Connect a firm’s cost table to a price-taking decision

Connect a firm’s cost table to a price-taking decision

Question and evidence

Can a firm produce while making a total loss?

A fictional price-taking firm has fixed cost 12. For quantities 0,1,2,3,4 its variable costs are 0,4,7,12,20. Market price is 6 per unit; all output can sell at that price. Fixed cost is unavoidable in the short run.

This packet uses fictional data to isolate a mechanism. It is not an empirical estimate.

Mechanism and worked example

Marginal cost is the change in total cost from one more unit; average variable cost divides variable cost by output. A price taker compares price with marginal cost while checking profit across feasible outputs. Producing can cover variable cost and part of fixed cost even with a total loss. Entry and exit change longer-run competitive conditions.

Marginal costs are 4,3,5,8. At quantity 3 revenue is 18, total cost 24 and profit −6. Closing loses the fixed 12. Quantity 4 gives revenue 24 and cost 32, loss −8, so three is best among the listed choices.

Put the cost measures on a shared scale

At quantity 2, the fixed 12 credits contribute 12÷2=6 credits per unit (AFC). Variable cost contributes 7÷2=3.5 (AVC), so ATC=6+3.5=9.5. The second unit itself costs 7−4=3 (MC). “Average” allocates the relevant total across output; “marginal” compares adjacent feasible choices. Neither is the total bill.

Reconstruct costs and test shutdown

Use the original fictional technology: outputs 0–4 have variable costs 0, 4, 7, 12 and 20 credits. Every chosen unit sells at the selected price. The fixed cost must be paid even at zero output. Predict the best output before changing a control.

Price per output unit3 credits3.5 credits5 credits6 credits8 credits Unavoidable fixed cost12 credits20 credits

AFC = fixed cost ÷ quantity; AVC = variable cost ÷ quantity; ATC = total cost ÷ quantity. Thus ATC = AFC + AVC. MC is the extra cost of the indicated whole unit. All four measures below use credits per output unit; averages and MC at zero are undefined.

Square: AFC. Circle: AVC. Diamond: ATC. Triangle: MC. Dashed line: price 6. Shapes can overlap when values coincide. Points are not joined: this table does not specify a continuous technology or prove smooth-curve intersections. Both controls retain the same axes.

Costs per output unit (noninteger values rounded to two decimals)

Quantity	AFC	AVC	ATC	MC
0	Undefined	Undefined	Undefined	Undefined
1	12	4	16	4
2	6	3.50	9.50	3
3	4	4	8	5
4	3	5	8	8

Complete one-period ledger; costs, revenue and profit in credits

Quantity	Variable cost	Total cost	Revenue	Profit	Maximum?
0	0	12	0	-12	No
1	4	16	6	-10	No
2	7	19	12	-7	No
3	12	24	18	-6	Yes
4	20	32	24	-8	No

Maximum profit: -6 credits. Maximizing quantities: 3. Minimum AVC among positive feasible outputs: 3.5 credits per unit. The best listed choice is positive production.

Try prices 3, 3.5 and 6. At 3.5, why can quantity 2 tie with shutdown even though the first unit’s MC exceeds price? Then keep price fixed and raise the unavoidable cost to 20. Name the measures that move and those that do not. Record your inputs and explanation in the Experiment stage’s source notebook.

Restore original cost example

Temporary controls reset on reload and are not included in source captures. The calculation checks every feasible quantity; it does not infer market entry, long-run viability or measured business outcomes. No timer or background work runs.

At price 3.5, quantity 2 earns revenue 7, exactly covering variable cost 7. Its profit is −12, the same as shutdown. No positive choice does better. At price 3, every positive output fails to cover its variable cost, so shutdown is uniquely best. At price 6, quantity 3 covers its variable cost and contributes 6 toward the fixed bill; its loss of 6 is smaller than losing 12 by shutting down.

Do not stop because the first unit costs more than price: at price 3.5 the first unit loses an additional 0.5, but the cheaper second unit recovers that amount. Enumerate complete feasible plans. This discrete table has no fractional-output option and does not justify drawing a smooth MC curve crossing AVC at its minimum.

Holding variable costs fixed, raising unavoidable fixed cost from 12 to 20 increases AFC and ATC by 8÷quantity, lowers each profit by 8, and leaves AVC, MC and all maximizing quantities unchanged. A fee avoidable through shutdown would need a different zero-output comparison. OpenStax’s output and shutdown discussion explains the distinction between a short-run loss and shutdown; the workbench’s numbers are original teaching assumptions.

