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:**

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

Taking the absolute value, we have $$0.3$$.

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

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

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

Now, substituting these values into the elasticity formula:

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

This result indicates that the demand is elastic since the elasticity of demand is greater than 1. An elasticity of 1.5 suggests that a 1% increase in price would lead to a 1.5% decrease in quantity demanded, highlighting the sensitivity of consumers to price changes.

Understanding these calculations allows businesses to make informed pricing decisions based on consumer responsiveness, ultimately impacting revenue and market strategy.

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 reduced 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) = \(\frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Price}}\)

To find the percentage change in quantity demanded, we use the formula:

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

Substituting the values:

\(\%\text{ Change in Quantity Demanded} = \frac{2000 - 1400}{1400} \times 100 = \frac{600}{1400} \approx 0.429\)

Next, we calculate the percentage change in price using a similar formula:

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

Substituting the values:

\(\%\text{ Change in Price} = \frac{5 - 6}{6} \times 100 = \frac{-1}{6} \approx -0.167\)

Since we are interested in the absolute value, we take the positive value of the percentage change in price, which is approximately 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 values can differ based 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 for both quantity and price in the denominator.

By averaging the original and new quantities and prices, we can refine our calculations to ensure that the elasticity of demand remains consistent regardless of whether the price is increasing or decreasing. This method will provide a more accurate representation of how sensitive the demand is to price changes.