Apply the average variable cost formula (AVC = TVC / Q) alongside AFC, ATC and the marginal cost formula. Plot the whole cost-curve family from a cost table or a TC(Q) polynomial and read off the shutdown price (minimum AVC) and the break-even price.
The Cost Curve Family Plotter turns a short-run cost table or a total-cost polynomial into the full family of production cost curves. Enter quantity with fixed and variable cost, or the four coefficients of TC(Q) = a3Q^3 + a2Q^2 + a1Q + a0, and see AFC = TFC/Q, AVC = TVC/Q, ATC = TC/Q and marginal cost plotted on one chart.
The plot annotates exactly where marginal cost cuts AVC and ATC — the shutdown price and the break-even price — and a six-step derivation shows the arithmetic behind every column.
Average variable cost is total variable cost divided by output: AVC = TVC / Q. It is undefined at zero output, and its minimum value is the short-run shutdown price.
Marginal cost is the change in total cost per extra unit. From a cost table, MC = (TC this row - TC previous row) / (Q this row - Q previous row). From a total-cost polynomial, marginal cost is the derivative MC(Q) = 3a3Q^2 + 2a2Q + a1.
The shutdown price is the minimum of the AVC curve. Below it a firm cannot cover even its variable costs, so it produces nothing in the short run. The break-even price is the minimum of ATC.
While marginal cost is below an average curve it pulls that average down, and once it rises above the average it pulls the average up. The average therefore turns exactly where MC crosses it, which is its minimum point.
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