Percentage Change and Price Elasticity of Demand: Videos & Practice Problems

Understanding price elasticity of demand is crucial for analyzing how changes in price affect consumer behavior. The formula for calculating price elasticity of demand involves the percentage change in quantity demanded divided by the percentage change in price. This can be expressed as:

$$E_d = \frac{\%\Delta Q_d}{\%\Delta P}$$

Where:

• $$E_d$$ is the price elasticity of demand.
• $$\%\Delta Q_d$$ is the percentage change in quantity demanded.
• $$\%\Delta P$$ is the percentage change in price.

To calculate the percentage change, we use the formula:

$$\%\Delta = \frac{\text{New} - \text{Original}}{\text{Original}}$$

In a practical example, consider a pizza company that raises the price of its lunch special from $5 to $6, resulting in a decrease in weekly demand from 2,000 to 1,400 lunch specials. To find the price elasticity of demand, we first calculate the percentage change in quantity demanded:

1. **Calculate the change in quantity demanded:**

$$\%\Delta Q_d = \frac{1400 - 2000}{2000} = \frac{-600}{2000} = -0.3$$

2. **Calculate the change in price:**

$$\%\Delta P = \frac{6 - 5}{5} = \frac{1}{5} = 0.2$$

3. **Calculate the elasticity of demand:**

$$E_d = \frac{-0.3}{0.2} = -1.5$$

Since we are interested in the absolute value, we take 1.5. An elasticity greater than 1 indicates that the demand is elastic, meaning consumers are sensitive to price changes. In this case, the elasticity of demand is 1.5, suggesting that a price increase leads to a proportionally larger decrease in quantity demanded.

This example illustrates how different price changes can yield varying elasticities, emphasizing the importance of understanding consumer responsiveness in pricing strategies.

To determine the price elasticity of demand, we analyze how the quantity demanded of a product changes in response to a change in its price. In this scenario, a pizza company's lunch special is priced at $6, with a weekly demand of 1,400 specials. When the price is lowered to $5, the demand increases to 2,000 specials. The price elasticity of demand (PED) can be calculated using the formula:

Price Elasticity of Demand (PED) = \(\frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Price}}\)

First, we calculate the percentage change in quantity demanded. The formula for percentage change is:

\(\%\text{ Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\)

For quantity demanded:

New quantity = 2,000

Original quantity = 1,400

Percentage change in quantity demanded = \(\frac{2,000 - 1,400}{1,400} = \frac{600}{1,400} \approx 0.429\) or 42.9%.

Next, we calculate the percentage change in price:

New price = $5

Original price = $6

Percentage change in price = \(\frac{5 - 6}{6} = \frac{-1}{6} \approx -0.167\) or -16.7%.

Since we are interested in the absolute value for elasticity, we take the positive value of the price change, which is 0.167.

Now, substituting these values into the elasticity formula gives:

PED = \(\frac{0.429}{0.167} \approx 2.569\).

This indicates that the demand is elastic, meaning that the quantity demanded is quite responsive to price changes. However, it is important to note that the elasticity can yield different results depending on the direction of the price change due to the original values used in the calculations. To achieve consistency, it is advisable to use the average of the original and new values in the denominator for both quantity and price changes.

In summary, the price elasticity of demand is a crucial concept in understanding consumer behavior in response to price changes, and using averages in calculations can provide a more reliable measure of elasticity.