Profit, output and shutdown · printable packet

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1. What you will learn

Analyze profit, output and shutdown using explicit assumptions, calculated results and a stated limit of the model.

2. Starting point

Total revenue is price times quantity. Economic costs include all relevant opportunity costs. Marginal cost measures the extra cost of output, while average variable cost and average total cost divide different totals by output.

3. Terms and units

4. The market supplies the price; the firm chooses output

Perfect competition is a benchmark with many buyers and sellers, a homogeneous product, relevant information and conditions that prevent a single firm from controlling the market price. A small firm's feasible output is too small to change that price appreciably. It therefore chooses how much to produce at the price it faces. This does not mean it can sell unlimited output in every real circumstance; the price-taking assumption applies over the relevant modeled range.

The industry's demand curve can slope downward even while an individual competitive firm faces a horizontal demand curve at the market price. The two diagrams answer different questions. Market demand records how all buyers' purchases vary with price. The firm's horizontal line records the price it can obtain for its own small output decisions given the market outcome. Confusing them can lead to applying a monopoly's marginal-revenue rule to a competitive firm.

For a price taker, selling one more unit at the unchanged price adds exactly that price to total revenue. Thus marginal revenue equals price. Average revenue also equals price because total revenue P times Q divided by Q is P for positive output. These equalities depend on the unchanged-price assumption. A seller that must lower the price on earlier units to expand sales faces a different marginal-revenue relationship, studied in the monopoly lesson.

Profit maximization compares revenue and economic cost. Economic cost includes explicit payments and implicit opportunity costs, such as the owner's forgone wage or the return forgone on owned resources. If a problem says its total cost already includes all opportunity costs, do not subtract those implicit items again. Accounting profit can exceed economic profit because its specified cost account may omit some implicit costs. A firm can report positive accounting profit while earning zero or negative economic profit.

Term	What it means
Price taker	A firm that treats the market price as unaffected by its own feasible output choices.
Marginal revenue	The change in total revenue divided by the change in sales.
Economic profit	Revenue minus explicit and implicit opportunity costs.
Accounting profit	Revenue minus the explicit costs counted by the specified accounts.
Shutdown	Producing zero temporarily while still incurring costs that are unavoidable in the short run.
Contribution toward fixed cost	Revenue minus variable cost, which measures the gain from operating rather than shutting down under the stated assumptions.

Another way: Choose worthwhile increments and check the whole alternative

An extra unit increases profit when its marginal revenue exceeds its marginal cost. It reduces profit when marginal cost exceeds marginal revenue. In a smooth interior solution on the relevant rising marginal-cost range, the maximizing quantity satisfies MR = MC. For a competitive firm, that becomes P = MC. The economic logic is the comparison of changes in revenue and cost; the equation is a compact statement of that comparison under suitable conditions.

For indivisible units, exact equality may never occur. Suppose successive marginal costs are four, six, nine and thirteen dollars while price is ten. The first three units add positive amounts to profit; the fourth subtracts three dollars. Producing three is the appropriate choice in this supplied sequence, even though no listed marginal cost equals ten. If an increment has MC exactly equal to price, adjacent output levels can tie. A problem must specify whether to report the lower or higher maximizing quantity when a unique answer is required.

The marginal condition alone is not sufficient in every possible cost shape. A point where MR equals MC on a falling marginal-cost segment may be a minimum or otherwise fail to maximize total profit. Feasible boundaries and shutdown must also be considered. In introductory examples, the relevant rising MC segment and the candidate output are often supplied explicitly. When a full table is given, calculate total revenue minus total cost at each feasible output as an independent check.

Sunk or unavoidable fixed costs affect the level of profit but cancel when comparing two positive output levels with the same fixed commitment. If producing three rather than two units adds nine dollars of variable cost and ten dollars of revenue, the extra unit adds one dollar to profit regardless of a fixed fee paid under both options. This does not mean fixed costs never matter. They matter for total profit and for choices, such as long-run exit, that can avoid them.

Another way: Calculate profit as a total, not a price gap

Suppose a competitive firm chooses six units at a price of twelve dollars. Revenue is seventy-two dollars. Variable cost is forty-eight and fixed economic cost is twenty-two, so total economic cost is seventy. Economic profit is two dollars. The difference between price and ATC, multiplied by output, gives the same result: ATC is seventy divided by six, and the per-unit margin times six equals two.

The formula profit = (P - ATC) times Q applies when ATC is measured at the chosen quantity and includes the appropriate economic costs. The vertical gap P - ATC alone is profit per unit, not total profit. A graph's profit rectangle therefore uses both the gap as height and the chosen quantity as width. If price lies below ATC, the rectangle measures a loss rather than a gain.

Producer surplus is revenue minus variable cost in this short-run firm interpretation. In the example it is seventy-two minus forty-eight, or twenty-four dollars. Economic profit is producer surplus minus fixed cost, yielding two. A firm can have a positive contribution toward fixed cost while suffering an economic loss if that contribution is smaller than fixed cost. Those are compatible statements, not competing definitions of whether the business is doing well.

The analysis must also keep the time period consistent. A daily price-and-output calculation cannot subtract an entire annual fixed cost without allocating the period appropriately. Nor should a total profit in dollars be compared directly with a percentage return or a per-unit margin. Before interpreting a number, state what it measures, over which period and with which opportunity costs included. That discipline makes later comparisons between operating, shutting down and exiting meaningful.

Another way: Shutdown is a comparison with zero output

Temporary shutdown avoids variable costs but does not avoid the fixed costs designated unavoidable for the short-run decision. If the firm shuts down in the example, revenue and variable cost become zero, leaving a loss of twenty-two dollars. If it operates at six units, profit is two. Operating improves the outcome by twenty-four dollars, exactly revenue minus variable cost. That improvement is the correct shutdown comparison under the assumptions.

Now raise fixed cost to forty dollars while keeping revenue seventy-two and variable cost forty-eight. Operating profit becomes negative sixteen, but shutdown profit is negative forty. Producing still improves the outcome by twenty-four. 'The firm makes a loss' is therefore insufficient to conclude that immediate shutdown is optimal. The choice compares the sizes of the feasible losses, not merely whether one alternative has a negative sign.

At the best positive output, the firm operates when revenue covers variable cost and shuts down when every positive output yields a lower contribution than zero. In the conventional smooth competitive model, the shutdown price is minimum AVC. Above that threshold, there is a relevant output where price covers AVC; below it, producing cannot cover avoidable variable cost. At equality, operating at the minimum-AVC quantity and shutting down can tie, assuming the fixed cost is unavoidable and no other operating consequences are modeled.

Do not compare price with AVC at an arbitrary output and treat that as the whole rule. The firm can choose its output. The threshold involves the minimum of AVC, while the actual operating decision also identifies the profit-maximizing quantity on the relevant MC segment. In a finite activity, we either provide that candidate with its cost information or ask the learner to compare all listed feasible alternatives. This avoids implying that a single accidental production level settles the entire decision.

Exit is different from shutdown. In the long run, leaving the industry can avoid commitments that were fixed in the short run. A firm may rationally operate at a short-run loss while planning to exit when those commitments end. The next lesson examines that adjustment and the entry of firms attracted by positive economic profit. Both decisions build on the same principle: compare the revenue and opportunity costs that actually differ between the available alternatives.

Another way: Interpret the competitive supply segment carefully

In the standard short-run model, the competitive firm supplies along the rising part of marginal cost at prices above minimum average variable cost. The portion below the shutdown threshold is not an operating supply curve simply because it appears on the same graph. At a lower price, zero output is the better short-run alternative. Summing firms quantities at each common price gives market supply for the specified set of firms. That aggregation holds entry and exit fixed; it is not yet the long-run industry supply relationship. A price increase can therefore raise current industry output through existing firms producing more, while a later increase may also attract additional firms. The diagrams must identify which adjustment margins are available.

