Optimal Price Calculator — Profit-Maximising Pricing
Determine the price that maximises profit given your marginal cost and the price elasticity of demand, using the Lerner markup rule. Optionally enter current price and volume to see the demand curve and estimated profit improvement.
P* = MC × |ε| / (|ε| − 1) — the Lerner optimal price
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Denominator (|ε| − 1)
2.5 − 1 = 1.5 - 2
Numerator (MC × |ε|)
20 × 2.5 = 50 - 3
Profit-maximising price P*
50 ÷ 1.5 = 33.33P* = MC × |ε| / (|ε| − 1) — the Lerner pricing rule.
How does this calculator work?
Profit-maximising price P* = MC × |ε| / (|ε| − 1) applies when |ε| > 1. Optimal markup over MC = 1 / (|ε| − 1); Lerner index = 1 / |ε|. Enter marginal cost and price elasticity of demand — optionally add current price and volume to see the demand curve and profit-lift estimate.
Formula
How this is calculated
The profit-maximising price is found where marginal revenue equals marginal cost (MR = MC). For a firm facing a constant-elasticity demand curve Q = A × P^(−|ε|), marginal revenue is MR = P × (1 − 1/|ε|), and setting MR = MC gives the Lerner optimal price P* = MC × |ε| / (|ε| − 1). This can be rewritten as a markup formula: the optimal price-cost margin (Lerner index) is L = (P* − MC) / P* = 1/|ε|. The lower the price elasticity (closer to 1), the higher the optimal markup; the more elastic demand is, the closer the optimal price is to marginal cost.
This result requires |ε| > 1 (elastic demand). If demand is inelastic (|ε| ≤ 1), raising price always raises revenue, so there is no interior profit-maximising price — other constraints (regulation, capacity, competition) determine the limit. In competitive markets, competition drives prices toward MC and the formula gives large markups that cannot be sustained.
If you supply a current price and quantity, the calculator anchors a constant-elasticity demand curve at that point (Q = Q₀ × (P/P₀)^(−|ε|)) and estimates current and optimal profit, as well as the quantity change implied by moving to P*. Treat the profit lift as an upper bound — in practice, shifting the price may change consumer behaviour in ways not captured by a simple elasticity.
Frequently asked questions
Common methods include: (1) running a price experiment and measuring the quantity response; (2) econometric regression of historical sales vs price data; (3) conjoint analysis surveys; (4) using industry-level academic estimates as a starting point. Typical retail elasticities range from −1.5 (broadly inelastic) to −4 or more (very price-sensitive categories like commodity goods).
Strictly, the Lerner rule derives from a monopoly or monopolistically competitive market where the firm faces a downward-sloping demand curve. In perfect competition, the firm faces a flat demand curve (|ε| → ∞) and P* = MC. For competitive businesses, the key is the elasticity of demand for your specific brand or product, not the market as a whole — brand loyalty reduces your effective elasticity.
The formula uses marginal cost (variable cost per additional unit), not average total cost. Fixed costs do not affect the optimal price in this model, but they determine whether it is profitable to operate at all. If marginal costs change with output, you need to use the marginal cost at the profit-maximising quantity, which requires solving the full MR = MC condition numerically.
Also known as
TG we-Calculate Editorial Team. (2026). Optimal Price Calculator — Profit-Maximising Pricing [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/optimal-price-calculator
TG we-Calculate Editorial Team. "Optimal Price Calculator — Profit-Maximising Pricing." TG we-Calculate. 2026. https://we-calculate.com/calculator/optimal-price-calculator.
TG we-Calculate Editorial Team, "Optimal Price Calculator — Profit-Maximising Pricing," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/optimal-price-calculator
@misc{wecalculate_optimal_price_calculator, title = {Optimal Price Calculator — Profit-Maximising Pricing}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/optimal-price-calculator}}, year = {2026}, note = {TG we-Calculate} }
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