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Profit maximisation and the shutdown decision, from one cost table

A firm facing a loss has two separate questions to answer, and the second is not the one most people reach for. This page works both from a single cost table: how much to make, and whether to make anything at all.

CB2 · Business Economics · 10 min read

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Find the profit-maximising output from a cost table and decide, at any given price, whether the firm should produce, operate at a loss, or shut down

Two questions, asked in order

A firm with a cost structure and a price has two decisions, and keeping them apart is most of this topic.

How much should I make? Answer: carry on to the point where the cost of one more unit equals the money it brings in.

Should I make anything at all? Answer: compare the best you can do by producing with what happens if you stop. In the short run, stopping does not get you out of your fixed costs, so the comparison is not the one it looks like.

Most mistakes in this topic come from answering the second question with the tool built for the first.

The first question: why marginal cost meets marginal revenue

Marginal cost is what one more unit adds to total cost. Marginal revenue is what one more unit adds to total revenue. For a firm small enough that its own output does not move the market price — a price taker — marginal revenue is simply the price.

The mechanism is a one-line argument, and it is worth being able to give it rather than quote the rule.

Suppose marginal cost is below marginal revenue. Then the next unit adds more to receipts than to costs, so making it raises profit. Keep going. Suppose marginal cost is above marginal revenue. Then the last unit added more to costs than to receipts, so not making it raises profit. Pull back. The only place where neither move helps is where the two are equal, and that is the maximum.

produce where MC = MR, and for a price taker MR = P

One condition has to be attached. MC must be rising through the crossing. Cost curves typically fall and then rise, so marginal cost can equal price twice; at the lower crossing, with MC falling, the next unit is cheaper than the price and you should push on, which makes that point a minimum of profit, not a maximum. Take the crossing on the rising branch.

Why marginal cost rises, which is the part that is not arbitrary

In the short run some input is fixed — a shop, a machine, a kitchen. Add more of a variable input to a fixed one and each extra unit of the variable input eventually produces less than the one before, because it has less of the fixed thing to work with. That is diminishing marginal returns, and it is a statement about crowding, not about effort or skill.

Now read it as a cost. If each extra worker adds fewer units than the last, then each extra unit needs more labour than the last, and so costs more. Marginal cost rising is diminishing marginal product read upside down. They are the same fact priced two different ways, and that is why the cost curve has the shape it does rather than any other.

The second question: the mechanism behind the shutdown rule

Here is the step that catches people. A firm is losing money at its best output. Should it close?

Closing does not remove the fixed costs. Rent still runs, the lease on the machine still runs, the licence still has to be paid. In the short run those are unavoidable, so they are the same whichever way the decision goes — which means they cannot affect the decision at all. A cost you pay either way is irrelevant to a choice between the two.

Strip them out and what is left is: does the revenue cover the costs that would go away — the variable costs? If it does, the excess is a contribution towards the fixed costs you are stuck with, and producing leaves you with a smaller loss than stopping. If it does not, every unit you make deepens the hole, and stopping is better.

keep producing while P ≥ AVC  ·  shut down while P < AVC

So the test is against average variable cost, not average total cost. Three zones follow, and the two thresholds that separate them are the minimum of AVC and the minimum of AC.

P above minimum AC. Revenue covers everything. The firm makes a profit above the normal return.

P between minimum AVC and minimum AC. The firm makes a loss and should still produce. It is covering its variable costs and part of its fixed ones, so the loss is smaller than the fixed costs it would carry if it closed.

P below minimum AVC. Shut down. Producing adds to the loss.

The long run has only one threshold

Given time, every cost becomes avoidable: the lease ends, the machine is sold, the licence is not renewed. There are no fixed costs in the long run, so the distinction between the two averages disappears and only one test is left: price must cover average total cost, or the firm leaves the industry.

That is the engine of the competitive long run. If price is above minimum average cost, firms are making more than the normal return, so new firms come in, supply rises and price is pushed down. If price is below it, firms leave, supply falls and price is pushed up. The resting point is price equal to minimum average cost — normal profit, which means exactly enough to keep the capital and the owner's effort where they are, and not a rupee more.

Questions students ask

Why not just maximise revenue, or minimise average cost?

Because neither is the objective. Maximising revenue ignores what the output cost. Minimising average cost finds the most efficient scale, which is only the right output when the price happens to equal that minimum — which is the long-run resting point of a competitive industry and not a general rule. Profit is total revenue minus total cost, and the output that maximises it is where marginal cost meets marginal revenue, nowhere else.

Does the rule change if the firm has market power?

The rule does not change; the value of MR does. A price maker that wants to sell more has to lower the price on everything it sells, not only on the extra unit, so marginal revenue falls below the price. MC = MR still gives the output, and the price then comes off the demand curve at that output. The shutdown logic is untouched: fixed costs that cannot be escaped cannot influence the decision whatever the market structure.

Is the shutdown point the same as the break-even point?

