculate the price elasticity of demand for cheese pizzas.
	Price elasticity is the change in percentage of quantity/change in percentage of price


To calculate the **price elasticity of demand (PED)**, we use the formula:

\[
\text{Price Elasticity of Demand (PED)} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}
\]

### Step 1: Calculate the percentage change in quantity demanded
The initial quantity ($ Q_1 $) is 500 pizzas, and the new quantity ($ Q_2 $) is 1,100 pizzas. The percentage change in quantity is:

\[
\% \text{ change in quantity} = \frac{Q_2 - Q_1}{Q_1} \times 100
\]

Substituting the values:

\[
\% \text{ change in quantity} = \frac{1,100 - 500}{500} \times 100 = \frac{600}{500} \times 100 = 120\%
\]

### Step 2: Calculate the percentage change in price
The initial price ($ P_1 $) is $10, and the new price ($ P_2 $) is $8. The percentage change in price is:

\[
\% \text{ change in price} = \frac{P_2 - P_1}{P_1} \times 100
\]

Substituting the values:

\[
\% \text{ change in price} = \frac{8 - 10}{10} \times 100 = \frac{-2}{10} \times 100 = -20\%
\]

### Step 3: Calculate the Price Elasticity of Demand
Now, we can substitute these percentage changes into the PED formula:

\[
PED = \frac{120\%}{-20\%} = -6
\]

### Interpretation:
The price elasticity of demand is -6, which indicates that demand is **highly elastic**. A 1% decrease in price results in a 6% increase in the quantity of pizzas demanded.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How does price elasticity impact total revenue for the pizzeria?
2. What factors can make a product more or less elastic?
3. Can the pizzeria use this elasticity to optimize their pricing strategy?
4. How might the elasticity differ for other types of pizza or products?
5. What happens to demand if the price drops to $7?

**Tip**: Highly elastic products have large demand responses to small price changes, so price adjustments should be considered carefully to maximize revenue!

Suppose a pizzeria, appropriately named, “MPA = Master’s of Pizza Administration” sells 500 cheese pizzas when the price is $10/pizza, and 1,100 cheese pizzas when the price is $8/pizza. Use these figures to calculate the price elasticity of demand for cheese pizzas.

Learn how to calculate the price elasticity of demand (PED) for cheese pizzas with detailed steps. The problem involves understanding percentage changes in quantity and price, applying the PED formula, and interpreting the result. A 20% price drop leads to a 120% increase in demand, resulting in a PED of -6, indicating high elasticity. Ideal for students studying economics or business.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation