Costs, revenue and profit maximisation

What you'll learn

A firm's costs are where the law of diminishing returns shows up in money terms, and its revenue is where demand shows up. Put the two together and you can find the output at which profit is greatest — which is the single most useful result in the theory of the firm, and the foundation of every market structure studied afterwards.

The profit-maximising rule is that a firm should produce where marginal cost equals marginal revenue. The reasoning is worth holding onto rather than memorising: while the revenue from one more unit exceeds the cost of producing it, that unit adds to profit and should be made. Once the cost of the next unit exceeds the revenue it brings, it subtracts from profit and should not be. Profit is therefore greatest where the two are equal.

The second essential idea is the difference between the short run, where some costs are fixed, and the long run, where none are. That distinction decides whether a loss-making firm should keep producing or shut down — a question with a precise answer that surprises most students the first time they meet it.

By the end you should be able to build a full cost schedule, explain the shape of each curve and the relationships between them, apply the MC = MR rule, distinguish normal from supernormal profit, and apply the shutdown rule.

Key terms and definitions

Fixed cost — a cost that does not vary with output in the short run: rent, insurance, a supervisor's salary.

Variable cost — a cost that varies with output: materials, piece-rate labour, power.

Total cost (TC) — fixed cost plus variable cost.

Average total cost (ATC) — total cost ÷ output. Also equals AFC + AVC.

Average variable cost (AVC) — variable cost ÷ output.

Average fixed cost (AFC) — fixed cost ÷ output. Falls continuously as output rises.

Marginal cost (MC) — the addition to total cost from producing one more unit.

Average revenue (AR) — total revenue ÷ output, which equals the price.

Marginal revenue (MR) — the addition to total revenue from selling one more unit.

Normal profit — the minimum return needed to keep the firm in the industry. It is counted as a cost, so a firm earning only normal profit shows zero economic profit.

Supernormal (abnormal) profit — profit above normal profit.

Core concepts

Why the cost curves have the shapes they do

AFC falls continuously, because the same fixed cost is spread over more units. It never rises and never reaches zero.

MC falls at first and then rises. The fall reflects increasing returns as the fixed factor is used more fully; the rise reflects diminishing returns as it is spread too thinly. Marginal cost is therefore the law of diminishing returns translated into money.

AVC and ATC are both U-shaped, for the same reason. ATC lies above AVC by exactly the amount of AFC, so the two converge as output rises and AFC shrinks — but they never meet, because AFC never reaches zero.

The relationship between marginal and average

This is the relationship most worth understanding rather than memorising: marginal cost cuts both AVC and ATC at their minimum points.

The logic is arithmetic, not economic. Whenever the marginal value is below the average, it pulls the average down. Whenever it is above, it pushes the average up. The average therefore stops falling and starts rising exactly where the marginal crosses it — which is its minimum.

It is the same reason a batsman's average rises when they score above their average and falls when they score below it. Being able to give that reasoning, rather than asserting that the curves cross at the minimum, is what separates a strong answer.

Revenue under different market conditions

For a firm in perfect competition, the price is set by the market and the firm can sell any quantity at that price. So AR = MR = price, and the demand curve facing the individual firm is horizontal.

For a firm with market power — a monopolist or a firm in imperfect competition — selling more requires lowering the price, and lowering it on all units sold, not just the extra one. MR is therefore below AR and falls faster. That single fact drives most of the differences between market structures, and it is worth being able to explain rather than merely state.

Profit maximisation: MC = MR

Produce where MC = MR. Where MR exceeds MC, the next unit adds more revenue than cost and should be produced; where MC exceeds MR, it should not.

A second condition is needed for completeness: MC must be rising through the intersection. Where MC is falling and equal to MR, the firm is at a point of minimum profit rather than maximum, which is a refinement examiners occasionally test.

Normal and supernormal profit

Normal profit is the return just sufficient to keep the entrepreneur in this industry rather than the next best one — an opportunity cost, and therefore treated as a cost in economics.

A firm earning only normal profit has total revenue exactly equal to total cost, and price exactly equal to ATC. In economics that is not a bad outcome; it is the long-run equilibrium of a competitive market.

Supernormal profit exists where price exceeds ATC. In a competitive market it attracts entry, which increases supply, lowers price and competes the supernormal profit away.

The shutdown decision

A loss-making firm in the short run should keep producing as long as price covers average variable cost. Fixed costs are paid whether or not it produces, so any revenue above variable cost makes a contribution towards them and reduces the loss.

The firm shuts down in the short run only when price falls below AVC, because then each unit produced adds more to cost than to revenue and shutting down loses less.

In the long run all costs are variable, so a firm must cover average total cost to remain in the industry.

The two rules together are frequently examined: produce in the short run if P ≥ AVC; remain in the industry in the long run only if P ≥ ATC.

Worked examples

Example 1 — Building the cost schedule (7 marks)

A firm has fixed costs of $60. Variable costs are $40, $70, $96, $128, $175 and $240 for one through six units.

Total cost is fixed plus variable: at three units, $60 + $96 = $156. Marginal cost is the difference between consecutive totals: $156 − $130 = $26. Averages are the totals divided by output: ATC at four units is $188 ÷ 4 = $47.

