Short-Run Supply Curve: Marginal Cost and the Shutdown Rule

Each possible price selects a profit-maximizing quantity.

Compare Two Supply Cases

The original cases use a price-taking firm with a usual rising marginal-cost branch, continuously adjustable output and fixed costs that cannot be avoided by shutting down for the period. Variable cost is avoidable at zero output. These assumptions matter: at the shutdown price, operating and producing nothing can both be optimal.

Build the Competitive Supply Rule

For a given market price, compare the best operating choice with zero output. In the usual single-minimum AVC model, price below minimum AVC makes every positive quantity lose variable cost, so the firm shuts down. Above the threshold, the relevant rising MC intersection selects output. At the threshold, include the tie between zero and the shutdown-point quantity. Add quantities across firms at the same price to obtain market supply.

Distinguish a Movement from a Shift

Supply connects possible prices with quantities the firm would choose, holding technology, input prices and other relevant costs fixed. A higher own price moves along this supply relationship. A change in marginal production cost can shift it. For a nonconvex cost curve, an MC intersection is only a candidate; verify that it beats other operating quantities and shutdown rather than selecting any intersection.

Include the Shutdown-Price Tie

At the exact minimum of AVC, the best positive output covers variable cost but contributes nothing toward unavoidable fixed cost. It earns the same economic profit as zero output: the negative of that fixed cost. The standard graph may draw the positive endpoint, but the full supply relationship includes both choices at that one price. Just below the threshold, every positive output is strictly worse than shutdown.

Separate Fixed Cost from a Unit Tax

Increasing an unavoidable fixed cost shifts ATC and lowers profit but changes neither MC nor AVC. Because the cost is paid whether the firm operates or not, it does not change the short-run maximizing quantity. A per-unit production tax instead raises both MC and AVC by the tax per unit. Long-run entry and exit allow costs that are unavoidable now to become avoidable later.

Ask Whether a Fee Is Avoidable

Classify a license fee by the decision period and payment rule, rather than by its annual label. A nonrefundable fee already paid, or otherwise owed even during shutdown, is unavoidable for the current decision. A new fee charged only if production occurs is avoidable when output is zero. The latter can change whether the business opens even though it adds nothing to the marginal cost of an extra unit once operating. The independent example below shows why a blanket fixed-fee rule can fail.

Separate Shutdown from Exit

Temporary shutdown sets current output to zero while leaving the relevant unavoidable costs payable. It can be a rational response to a low-price period without permanently leaving the industry. Exit concerns a different horizon in which the firm can leave the market and avoid costs that remain committed in the short run. Neither label specifies a universal number of days or months.

Read Two Separate Graph Points

In this separate supplied graph example, minimum AVC is $8. Rising MC equals $11 at twenty units and $16 at thirty-two units. The choices are zero at $7, twenty at $11 and thirty-two at $16, provided those operating intersections are the global best choices under the stated usual cost shape. ATC determines economic profit at each selected output; it does not replace the operating and shutdown comparison.

Add Firms at a Common Price

Add firm quantities at each common price. If one hundred identical price-taking firms each choose twenty at $11, total quantity supplied is two thousand. This aggregation holds the set of firms fixed for the short-run comparison. Entry changes the number of firms summed, while an own-price change moves along the existing short-run supply relationship.

Check the Price-Taking Assumption

The competitive supply result relies on price taking. A monopolist also uses MC, but its demand and marginal revenue jointly determine the price and quantity it chooses. MC alone does not map an independently given market price into a monopoly quantity supplied. Check market structure before labelling a marginal-cost curve as a supply curve.

Keep Shutdown and Break-Even Separate

For the standard competitive graph, start the operating supply branch at minimum AVC rather than minimum ATC. The first is the shutdown threshold; the second is the lowest break-even price for the stated total cost. Prices between the two can justify loss-minimizing production when operating loses less than shutdown. At minimum AVC itself, keep the zero-output tie explicit.

Allow Different Firm Thresholds

For nonidentical firms, add the chosen quantity at each price, including zero for firms below their own shutdown thresholds. A price rise can increase output at active firms and make operating worthwhile for previously inactive firms already in the industry. That short-run activation is different from long-run entry by new firms. At a threshold price, indifference can make aggregate supply a set of possible quantities.

Use an Avoidable-Cost Checklist

A practical solution order is: identify which costs can be avoided now; find the best positive output at the given price; compare its profit with the zero-output payoff; then aggregate firms if the question asks for market supply. Keep a new operating-only fee separate from a sunk license payment. The same cost label can conceal different shutdown incentives.

Read the Output and Shutdown Explanation

OpenStax’s competitive output lesson explains price taking, marginal-cost output choices and shutdown comparisons. The cubic-cost example, avoidable-fee counterexample and questions below are independent hypothetical teaching material; no textbook exercise or figure is copied.

Calculate an Original Supply Schedule

Let q be continuous output and let variable cost be VC = q³ − 8q² + 25q for q at least zero. Unavoidable fixed economic cost is $16 per period. For positive output, AVC = q² − 8q + 25 = (q − 4)² + 9, while MC = 3q² − 16q + 25. Minimum AVC is therefore $9 at q = 4. The firm’s total cost when operating is VC + 16; shutdown still costs $16.

At $7, price is below the lowest AVC, so any positive q loses variable cost. At $9, operating contribution is 9q − VC = −q(q − 4)², which is zero at q = 0 and q = 4 and negative elsewhere. Both quantities therefore yield the same −$16 profit. This is an explicit tie, not an unknown quantity caused by missing fixed-cost information.

For a price above $9, solve P = MC on its relevant upper branch to obtain q = [8 + √(3P − 11)]/3. This gives five units at $20 and six at $37. To verify the global choice, call this selected output s. At P = MC(s), its operating contribution exceeds that of any other nonnegative q by (q − s)²(q + 2s − 8). Since s is above four, this expression is nonnegative. The positive-output choice also beats shutdown above $9.

Compare Three Different Cost Changes

First raise unavoidable fixed cost from $16 to $36. At price $20, output remains five, revenue remains $100 and variable cost remains $50. Economic profit falls from $34 to $14; the shutdown payoff falls from −$16 to −$36. The fixed-cost increase changes the payoff levels without changing the quantity that maximizes the difference.

Next instead keep fixed cost at $16 and add a $2 tax on each unit produced. The firm receives gross market price P but keeps P − 2 per unit after the tax. Its gross-price shutdown threshold rises from $9 to $11. A gross market price of $22 gives the same net price as $20 before the tax, hence output five and profit $34. This example holds the market price given; calculating a new market equilibrium would also require demand and the other firms’ supply.

Finally remove that unit tax and instead charge a $50 fee only when q is positive; no fee is paid at zero output. The usual unavoidable $16 remains payable either way. Once operating, the fee leaves MC unchanged, but average avoidable cost is now AVC + 50/q. Its minimum is $20 at q = 5 because q[(AVC + 50/q) − 20] = (q − 5)²(q + 2), nonnegative for positive q. The operating threshold rises even though the positive-output MC curve has not moved.

Check the Operating-Fee Decision

At a market price of $20 with the operating-only fee, must the firm produce five units just because P = MC there?

Try Three Short-Run Supply Questions

Connect Supply with Market and Firm Decisions

Trace price between the market and firm graphs, compare the long-run equilibrium conditions, or continue with the CLEP Microeconomics learning hub.