No, and the difference is the whole point of having two thresholds. Break-even is where price equals average total cost: the firm makes neither a profit nor a loss. The shutdown point is lower, where price equals average variable cost. Between the two the firm is losing money and is right to keep trading. Calling them the same name is how the middle zone gets missed.

A worked example

An invented firm, built for this page. A small bakery in Coimbatore makes celebration cakes to order. It has one oven and one lease, so its daily fixed cost is ₹4,000 — rent, the oven on finance, and the licence — payable whether or not it bakes. Its variable cost schedule is below. All figures are illustrative and chosen for clean arithmetic.

  1. The cost table

    Cakes/dayMCVCAVCTCAC
    1900900900.004,9004,900.00
    27001,600800.005,6002,800.00
    36002,200733.336,2002,066.67
    46502,850712.506,8501,712.50
    58003,650730.007,6501,530.00
    61,0004,650775.008,6501,441.67
    71,3005,950850.009,9501,421.43
    81,7007,650956.2511,6501,456.25
    92,2009,8501,094.4413,8501,538.89
    102,80012,6501,265.0016,6501,665.00

    Marginal cost falls to the third cake and rises from the fourth: one baker gets into a rhythm, and after that the single oven starts to be the constraint. The two thresholds the decision needs are already visible in the table:

    minimum AVC = ₹712.50, at 4 cakes
    minimum AC = ₹1,421.43, at 7 cakes

    Check the shape of the averages against MC, which is a free error-check on any cost table. AVC falls while MC sits below it (through cake 4, where MC 650 < AVC 712.50) and rises once MC is above it (cake 5, MC 800 > 712.50). AC falls while MC is below it (cake 7, MC 1,300 < AC 1,421.43) and rises once MC passes it (cake 8, MC 1,700 > AC). Both averages behave as they must.

  2. Price ₹1,700: the comfortable case

    MC equals 1,700 at 8 cakes, on the rising branch. Produce 8.

    TR = 8 × 1,700 = ₹13,600
    TC = ₹11,650
    profit = +₹1,950

    Check through the average: (1,700 − 1,456.25) × 8 = 243.75 × 8 = ₹1,950. The same figure.

    And the threshold predicted it: ₹1,700 is above minimum AC of ₹1,421.43, so a profit above normal was expected.

  3. Price ₹1,000: loss-making, and right to carry on

    MC equals 1,000 at 6 cakes. Produce 6.

    TR = 6 × 1,000 = ₹6,000
    TC = ₹8,650
    profit = −₹2,650

    Now ask the second question properly. Baking 6 cakes loses ₹2,650. Closing the shutters for the day loses the fixed cost, ₹4,000. Baking is ₹1,350 better than not baking, so the bakery opens.

    Check that ₹1,350 the other way: each cake contributes 1,000 − 775 = ₹225 towards fixed costs, and 6 × 225 = ₹1,350. So the loss is 4,000 − 1,350 = ₹2,650 — the same answer, reached without using total cost at all.

    And the thresholds predicted this too: ₹1,000 sits between minimum AVC (₹712.50) and minimum AC (₹1,421.43), which is exactly the middle zone.

  4. Price ₹650: shut down

    MC equals 650 at 4 cakes. Suppose the bakery produced them anyway.

    TR = 4 × 650 = ₹2,600
    TC = ₹6,850
    profit = −₹4,250

    Closing loses ₹4,000. Baking loses ₹4,250. Baking is ₹250 worse, so the bakery should not open.

    Check the ₹250: each cake now contributes 650 − 712.50 = −₹62.50, and 4 × (−62.50) = −₹250. Every cake makes the day worse, which is what a negative contribution means.

    The threshold again: ₹650 is below minimum AVC of ₹712.50. The rule and the arithmetic agree at all three prices.

  5. The three cases side by side

    PriceOutputProfit if it producesProfit if it closesDecision
    ₹1,7008+₹1,950−₹4,000produce
    ₹1,0006−₹2,650−₹4,000produce at a loss
    ₹6504−₹4,250−₹4,000shut down

    Read the middle row once more, because it is the one worth remembering. The bakery loses ₹2,650 by opening and ₹4,000 by closing. Anyone testing the price against average total cost — ₹1,000 against ₹1,441.67 — would have told the owner to shut, and it would have cost them ₹1,350 in a single day.

  6. And in the long run

    At ₹1,000 the bakery should bake today and plan to leave. The middle zone is a short-run answer only: it is worth covering some of a cost you cannot escape, but it is not worth renewing a lease to do it. Once the lease and the oven finance come up for renewal, the only test left is ₹1,000 against minimum average cost of ₹1,421.43 — and that fails.

Where this fits in CB2

This page explains one idea from CB2 Business Economics. The full CB2 syllabus, with what each part is examined on, sits on the course page, and past-paper style mock exams with full solutions are where you find out whether the idea has stuck under time pressure.

Other CB2 topics explained

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