Enter Values
Cost Function Reference
TC = FC + aQ + bQ²
MC = a + 2bQ |
AVC = a + bQ |
ATC = FC/Q + a + bQ
Profit max: P = MC → Q* = (P − a) / (2b)
Cost Curves & Market Price
Firm Decision
Produce
Earning economic profit
Profit / Loss
$12.50
Detailed Results
Optimal Output (Q*)
15.00
Total Revenue
$375.00
Total Cost
$362.50
ATC at Q*
$24.17
AVC at Q*
$17.50
MC at Q*
$25.00
Break-Even Price
$24.1421
Shutdown Price
$10.0000
Decision Rules
| Condition | Decision |
|---|---|
| P > min ATC | Produce (economic profit) |
| P = min ATC | Break-even (zero economic profit) |
| min AVC < P < min ATC | Produce (minimizing losses) |
| P < min AVC | Shut Down |
Formula Breakdown
Profit Max: P = MC → Q* = (P − a) / (2b)
Model Assumptions
- Firm is a price taker (perfectly competitive market)
- Cost function: TC = FC + aQ + bQ² (quadratic variable cost)
- Single product produced
- Short-run analysis (fixed costs are sunk and cannot be avoided)
- Firm maximizes profit by setting P = MC
- For educational purposes. Not financial advice. Market conventions simplified.
Understanding the Competitive Firm's Decision
How Does a Competitive Firm Maximize Profit?
A perfectly competitive firm is a price taker: it sells its product at the market price and cannot influence that price. The firm maximizes profit by choosing the output quantity where Price = Marginal Cost (P = MC). At this quantity, the revenue from selling one more unit exactly equals the cost of producing it.
Profit Maximization Rule
P = MC = a + 2bQ
Q* = (P − a) / (2b)
Produce where price equals marginal cost (if P > min AVC)
Q* = (P − a) / (2b)
Produce where price equals marginal cost (if P > min AVC)
The Shutdown Decision
Continue Producing
P > min AVC
Revenue covers all variable costs and at least some fixed costs. Producing reduces the firm's losses compared to shutting down. At P = min AVC exactly, the firm is indifferent.
Shut Down
P < min AVC
Revenue cannot even cover variable costs. The firm minimizes losses by producing nothing and paying only fixed costs.
Key Price Thresholds
- Shutdown Price (min AVC = a): The lowest price at which the firm will produce any output at all.
- Break-Even Price (min ATC = 2√(FC × b) + a): The price at which economic profit is exactly zero.
- Between these prices: The firm produces at a loss, but the loss is smaller than fixed costs alone.
Long-Run Equilibrium: In the long run, free entry and exit drives the market price to the break-even level. All firms earn zero economic profit, but they still earn normal accounting profit sufficient to keep resources in their current use.
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Frequently Asked Questions
A perfectly competitive firm maximizes profit by producing the quantity where price equals marginal cost (P = MC), provided that price is at least as high as minimum average variable cost. If P < min AVC, the firm should shut down and produce zero. For a cost function TC = FC + aQ + bQ², the marginal cost is MC = a + 2bQ, so the optimal quantity is Q* = (P − a) / (2b).
The shutdown rule states that a firm should cease production in the short run when the market price falls below the minimum average variable cost (min AVC). At prices below min AVC, the firm cannot even cover its variable costs, meaning it loses more by producing than by shutting down. When shut down, the firm's loss equals its fixed costs only.
The shutdown price is the minimum average variable cost (min AVC) — the lowest price at which the firm will produce anything. The break-even price is the minimum average total cost (min ATC) — the price at which the firm earns zero economic profit. Between these two prices, the firm produces at a loss but that loss is smaller than its fixed costs, so producing is still the better choice.
In the long run, free entry and exit drives economic profit to zero. When existing firms earn positive economic profit, new firms enter the market, increasing supply and driving the price down. When firms earn losses, some exit, decreasing supply and raising the price. This process continues until price equals minimum ATC and all firms earn exactly zero economic profit (though they still earn normal accounting profit).
Accounting profit equals total revenue minus explicit costs (actual payments for inputs). Economic profit equals total revenue minus both explicit and implicit costs (opportunity costs of the owner's resources, including time and capital). A firm earning zero economic profit is still earning enough to cover all opportunity costs — this is called "normal profit." Economic profit is the relevant measure for entry/exit decisions.
A competitive firm's short-run supply curve is the portion of its marginal cost (MC) curve that lies above the minimum average variable cost (min AVC). Below min AVC, the firm shuts down and supplies zero. Above min AVC, the firm produces where P = MC, so each price maps to a specific quantity along the MC curve: Q = max(0, (P − a) / (2b)). This is why the supply curve slopes upward — higher prices induce more output.
Disclaimer
This calculator is for educational purposes only and uses a simplified quadratic cost function. Real-world firms face more complex cost structures, market dynamics, and regulatory considerations. Results should be used for learning about microeconomic theory, not for actual business decisions.
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