5. An invented stand decides whether to open today

A fictional stand has already committed to a twenty-two-dollar site fee for the day. The fee cannot be recovered if the stand stays closed. It can sell six units at a competitive price of twelve dollars, with forty-eight dollars of variable cost. The supplied marginal-cost schedule says all earlier units are worthwhile and the next unit would cost more than twelve dollars. Six is therefore the candidate operating quantity. Revenue is seventy-two, full economic cost is seventy and profit is two dollars.

Closing produces no revenue and avoids the forty-eight-dollar variable cost, but the fee remains. The closed stand loses twenty-two dollars. Opening improves the outcome by twenty-four dollars, the revenue minus variable cost. The owner should not compare seventy-two dollars of revenue with the fee alone or treat all historical expenditure as the marginal cost of one more unit.

Suppose an extra unavoidable fixed charge raises the total fixed commitment to forty dollars. Opening now loses sixteen dollars, while closing loses forty. The short-run operating comparison still favors opening by twenty-four. This bounded result does not mean continuing forever is desirable. If the same forty-dollar fee can be avoided by declining tomorrow's contract, the future decision includes a different set of avoidable costs.

The lesson grades the arithmetic under those explicit assumptions. It does not advise a real business to open despite every possible risk or nonfinancial concern. The owner might face safety constraints, fatigue or uncertain demand absent from the model. A precise economic report identifies the current alternatives, the costs each avoids, the candidate output and the resulting profit difference, then states which omitted facts could change the conclusion.

6. Check the tempting shortcut

A negative economic profit does not automatically imply immediate shutdown. Compare operating profit with the loss from unavoidable fixed costs at zero output. Use the relevant rising-MC or finite-table comparison, and multiply a per-unit profit margin by quantity to obtain total profit.

7. In the fictional Alder model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 6 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 48 dollars and unavoidable fixed cost is 22 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

8. In the fictional Birch model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 7 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 56 dollars and unavoidable fixed cost is 24 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

9. In the fictional Cedar model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 8 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 64 dollars and unavoidable fixed cost is 26 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

10. In the fictional Dune model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 9 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 72 dollars and unavoidable fixed cost is 28 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

11. Guided practice

In the fictional Elm model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 10 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 80 dollars and unavoidable fixed cost is 30 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

12. Guided practice

In the fictional Dune model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 9 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 72 dollars and unavoidable fixed cost is 28 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

13. Guided practice

In the fictional Fern model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 11 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 88 dollars and unavoidable fixed cost is 32 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

14. Practice

In the fictional Grove model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 12 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 96 dollars and unavoidable fixed cost is 34 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

15. Practice

In the fictional Harbor model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 13 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 104 dollars and unavoidable fixed cost is 36 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

16. Somewhere new

A stand has already committed to a nonrefundable site fee and must choose whether to open for today's sales. The supplied operating quantity has been checked against marginal costs. Compare opening with closing rather than assuming that any fixed payment must be earned back by each extra unit. In the fictional Island model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 14 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 112 dollars and unavoidable fixed cost is 38 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

17. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

18. Test question

In the fictional Juniper model, a price-taking firm sells at 12 dollars. Its candidate profit-maximizing output is 15 units, where the next unit's marginal cost would exceed price and all earlier marginal costs are below price. Variable cost at this output is 120 dollars and unavoidable fixed cost is 40 dollars. Shutdown eliminates variable cost but not fixed cost. Calculate total revenue, economic profit, and how many dollars producing improves profit relative to shutting down. All opportunity costs are included in these costs.

19. What you can do now

Reconstruct the model without the worked example. Explain each requested measure's units and identify an assumption that the conclusion depends on.

Working for the steps left to you