Price Elasticity of Demand Calculator
Calculate midpoint arc and point price elasticity from two price and quantity observations, classify demand and find the profit-maximising price.
Demand is inelastic (|E| = 0.45 < 1). Volume moves less than price, so raising price raises revenue — the limit is what customers and competitors will tolerate.
| Scenario | Price | Quantity | Revenue | Contribution at MC |
|---|---|---|---|---|
| Before | $70.00 | 2,800 | $196,000 | $126,000 |
| After | $60.00 | 3,000 | $180,000 | $105,000 |
| Change | -$10.00 | 200 | -$16,000 | -$21,000 |
The price cut moves revenue by -$16,000 (-8.2%), and contribution by -$21,000 at a marginal cost of $25.00. Revenue is not profit — an elastic product can win volume and still lose money once the extra units are costed.
The Lerner mark-up rule only has a solution when demand is elastic (E below −1) and marginal cost is above zero. At |E| ≤ 1 the rule says price should rise until demand becomes elastic, so no finite optimum exists from these two data points alone.
arc E = ((Q₂−Q₁) ÷ ((Q₁+Q₂)÷2)) ÷ ((P₂−P₁) ÷ ((P₁+P₂)÷2)) · point E = (ΔQ÷ΔP) × (P÷Q) · P* = MC × E ÷ (E+1)
Worked example from an introductory economics text: price falls from $70.00 to $60.00 while quantity rises from 2,800 to 3,000. % change in quantity = 200 ÷ 2,900 = 6.90%; % change in price = −10 ÷ 65 = -15.38%; elasticity = -0.45 — reported in the textbook as an absolute value of 0.45, so demand is inelastic over that range. With a marginal cost of $10.00 and E = −2 the Lerner rule gives P* = 10 × (−2 ÷ −1) = $20.00, a Lerner index of 0.50.
The midpoint (arc) form is the one to quote, because it gives the same answer whether price went up or down; the point form depends on which end you measure from, which is why the base is selectable. Two observations only isolate elasticity if nothing else changed between them — season, promotion, competitor price, stock availability. All maths runs locally in your browser and nothing is uploaded. Estimates for planning, not pricing or financial advice.
What is the Price Elasticity of Demand Calculator?
Price elasticity of demand tells you how much volume moves when price moves. This calculator takes two observations — a price and the quantity sold at that price, before and after a change — and returns the midpoint arc elasticity, which gives the same answer whether the price went up or down, alongside the point elasticity measured from either end.
- Midpoint (arc) elasticity, symmetric in both directions
- Point elasticity from either the initial or the final observation
- Elastic, unit-elastic or inelastic classification with an explanation
- Revenue and contribution before, after and the change between
- Profit-maximising price and Lerner index when demand is elastic
- Identical prices show a dash rather than dividing by zero
How to use the Price Elasticity of Demand Calculator
- 1
Enter the original price and the quantity sold at that price.
- 2
Enter the new price and the quantity sold after the change.
- 3
Read the midpoint arc elasticity — the figure to quote — and the classification beneath it.
- 4
Switch the base point to see how point elasticity differs measured from either end.
- 5
Add your marginal cost to get the profit-maximising price from the Lerner rule.
About the Price Elasticity of Demand Calculator
Price elasticity of demand tells you how much volume moves when price moves. This calculator takes two observations — a price and the quantity sold at that price, before and after a change — and returns the midpoint arc elasticity, which gives the same answer whether the price went up or down, alongside the point elasticity measured from either end.
It classifies the result as elastic, unit-elastic or inelastic, shows what happened to revenue and contribution on both sides of the move, and where demand is elastic it applies the Lerner mark-up rule to suggest the profit-maximising price from your marginal cost.
All the arithmetic runs locally in your browser and nothing is uploaded, so you can model real prices and volumes safely. Two observations only isolate elasticity if nothing else changed between them — no promotion, no seasonal swing, no competitor move, no stock-out — so treat the result as a planning estimate rather than pricing advice.
Frequently asked questions
What is the midpoint formula for price elasticity?
E = ((Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2)) ÷ ((P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2)). Using the average of the two points as the base is what makes the answer identical whether you measure the move upward or downward, which the simple percentage-change formula does not.
What does an elasticity of −0.45 mean?
It means demand is inelastic: a 1% price rise loses only 0.45% of volume, so raising price increases revenue. The minus sign just reflects that price and quantity move in opposite directions, which is why elasticity is usually quoted as an absolute value.
Is elastic or inelastic demand better?
Neither is inherently better, but they call for opposite moves. With inelastic demand you have room to raise price; with elastic demand a price cut can win enough volume to grow revenue. What matters is profit, not revenue — an elastic product can win volume and still lose money once the extra units are costed.
How do you find the profit-maximising price from elasticity?
The Lerner mark-up rule gives P = MC × E ÷ (E + 1) for elasticity below −1. At E = −2 and a marginal cost of 10 that is 10 × (−2 ÷ −1) = 20, a 100% mark-up and a Lerner index of 0.5. The rule has no finite solution when demand is inelastic.
Why is my elasticity positive?
A positive elasticity means quantity moved in the same direction as price. Occasionally that reflects a genuine Veblen or Giffen effect, but far more often something else changed at the same time — a promotion, a season, a competitor's price, a stock-out. Two observations cannot separate those effects.
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