Reconstruct an unfamiliar cost table

A separate fictional firm can produce only 0, 1, 2 or 3 units. Total costs are respectively 10, 13, 18 and 25 credits. The zero-output 10 is entirely unavoidable fixed cost; all remaining cost is variable. Before opening feedback, reconstruct VC, AFC, AVC, ATC and MC. At price 4, compare every profit with shutdown. Find the shutdown-indifference price among these choices and predict what changes if unavoidable fixed cost becomes 20 while variable costs stay the same. Save your ledger and a labeled graph or description of its discrete points in your source notebook.

Check the reconstructed cost table

Variable costs are 0, 3, 8 and 15. For positive quantities, AFC is 10, 5 and 10/3; AVC is 3, 4 and 5; ATC is 13, 9 and 25/3. MC is 3, 5 and 7. At zero, average costs and the incremental cost of an added unit are undefined. At price 4, profits are −10, −9, −10 and −13, so quantity 1 uniquely minimizes the loss. At price 3, quantities 0 and 1 tie at −10; higher outputs are worse. With fixed cost 20, each total cost rises by 10, each profit falls by 10, and AFC/ATC rise by 10 divided by quantity. VC, AVC, MC and all maximizing choices remain unchanged. This result assumes the extra fixed cost remains unavoidable at zero output.

Inspect arithmetic, units, the zero-output option and every tied maximum before reviewing the explanation. Opening feedback makes subsequent revisions guided practice; it does not award independently demonstrated understanding.

Complication

A manager chooses output by the lowest average total cost alone. Another closes because total profit is negative. Neither compares avoidable costs and revenues at the available quantities. Long-run exit differs from short-run shutdown.

Your investigation

Use the cost workbench in the explanation to compare AFC, AVC, ATC and MC, then record all profit-maximizing choices at prices 3, 3.5 and 6. Change only unavoidable fixed cost and explain what moves. Reconstruct the unfamiliar cost table and distinguish shutdown from long-run exit.

Revise your answer to “Can a firm produce while making a total loss?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.

Vocabulary

Average variable cost: Variable cost divided by output, undefined at zero output.

Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.

Independent extension

Independently extend the investigation “Connect a firm’s cost table to a price-taking decision” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, compare a rival explanation and report why the teaching example cannot establish the real-world conclusion.

Inspect the original price-6 worked graph

This static graph shows the original price-6 example and does not change with the workbench controls. Points are discrete teaching values; no continuous interpolation is asserted.

Series	Unit number	Incremental credits
Marginal cost	1	4
Marginal cost	2	3
Marginal cost	3	5
Marginal cost	4	8
Price	1	6
Price	2	6
Price	3	6
Price	4	6

Build costs from a production plan

The first table gave you costs. Where could those costs come from? Consider a separate fictional workshop with one fixed machine. Its rental costs 12 credits per day. Each worker costs 6 credits per day; there are no other variable inputs. The workshop can hire only whole workers and must sell its entire daily output or shut down. The following outputs are assumptions, not measurements of a real factory.

Before calculating, predict: if each additional worker produces fewer extra units, will the cost of an extra unit rise or fall?

All rows describe one day. Output and added output are units; wages are total credits paid to workers.

On narrow screens, focus the table region and use the arrow keys to scroll.

Total product is total output: two workers produce 8 units. Marginal product is the extra output from an additional worker: the second adds 8−3=5 units. Average product is output per worker: two workers average 8÷2=4 units each. It is undefined with zero workers. The second worker raises the average because that worker’s marginal product, 5, exceeds the preceding average, 3.

The third worker adds 4 units: less than the second worker’s 5, even though total output still rises. This is diminishing marginal product with the machine held fixed. It does not mean total output has begun falling, and it is not a claim about changing all inputs in the long run. At three workers, average product is 12÷3=4; the added worker’s product equals that average. At four workers it falls to 14÷4=3.5.

Copy the four positive-output rows into your notebook. Calculate average product and average variable cost for each. Then calculate the extra wage bill divided by the extra output for each hiring step.

Check the production-to-cost calculation

Average products are 3, 4, 4 and 3.5 units per worker. Average variable costs are 2, 1.5, 1.5 and approximately 1.714 credits per unit. The incremental wage cost per extra unit is respectively 6÷3=2, 6÷5=1.2, 6÷4=1.5 and 6÷2=3.

