Economics Midpoint Formula Calculator

Midpoint Formula for Price Elasticity of Demand (PED):

\[ PED = \frac{\%\Delta Q}{\%\Delta P} = \frac{(Q_2 - Q_1)/[(Q_2 + Q_1)/2]}{(P_2 - P_1)/[(P_2 + P_1)/2]} \]

% Change in Quantity:

% Change in Price:

Price Elasticity of Demand (PED):

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1. What is the Midpoint Formula?

The midpoint formula calculates price elasticity of demand (PED) by using the average of initial and new values as the base, which provides more accurate results than simple percentage changes, especially when dealing with large price or quantity changes.

2. How Does the Calculator Work?

The calculator uses the midpoint formula:

\[ PED = \frac{\%\Delta Q}{\%\Delta P} = \frac{(Q_2 - Q_1)/[(Q_2 + Q_1)/2]}{(P_2 - P_1)/[(P_2 + P_1)/2]} \]

Where:

\( Q_1 \) — Initial quantity demanded
\( Q_2 \) — New quantity demanded
\( P_1 \) — Initial price
\( P_2 \) — New price
\( \%\Delta Q \) — Percentage change in quantity
\( \%\Delta P \) — Percentage change in price

Explanation: The formula calculates elasticity by comparing the percentage change in quantity demanded to the percentage change in price, using midpoints to avoid directionality bias.

3. Interpreting PED Results

Details:

|PED| > 1: Elastic demand (quantity change > price change)
|PED| = 1: Unit elastic
|PED| < 1: Inelastic demand (quantity change < price change)
PED = 0: Perfectly inelastic
PED = ∞: Perfectly elastic

4. Using the Calculator

Tips: Enter both initial and new quantity/price values. All values must be non-negative. The calculator will show percentage changes and the resulting PED value.

5. Frequently Asked Questions (FAQ)

Q1: Why use midpoint instead of regular percentage change?
A: The midpoint formula gives the same result regardless of whether price increases or decreases, eliminating directionality bias.

Q2: What does a negative PED value mean?
A: Negative PED is normal - it shows the inverse relationship between price and quantity demanded. We typically use absolute value for interpretation.

Q3: When is demand considered elastic?
A: When |PED| > 1, meaning quantity demanded changes by a larger percentage than price.

Q4: What factors affect elasticity?
A: Availability of substitutes, necessity vs luxury, time horizon, and proportion of income spent on the good.

Q5: How is this different from arc elasticity?
A: The midpoint formula is actually a specific case of arc elasticity calculation between two points on the demand curve.