Calculator Inputs
Enter demand, cost, tax, and constraint values. The result appears above this form after submission.
Example Data Table
This worked example uses the same model as the calculator so you can verify the logic before entering your own figures.
| Example item | Value |
|---|---|
| Demand intercept (a) | 120.00 |
| Demand slope (b) | 1.50 |
| Variable cost (v) | 30.00 |
| Quadratic cost (c) | 0.20 |
| Fixed cost (F) | 500.00 |
| Tax rate | 20.00% |
| Capacity limit | 50.00 |
| Optimal quantity | 26.47 |
| Optimal price | 80.29 |
| Operating profit | 691.18 |
| After-tax profit | 552.94 |
| Break-even quantities | 6.31 and 46.63 |
Formula Used
Demand equation: P(q) = a - bq
Revenue function: R(q) = P(q) × q = aq - bq2
Cost function: C(q) = F + vq + cq2
Operating profit: π(q) = R(q) - C(q)
After-tax profit: πafter tax = π(q) × (1 - tax rate) when profit is positive.
Marginal revenue: MR = a - 2bq
Marginal cost: MC = v + 2cq
Optimal interior quantity: q* = (a - v) / [2(b + c)]
The calculator checks the interior solution, zero output, and the feasible capacity edge. It returns whichever quantity gives the highest operating profit.
How to Use This Calculator
- Enter the demand intercept to represent the starting market price.
- Enter the demand slope to show how price falls with quantity.
- Provide variable cost, quadratic cost, and fixed cost values.
- Add the applicable tax rate and production capacity limit.
- Choose graph points and decimal places for the output style.
- Press the calculate button to display results above the form.
- Review the table, break-even levels, and the plotted curves.
- Download the summary as CSV or PDF when needed.
Frequently Asked Questions
1. What does this calculator maximize?
It maximizes operating profit using a linear demand model and a cost model with fixed, variable, and quadratic terms. It also reports after-tax profit, margins, and break-even quantities for practical interpretation.
2. Why are marginal revenue and marginal cost included?
They help explain why the recommended quantity is optimal. For an interior maximum, marginal revenue and marginal cost should be equal or nearly equal after rounding.
3. What is the quadratic cost coefficient used for?
It models rising production difficulty. As output increases, extra units can become more expensive because of overtime, equipment strain, waste, or congestion.
4. What happens if capacity is very high?
The calculator still checks market feasibility. If the selling price would fall to zero before full capacity, the feasible quantity range is shortened automatically.
5. Why can there be two break-even quantities?
With curved revenue and curved cost, profit can rise above zero and later fall back below zero. That creates one lower break-even point and one upper break-even point.
6. Does the calculator support taxes?
Yes. It reports both operating profit and after-tax profit. The tax adjustment is applied only when the operating profit is positive.
7. Is this tool useful for pricing strategy?
Yes. Because price comes from the demand equation, the result gives both the output level and the implied selling price that jointly support the best profit outcome.
8. Can I use decimals and non-integer quantities?
Yes. The model accepts decimal inputs and can return fractional quantities. That is helpful for continuous analysis, estimation, or planning before rounding to operational units.