Notice that AFC falls continuously from $60 to $10, and that ATC exceeds AVC by exactly AFC at every output — at five units, $35 + $12 = $47.

Example 2 — Marginal cutting average at the minimum (5 marks)

From the schedule, AVC reaches its minimum of $32 at four units, and MC at four units is also $32. ATC reaches its minimum of $47 at five units, and MC at five units is also $47.

In both cases marginal cost equals the average exactly where the average bottoms out. Below that output, MC is beneath the average and drags it down; above it, MC is above the average and pulls it up.

That is the relationship stated as arithmetic rather than assertion, and it is the version that earns the explanation mark.

Example 3 — Profit maximisation with a market price (6 marks)

The firm can sell any quantity at $47, so AR = MR = $47.

Apply MC = MR. Marginal cost reaches $47 at the fifth unit, so the profit-maximising output is 5 units.

Total revenue = 5 × $47 = $235. Total cost at five units = $235. Profit = nil in economic terms — the firm earns exactly normal profit.

That is not failure. It is the long-run equilibrium of a competitive market, where price has been competed down to the minimum of average total cost.

Example 4 — Supernormal profit and the shutdown point (7 marks)

Now suppose price rises to $65. MC reaches $65 at the sixth unit, so output is 6 units. Total revenue = 6 × $65 = $390. Total cost = $300. Supernormal profit = $90, or $15 per unit, since ATC at six units is $50.

Now suppose price falls to $32. MC equals $32 at the fourth unit, so output is 4 units. Total revenue = 4 × $32 = $128. Total cost = $188, so the firm makes a loss of $60 — exactly its fixed costs.

Should it produce? AVC at four units is $32, which the price exactly covers. The firm is at the shutdown point: producing or closing gives the same $60 loss, because revenue covers variable cost precisely and nothing more. Below $32 it should shut down; above $32 it should produce, because the excess over AVC contributes towards the fixed costs.

Common mistakes and how to avoid them

Saying a firm earning only normal profit should leave the industry. Normal profit is the return that keeps it there.

Treating normal profit as zero profit in the everyday sense. It is counted as a cost, so zero economic profit means a satisfactory return.

Applying the long-run rule to a short-run decision. In the short run the test is AVC, not ATC.

Saying MC cuts ATC at ATC's minimum without explaining why. Give the arithmetic reason — marginal below average pulls it down, above pushes it up.

Forgetting that AFC never reaches zero. ATC and AVC converge but never meet.

Assuming MR equals price for every firm. That holds only where the firm is a price taker.

Ignoring the rising-MC condition. MC = MR at a falling MC is a minimum, not a maximum.

How this links to your Internal Assessment

Cost theory suits an Internal Assessment on a real producer, and the achievable version is a cost schedule rather than a full set of curves.

Obtain the firm's fixed costs and its variable costs at two or three levels of output, then compute AFC, AVC, ATC and MC. Even a three-point schedule shows whether average total cost is falling, and whether the firm is operating near the minimum of its ATC or well away from it.

Then ask the decision question. If the firm is loss-making, does price cover average variable cost? That is a precise, useful piece of advice that very few small business owners have ever framed properly, and it can be the recommendation your assessment turns on.

State clearly that you have treated a cost as fixed or variable and why. In a small business the classification is often genuinely ambiguous — an owner's own wage, a vehicle used for both business and personal purposes — and explaining your treatment is better than presenting it as settled.

Exam technique for costs, revenue and profit maximisation

Build the table in a fixed order: TC first, then MC as the differences, then the averages. Working left to right prevents the common error of computing marginals from averages rather than from totals.

Label every figure with its unit and state the output at which each minimum occurs. The output level, not just the cost figure, is usually what the question asks for.

For profit questions, set out total revenue and total cost separately and subtract. Stating profit per unit as price minus ATC is a useful cross-check on the total.

Command words are predictable. Calculate marginal cost wants the differences shown. Explain why MC cuts ATC at its minimum wants the marginal-and-average reasoning. Determine the profit-maximising output wants MC = MR applied and the output stated. Advise whether a loss-making firm should continue wants the AVC test, the figures, and a conclusion.

Where a question gives a price and a cost schedule, always check both the profit-maximising output and whether the firm should be producing at all. Candidates routinely answer the first and omit the second.

Quick revision summary

• TC = fixed + variable. ATC = AFC + AVC. MC is the difference between consecutive total costs.
• AFC falls continuously and never reaches zero, so ATC and AVC converge but never meet.
• MC falls then rises, reflecting increasing and then diminishing returns.
• MC cuts AVC and ATC at their minimum points, because a marginal below the average pulls it down and above pushes it up.
• Price taker: AR = MR = price. Firm with market power: MR lies below AR and falls faster.
• Profit is maximised where MC = MR, with MC rising through the intersection.
• Normal profit is a cost — the return needed to keep the firm in the industry.
• Supernormal profit exists where price exceeds ATC, and in a competitive market it attracts entry.
• Short-run shutdown rule: produce if price is at or above AVC; shut down below it.
• Long-run rule: remain in the industry only if price is at or above ATC.
• Always answer both questions — what output, and whether to produce at all.