How the Optimal Price Calculator works
This calculator finds the profit-maximizing price for a product using the standard economic model of monopolistic pricing: marginal cost plus a markup that depends on how price-sensitive demand is. It applies the inverse-elasticity pricing rule taught in microeconomics and used in pricing strategy work, to the numbers you enter.
The formula
For a marginal cost MC and the absolute value of price elasticity of demand E (the percent change in quantity demanded divided by the percent change in price), the profit-maximizing price is:
P* = MC × E ÷ (E − 1)
This comes from setting marginal revenue equal to marginal cost for a demand curve with constant elasticity. It only produces a finite answer when demand is elastic (E > 1) — if E is 1 or less, the model implies profit keeps rising as price rises without limit, so there is no interior optimum. Rearranged, the same formula gives the Lerner Index: (P* − MC) ÷ P* = 1 ÷ E, the profit-maximizing price-cost margin.
Worked example
Take a marginal cost of $20 and a demand elasticity of 2 (a 1% price change moves quantity demanded about 2% in the opposite direction). The optimal price is $20 × 2 ÷ (2 − 1) = $40, a 100% markup over cost. If you currently charge $50 and sell about 800 units, the constant-elasticity demand curve implied by that elasticity projects roughly 1,250 units at $40 — and a profit of about $25,000, versus about $24,000 at the $50 reference price.
Projecting quantity and profit
To turn the optimal price into a quantity and profit estimate, the calculator anchors a constant-elasticity demand curve at your reference price and quantity: Q = Q0 × (P ÷ P0)−E. This is a standard simplifying assumption, not a guarantee — real demand curves bend, and elasticity itself can shift with price level, season, or competitor moves. Treat the projected quantity and profit as directional estimates, not forecasts.
What moves the optimal price most
- Marginal cost: the optimal price scales directly with marginal cost — a higher cost to produce one more unit raises the optimal price by the same multiplier, E ÷ (E − 1).
- Elasticity magnitude: the closer E is to 1, the larger the markup the formula supports; as E grows large (very price-sensitive customers), the markup shrinks toward zero and the optimal price approaches marginal cost.
- Reference price and quantity: these don't change the optimal price itself, but they anchor the demand curve used to project quantity sold and profit at that price.
What this model does not include
The inverse-elasticity rule prices off marginal cost only — fixed costs don't change with the next unit sold, so they don't affect the profit-maximizing price mathematically (though they still determine whether the business is profitable overall). The model also assumes you are a single price-setter facing a known, stable elasticity; it does not model competitor reactions, price discrimination across customer segments, psychological price points, or legal constraints on pricing. Use it as a starting estimate, not a final pricing decision.