Write the relationships in words first: average variable cost is the wage per worker divided by output per worker; incremental cost per unit is the extra wage bill divided by extra output. With a constant wage w and marginal product MP, the latter is w÷MP. Here w is 6 credits per worker-day and MP is extra units per additional worker-day. The result has units of credits per output unit. The formula requires positive extra output and the stated single-variable-input assumptions.

These are costs averaged over each discrete output increment, not a continuous marginal-cost curve. Draw total output against workers on one graph, and incremental cost against the corresponding output interval on a separate graph. Label the axes and do not join the points into a claimed smooth technology.

Try a new selling price

At a price of 2 credits per unit, choose among the five workshop plans. First calculate daily revenue and total cost for every row, including zero output. Explain why hiring the worker with the greatest marginal product does not by itself determine the best final workforce.

Compare all feasible plans

Revenue is 0, 6, 16, 24 and 28. Total cost is 12, 18, 24, 30 and 36. Profit is −12, −12, −8, −6 and −8. Three workers minimize the loss at −6. The fourth adds revenue of 2×2=4 but wages of 6; that step reduces profit. The first hiring step alone makes no improvement over shutdown, yet later productivity gains make the three-worker plan better. Checking every feasible plan avoids stopping at the first unfavorable incremental comparison.

At price 1, profits become −12, −15, −16, −18 and −22. Shutdown is now best. At neither price does this short-run comparison establish a long-run reason to renew the machine rental.

Audit what “profit” counts

A different fictional owner-operated repair business receives 120 credits per week. It pays 45 for materials, 15 for workspace rent and 20 for an assistant. The owner could instead earn 30 working elsewhere and could earn 5 by renting out owner-supplied equipment. These are the best feasible alternatives for the same week; the owner can combine those two alternatives. Ignore tax, depreciation, borrowing and changes in asset values in this teaching ledger.

The payments to others are explicit costs: 45+15+20=80. The income forgone from using the owner’s own resources is an implicit opportunity cost: 30+5=35. It is not an additional cash payment to a supplier.

Weekly calculation	Credits
Revenue	120
Explicit costs	80
Accounting profit: revenue minus explicit costs	40
Implicit opportunity costs	35
Economic profit: revenue minus both kinds of cost	5

Accounting profit answers what remains after the stated explicit costs. Economic profit compares operating with the specified best alternative uses of resources. Positive accounting profit can coexist with negative economic profit. Neither number alone is a complete cash-flow statement or a forecast.

Predict, then revise: the owner’s alternative wage rises from 30 to 42, with all other values unchanged. Does the bank balance change just because that offer becomes available? Does the economic comparison change?

Check the revised opportunity cost

Accounting profit remains 40. Implicit cost becomes 42+5=47, so economic profit is −7. The offer creates no payment by itself; it changes the forgone alternative. The negative economic profit suggests the specified alternatives are better by 7 credits, assuming they are genuinely available and all relevant nonfinancial benefits and switching costs have been considered.

If the alternative wage were 35, implicit costs would total 40 and economic profit would be zero. The business would still have accounting profit of 40. Normal profit means the owner’s resources receive their opportunity-cost return; zero economic profit does not mean the owner receives nothing.

Apply without copying the worked answer

An unfamiliar tutoring service receives 160 credits per week and pays explicit costs of 100. Its owner’s best alternative job pays 55; the owner’s room could instead earn rent of 12. Those alternatives can be taken together. Construct both profit measures, state the decision assumptions and repair this claim: “The service earns 60, so closing must make its owner poorer.” Save the ledger and your repaired argument in your source notebook. Label this as a fictional extension of the lesson’s cost packet, not observed business evidence.

Review after recording your answer

Accounting profit is 60; economic profit is 160−100−55−12=−7. Under the stated alternatives, closing and using both alternatives yields 67 rather than 60 before any omitted switching costs or nonfinancial differences. The 60-credit calculation is correct but does not settle the comparison. A supported argument names the available alternatives, avoids double-counting paid rent and forgone rent, and states what missing evidence could change the recommendation.

This is guided practice once the review is opened, not independent assessment. For a new case, change revenue or one available alternative, show both ledgers and explain why an unavailable job offer must not be counted as a feasible opportunity cost.