The more price-sensitive your customers (the more negative the elasticity), the lower the optimal markup. If demand is inelastic (−1 < e < 0), raising the price increases profit until demand becomes elastic.
How to use the Optimal Price Calculator
- Marginal cost per unit
- Initial price
- Initial quantity sold
- New price
- New quantity sold
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter your marginal cost and two observed price/quantity points.
Inputs explained
| Field | What to enter |
|---|---|
| Marginal cost per unit | Amount in your currency |
| Initial price | Amount in your currency |
| Initial quantity sold | A number |
| New price | Amount in your currency |
| New quantity sold | A number |
What each result means
- Price elasticity of demand = (([New quantity sold] – [Initial quantity sold])÷(([New quantity sold] + [Initial quantity sold])÷2))÷(([New price] – [Initial price])÷(([New price] + [Initial price])÷2))
- Profit at initial price = ([Initial price] – [Marginal cost per unit])×[Initial quantity sold]
- Profit at new price = ([New price] – [Marginal cost per unit])×[New quantity sold]
Example values
How the main result changes when Marginal cost per unit changes and everything else stays at the example values above:
| Marginal cost per unit | Optimal price |
|---|---|
| 6 | 14.54 |
| 9 | 21.81 |
| 12 | 29.08 |
| 15 | 36.35 |
| 18 | 43.62 |
| 24 | 58.15 |
Formula
Elasticity e = % change in quantity ÷ % change in price (midpoint method)
Optimal price = MC × e ÷ (1 + e) (only when demand is elastic, e < −1)
Equivalent markup over cost = −1 ÷ (1 + e)
Worked example
Inputs: Marginal cost per unit: $12; Initial price: $20; Initial quantity sold: 1,000; New price: $22; New quantity sold: 850.
Results: Price elasticity of demand = -1.703; Optimal price = $29.08; Optimal markup over marginal cost = 142.31 %; Profit at initial price = $8,000.00; Profit at new price = $8,500.00; Note = Demand is elastic – the optimal price is shown.
Frequently asked questions
How is the optimal price calculated?
Using the inverse elasticity rule: P = MC × e ÷ (1 + e).
Why must demand be elastic?
With inelastic demand, raising the price always increases profit.
How accurate is this?
It assumes constant elasticity; test prices in practice.