How this calculator works
Two observations fit Q = a + bP with b negative. With constant unit cost c, maximise (P - c)Q over non-negative quantity. Fixed costs are excluded from contribution and do not affect the interior optimum. The separate elasticity modes assume constant signed elasticity below -1; they do not reuse the midpoint elasticity from the two observations. If marginal cost reaches the choke price, the linear model chooses no production.
Formula
b = (Q2 - Q1) / (P2 - P1); a = Q1 - bP1; choke price = -a / b. Interior optimum P* = (choke price + c) / 2; Q* = (a + bc) / 2. For constant elasticity E < -1, P* = c / (1 + 1 / E).
Worked example
At $50 demand is 100 units; at $60 it is 80 units. The fitted curve is Q = 200 - 2P. With marginal cost $20, the optimum is $60 and 80 units, giving $3,200 of contribution. With constant elasticity -2 and marginal cost $20, the separate model gives $40.
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Frequently asked questions
Is this a forecast?
It is a model result. Two observations do not establish a stable demand curve or isolate price from seasonality and competing changes.
Can I infer optimal quantity from elasticity alone?
No. Elasticity and marginal cost identify the model price, but a demand scale or quantity observation is needed for volume.
Can every field be solved backwards?
The constant-elasticity relation solves for price, cost or elasticity. Two observed demand points are treated as evidence, not recovered from a single optimal price, because that inverse is not unique.