Free · Elasticity and market changes

Midpoint Demand Elasticity & Revenue Change

Calculate signed midpoint elasticity for a nonpositive price-demand relationship, plus revenue at both endpoints.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

Price moving from 10 to 20 while quantity moves from 20 to 10 gives midpoint elasticity of −1. Revenue is 200 at both endpoints.

Demand elasticity = [(Q₂ − Q₁)/(Q₂ + Q₁)] / [(P₂ − P₁)/(P₂ + P₁)]; revenue = price × quantity

Worked example

Enter these known values and leave the other values blank.

Initial price
10 USD
Final price
20 USD
Initial quantity demanded
20
Final quantity demanded
10
Signed midpoint demand elasticity
-1
Initial revenue
200 USD
Final revenue
200 USD
Revenue percentage change
0 %

Assumptions and limitations

  • This model accepts nonpositive signed demand elasticity. Positive co-movement cases require a broader demand model.
  • Prices must be positive and distinct. Initial quantity must be positive; final quantity can be zero.
  • Other demand influences should be held constant for an economic interpretation. Two observed endpoints alone do not prove causation.
  • Revenue change uses initial revenue as its denominator; it is separate from the midpoint percentage-change convention.
  • Use matching periods, currency and quantity units. Currency selectors use captured fixed exchange rates, not live rates.

Common questions

Why is demand elasticity negative?

For the modeled relationship, price and quantity move in opposite directions. Classification usually compares the magnitude with one.

What happens if both prices are equal?

The price-change denominator is zero, so this finite elasticity calculation is undefined.

References

Require distinct positive prices, allow zero final demand and keep finite elasticity classification boundaries precise.

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