Elasticity and the Midpoint Method: Videos & Practice Problems

To calculate price elasticity of demand using the midpoint method, use the formula: $\frac{∆Q}{∆P}$, where $Q$ is quantity demanded and $P$ is price. This method ensures consistent elasticity results regardless of price changes. A calculated elasticity greater than 1 indicates elastic demand, meaning quantity demanded is sensitive to price changes, while less than 1 indicates inelastic demand.

The Midpoint Method

The midpoint method for calculating price elasticity of demand provides a consistent approach to determine how quantity demanded responds to price changes, regardless of whether the price is increased or decreased. The formula for price elasticity of demand using this method is still based on the percentage change in quantity demanded divided by the percentage change in price, but it modifies how these percentage changes are calculated.

To compute the percentage changes, instead of using the original values, the midpoint method utilizes the average of the two quantities and the average of the two prices. This adjustment helps avoid discrepancies that can arise from using different starting points for the calculations. The formula can be expressed as:

\[E_d = \frac{\left( \frac{Q_2 - Q_1}{\frac{Q_1 + Q_2}{2}} \right)}{\left( \frac{P_2 - P_1}{\frac{P_1 + P_2}{2}} \right)}\]

Where \(E_d\) is the price elasticity of demand, \(Q_1\) and \(Q_2\) are the initial and new quantities demanded, and \(P_1\) and \(P_2\) are the initial and new prices.

To illustrate this method, consider a pizza company that raises its lunch special price from \$5 to \$6, resulting in a decrease in quantity demanded from 2,000 to 1,400 specials. The steps to calculate the elasticity of demand are as follows:

1. **Calculate the changes**: Subtract the two quantities to find the change in quantity demanded (600) and the change in price (1).

2. **Sum the quantities and prices**: Add the two quantities (3,400) and the two prices (11).

3. **Find the averages**: Divide the sums from step 2 by 2 to get the average quantity (1,700) and average price (5.50).

4. **Calculate the percentage changes**: Divide the change in quantity (600) by the average quantity (1,700) to get a percentage change in quantity demanded of approximately 0.353 (or 35.3%). Similarly, divide the change in price (1) by the average price (5.50) to get a percentage change in price of approximately 0.182 (or 18.2%).

Finally, substitute these values into the elasticity formula:

\[E_d = \frac{0.353}{0.182} \approx 1.934\]

This result indicates that the demand is elastic since the elasticity value is greater than 1. This means that the quantity demanded is quite sensitive to price changes, confirming that a small price increase leads to a relatively larger decrease in quantity demanded.

By following these steps, the midpoint method simplifies the calculation of elasticity, ensuring accuracy and consistency in determining how demand reacts to price fluctuations.

Assume that the price elasticity of demand for cigarettes is 0.4. If a pack of cigarettes currently costs \$6 and the government aims to decrease smoking by 20 percent, by how much should it increase the price?

• A. \$1.20
• B. \$2.40
• C. \$3.00
• D. \$4.80

Answer: (C)

Here’s what students ask on this topic:

What is the midpoint method in calculating price elasticity of demand?

The midpoint method is a technique used to calculate the price elasticity of demand, ensuring consistent results regardless of whether the price increases or decreases. The formula is:

$\frac{∆Q}{∆P}$

where $Q$ is the quantity demanded and $P$ is the price. Instead of using the original values, the midpoint method uses the average of the initial and final quantities and prices. This approach avoids discrepancies in elasticity calculations that can arise from different starting points.

How do you calculate the percentage change in quantity demanded using the midpoint method?

To calculate the percentage change in quantity demanded using the midpoint method, follow these steps:

1. Subtract the initial quantity from the final quantity to find the change in quantity ($∆Q$).

2. Sum the initial and final quantities and divide by 2 to find the average quantity.

3. Divide the change in quantity by the average quantity and multiply by 100 to get the percentage change.

Mathematically, it is represented as:

$\frac{∆Q}{\frac{Q}{}}$₁ + Q₂2 × 100

Why is the midpoint method preferred over the traditional method for calculating elasticity?

The midpoint method is preferred over the traditional method because it provides consistent elasticity results regardless of whether the price increases or decreases. The traditional method can yield different elasticity values depending on the direction of the price change, leading to potential inaccuracies. By using the average of the initial and final quantities and prices, the midpoint method eliminates this discrepancy, ensuring a more reliable and symmetric measure of elasticity.

What does an elasticity greater than 1 indicate in the midpoint method?

An elasticity greater than 1, calculated using the midpoint method, indicates that the demand for a product is elastic. This means that the quantity demanded is highly sensitive to changes in price. In other words, a small change in price leads to a relatively larger change in the quantity demanded. Elastic demand typically occurs for goods that have many substitutes or are not necessities.

Can you provide an example of calculating price elasticity of demand using the midpoint method?

Sure! Let's say a pizza company raises the price of its lunch special from \$5 to \$6, and the weekly demand drops from 2,000 to 1,400 lunch specials. Using the midpoint method:

1. Change in quantity demanded: 2,000 - 1,400 = 600

2. Average quantity: (2,000 + 1,400) / 2 = 1,700

3. Change in price: \$6 - \$5 = \$1

4. Average price: (\$6 + \$5) / 2 = \$5.50

5. Percentage change in quantity demanded: (600 / 1,700) × 100 ≈ 35.3%

6. Percentage change in price: (1 / 5.50) × 100 ≈ 18.2%

7. Elasticity of demand: 35.3% / 18.2% ≈ 1.94

Since the elasticity is greater than 1, the demand is elastic.