# Midpoint Method for Calculating Elasticity

When trying to calculate the elasticity of demand using two points on the demand curve, different results can be obtained depending on whether the elasticity is calculated from point A to point B or from point B to point A. The midpoint method for calculating elasticities avoids this confusion and reflects that consumer responses to price changes are identical whether moving from point A to point B or from point B to point A.

## Calculating Elasticity Using the Midpoint Method

The conventional procedure for calculating a percentage change involves dividing the change by the initial level; in contrast, the midpoint method divides the variation by the midpoint of the initial and final points, as shown in the following example:

Let's consider the following points on a demand graph:

**Point A:**Price = 10, Quantity Demanded = 100**Point B:**Price = 15, Quantity Demanded = 80

**Elasticity from point A to point B:**

We use the price elasticity of demand formula:

\[ E_d = \frac{\left( \frac{\text{Final Quantity} - \text{Initial Quantity}}{\text{Initial Quantity}} \right)}{\left( \frac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}} \right)} \]

Substituting the values:

\[ E_d = \frac{\left( \frac{80 - 100}{100} \right)}{\left( \frac{15 - 10}{10} \right)} = \frac{-0.20}{0.50} = -0.4 \]

Therefore, the **elasticity from point A to point B** is **-0.4**.

**Elasticity from point B to point A:**

Now we calculate the elasticity by reversing the points (from B to A):

\[ E_d = \frac{\left( \frac{100 - 80}{80} \right)}{\left( \frac{10 - 15}{15} \right)} = \frac{0.25}{-0.3333} \approx -0.75 \]

Therefore, the **elasticity from point B to point A** is approximately **-0.75**.

Consequently, demand elasticity is not symmetrical. If we calculate from point A to point B, we obtain an elasticity of **-0.4**, while from point B to point A, we get **-0.75**.

This difference is due to the fact that percentage variations are calculated based on a different base for each case. Now let's calculate the elasticity using the midpoint method.

**Price Elasticity of Demand Formula (Midpoint Method):**

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

**E**Price elasticity of demand._{d}:**Q**Quantity demanded at the first point (Point A)._{1}:**Q**Quantity demanded at the second point (Point B)._{2}:**P**Price at the first point (Point A)._{1}:**P**Price at the second point (Point B)._{2}:

This formula measures the sensitivity of quantity demanded to price changes, using the average of quantities and prices to obtain a more accurate elasticity. Note that the numerator is the percentage change in quantity according to the midpoint method, and the denominator is the percentage change according to the midpoint method.

**Now let's take the same two previous points from a demand graph:**

**Point A:**Price = 10, Quantity Demanded = 100**Point B:**Price = 15, Quantity Demanded = 80

**Elasticity from point A to point B (midpoint method):**

We use the price elasticity of demand formula:

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

Substituting the values:

1. Differences:

- \( Q_2 - Q_1 = 80 - 100 = -20 \)
- \( P_2 - P_1 = 15 - 10 = 5 \)

2. Averages:

- \( \frac{Q_1 + Q_2}{2} = \frac{100 + 80}{2} = 90 \)
- \( \frac{P_1 + P_2}{2} = \frac{10 + 15}{2} = 12.5 \)

3. Substitution into the formula:

\[ E_d = \frac{-20 / 90}{5 / 12.5} = \frac{-0.2222}{0.4} \approx -0.5556 \]

**Elasticity from point B to point A (midpoint method):**

Now we calculate the elasticity by reversing the points (from B to A):

1. Differences:

- \( Q_1 - Q_2 = 100 - 80 = 20 \)
- \( P_1 - P_2 = 10 - 15 = -5 \)

2. Averages:

- \( \frac{Q_1 + Q_2}{2} = \frac{100 + 80}{2} = 90 \)
- \( \frac{P_1 + P_2}{2} = \frac{10 + 15}{2} = 12.5 \)

3. Substitution into the formula:

\[ E_d = \frac{20 / 90}{-5 / 12.5} = \frac{0.2222}{-0.4} \approx -0.5556 \]

Therefore, the demand elasticity is approximately **-0.5556** both from point A to point B and from point B to point A, which shows that elasticity is symmetrical when using the midpoint method.

Since the midpoint method yields the same result regardless of the direction of the change, it reflects a clearer outcome and better illustrates that consumers respond to increases or decreases in consumption by the same magnitude, regardless of whether moving from point A to point B or from point B to point A.