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Finance Calc Kit
Business

Optimal Price

Calculate the optimal selling price that maximizes profit using marginal cost, price elasticity of demand, and price-quantity data points.

Price and quantity data

$
$
$

Price elasticity of demand

-1.2398

Estimated from two price-quantity observations

Optimal price

$51.70

Profit-maximizing price when demand is elastic

Optimal quantity

216

Estimated units at optimal price

Profit at initial price

$5,000.00

Profit at final price

$7,000.00

Profit at optimal price

$8,991.99

How we calculated this

Open to see each step from your inputs to the result.

  1. 1. Estimate price elasticity of demand

    PED=ln⁡(Q2/Q1)ln⁡(P2/P1)PED = \frac{\ln(Q_2 / Q_1)}{\ln(P_2 / P_1)}

    PED = ln(700.00 / 1,000.00) / ln(20.00 / 15.00) = -1.24

  2. 2. Solve profit-maximizing price

    P∗=MC×PEDPED+1P^* = MC \times \frac{PED}{PED + 1}

    Optimal price = $10.00 * (-1.24 / (-1.24 + 1)) = $51.70

  3. 3. Estimate quantity at optimal price

    Q∗=Q1×(P∗P1)PEDQ^* = Q_1 \times \left(\frac{P^*}{P_1}\right)^{PED}

    Optimal quantity = 1,000.00 * (51.70 / 15.00)^-1.24 = 215.65 units

  4. 4. Compare profit scenarios

    π=(P−MC)×Q\pi = (P - MC) \times Q

    Initial profit = $5,000.00, final profit = $7,000.00, optimal profit = $8,991.99

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How to find the profit-maximizing price

The optimal price is the selling price that maximizes total profit given your marginal cost and how sensitive customer demand is to price changes. This calculator estimates price elasticity of demand from two observed price-quantity points, then solves for the profit-maximizing price when demand is elastic.

Pricing managers use elasticity estimates to decide whether a price increase will raise or lower total profit. Once you know your break-even volume at a given price, compare scenarios with the break-even calculator. To evaluate gross margin at different price points, use the margin calculator. For markup-based pricing from cost, try the markup calculator.

Price elasticity of demand

Using two price-quantity observations on a constant-elasticity demand curve, elasticity is estimated as:

PED=ln⁡(Q2/Q1)ln⁡(P2/P1)PED = \frac{\ln(Q_2 / Q_1)}{\ln(P_2 / P_1)}

When demand is elastic (|PED| > 1), the profit-maximizing price is:

P∗=MC×PEDPED+1P^* = MC \times \frac{PED}{PED + 1}

Quantity at the optimal price follows the same elasticity curve:

Q∗=Q1×(P∗P1)PEDQ^* = Q_1 \times \left(\frac{P^*}{P_1}\right)^{PED}

Worked example

A product sells 1,000 units at $15 and 700 units at $20, with a marginal cost of $10 per unit.

  • PED = ln(700/1000) / ln(20/15) = -1.24
  • Optimal price = $10 * (-1.24 / -0.24) = $51.67
  • Optimal quantity = 1,000 * (51.67/15)^-1.24 = 216 units
  • Optimal profit = ($51.67 - $10) * 216 = $8,994

Profit at the initial price was $5,000 and at the final price was $7,000, so the estimated optimum is substantially higher on this elastic demand segment.

Frequently asked questions

What if demand is inelastic?
When |PED| is 1 or less, total revenue rises as price increases. There is no interior profit maximum on this curve segment, and the calculator will not show an optimal price. In practice, inelastic demand suggests room for price increases.
What is marginal cost?
Marginal cost is the additional cost to produce one more unit. For pricing decisions, use the variable cost per unit rather than average fixed overhead unless you are doing full absorption costing.
How many data points do I need?
This tool uses two price-quantity observations to estimate a constant-elasticity demand curve. More data points improve accuracy; consider A/B price tests or historical sales at different price levels.
Are results stored?
No. All math runs in your browser. Nothing is sent to the server.
Can I share my inputs?
Yes. Changing the fields updates the page URL so you can copy and share it.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.