Distinguish marginal decisions from total profit and explain why firms coordinate work internally.
By the end: Choose output under stated costs and distinguish shutdown from long-run viability.
Why organize rather than buy every task?
A firm coordinates workers, equipment, information, and suppliers. Negotiating a new market contract for every small task can be costly, especially when quality is hard to specify or investments are specific to one relationship. Managers instead receive authority over some decisions. Internal organization also creates costs: bureaucracy, poor incentives, and conflicts between owners, managers, and workers.
An employment contract cannot usually specify and verify every action needed for good work. This incompleteness helps explain supervision, trust, workplace norms, and incentive pay. It also creates room for unequal power. A firm's boundary is therefore an institutional choice between forms of coordination, not proof that either hierarchy or outsourcing is always efficient.
Authority changes coordination without removing conflict
A boundary around a firm identifies which decisions managers can direct under employment and ownership arrangements, and which require agreement with another organization. Buying a finished component leaves its supplier responsible for organizing production under the purchase contract. Employing a machinist and owning the equipment puts more scheduling decisions inside the purchasing firm. Neither arrangement removes dependence on other people. The question is which organization handles adaptation, verification, and risk, and what powers each participant retains. A low quoted component price is only one part of that comparison. Quality, delivery, and the cost of enforcing promises also affect the feasible alternatives.
Consider a paper workshop needing ten identical inspections per week. An outside inspector charges four currency units per inspection, making a quoted weekly bill of forty. Searching for availability and coordinating files costs another eight in staff time valued at its forgone use. The total relevant cost of outsourcing is forty-eight. An employee can perform the same inspections for thirty-six per week, but supervision and equipment services cost nine more, giving forty-five. Assume equal quality, reliability, capacity, and no other differences. Internal production saves three per week in this case. The saving is a conditional resource comparison, not a universal advantage of employment.
Change one assumption. Suppose maintaining the internal inspection arrangement now requires eighteen rather than nine in supervision and equipment services. Internal cost becomes fifty-four, six above outsourcing at forty-eight. Alternatively, the supplier might require a costly minimum contract or hold up production after the workshop invests in compatible equipment. Those changes could favor integration again. An asset is relationship-specific when it loses value outside the particular relationship. The threat of losing that value can change bargaining even without changing physical productivity. A full comparison must identify who owns the equipment and what alternative uses remain available.
Coordination costs can reverse the boundary choice
All rows deliver ten identical inspections with equal quality, reliability, and capacity in this invented workshop. Direct payment alone favors employment, but adding coordination and equipment costs narrows its advantage to three. Raising internal overhead reverses the ranking: fifty-four exceeds forty-eight. Contract risks or unequal service quality would require another comparison rather than this simple cost ranking.
Employment permits direction over a range of tasks but does not transfer unlimited authority over a person. Applicable law and the contract constrain hours, safety, dismissal, and managerial instructions. A manager may observe attendance while being unable to verify every act that produces reliable work. Pay tied to measured inspections might reward speed while missing careful diagnosis. Trust and professional standards can support quality where a numerical target is incomplete. These are mechanisms explaining why writing a complete contract is difficult. They do not establish that supervision always raises output or that a particular incentive scheme is effective.
Organizational efficiency and bargaining power can change together without being identical. Suppose integration creates the three-unit saving in the first case. That establishes a potential gain under the stated cost assumptions, but it does not determine whether customers receive a lower price, workers receive better pay, or owners keep the saving. If workers lose alternative employers when suppliers merge, their bargaining position may weaken even while coordination costs fall. Conversely, worker representation may constrain managerial discretion while improving information about production. Measuring total cost alone cannot establish the distribution of gains, workplace autonomy, or the legitimacy of the decision-making arrangement.
A coordination saving does not assign its gains
Consequences of workshop integration
Possible change
Mechanism
Not implied by saving
Lower customer price
Saving passed through
Automatic price cut
Higher worker pay
Bargain shares saving
Automatic wage rise
Employer alternatives
Merger narrows options
Stronger worker power
Worker representation
Information improves
Unlimited manager power
Return to the invented workshop's low-overhead case, where integration saves three per week. That resource saving leaves its division unresolved: customer prices, worker pay, and owner receipts require separate evidence. Losing alternative employers could weaken workers even while costs fall; representation could improve information while limiting authority. These are conditional mechanisms, not predicted distributions of the saving.
Fixed, variable, average, and marginal
A fixed cost does not change with output over the stated decision period. A variable cost does. Average cost divides total cost by units produced; marginal cost is the extra cost of an additional unit. These distinctions depend on horizon. A lease may be fixed this month but avoidable when the contract expires. A sunk cost is already incurred and unrecoverable, so it should not determine which future option has the better payoff.
In our price-taking firm, revenue is price times output. Profit is revenue minus fixed and variable costs. The lab compares every feasible integer output from zero to six, rather than applying a shortcut to a non-smooth cost schedule. For smooth competitive cases, producing until marginal cost meets price is useful under the appropriate curvature and shutdown conditions.
Construct the whole cost comparison before using a marginal rule
The firm widget fixes a decision period and allows only integer outputs from zero through six units. Its variable costs at those outputs are zero, twelve, twenty-two, thirty, forty, fifty-four, and seventy-four currency units per period. Fixed cost is eighteen at every output, including zero. These are assumed cost totals, not observations from a real business. Subtracting neighboring variable-cost totals gives the extra cost of each additional unit. The first costs twelve, the second ten, the third eight, the fourth ten, the fifth fourteen, and the sixth twenty. Fixed cost does not enter those differences because it is unchanged.
The marginal sequence first falls and then rises. That feature prevents an unqualified rule to stop at the first unit whose cost exceeds price. At price eleven, the first unit costs twelve, which looks unattractive in isolation. But three units together cost thirty, and revenue from them is thirty-three. Producing that batch contributes three toward fixed cost despite the unfavorable first step. The firm cannot assume every output increment has rising marginal cost. Comparing every feasible total avoids losing a beneficial batch merely because reaching it requires an initially costly unit. This is why the table is more informative than a smooth-curve shortcut here.
Average variable cost divides variable cost by positive output. At one unit it is twelve per unit; at two it is eleven; at three and four it is ten. At five it is 10.8, and at six it is about 12.33. Average total cost also spreads the fixed eighteen across output. At four units, total cost fifty-eight divided by four gives 14.5 per unit. Price eleven exceeds average variable cost ten but falls below average total cost 14.5. The two comparisons answer different questions. One asks whether revenue covers variable resources; the other asks whether it also covers the fixed cost.
An unfavorable first unit can lead to a useful batch
At price eleven, subtract total variable cost from revenue at each shown output. One unit loses one before fixed costs, yet three contribute three and four contribute four. Stopping at the first costly increment misses that batch advantage. This is contribution, not profit: the same unavoidable eighteen must still be subtracted, and higher outputs remain separate alternatives.
There is no average cost at zero output because division by zero has no defined value. There is still a meaningful total cost of eighteen and a profit of negative eighteen. Nor should fixed and sunk be treated as interchangeable descriptions. Fixed means unchanged across the output choices in the period. Sunk means already incurred and unrecoverable. A future license fee might be fixed once the firm chooses to operate but avoidable if it declines the license. The current widget instead assumes its eighteen cannot be avoided by choosing zero. Changing that assumption would change the shutdown comparison and require a different model.
Revenue minus recorded cost is an accounting relation once the recording rules and period are fixed. Choosing the row with the highest profit adds a behavioral assumption about the firm's objective and options. The model assumes all output sells at the stated price, costs are known, finance is available, and no unrecorded constraint prevents production. A real manager may face delivery commitments, uncertain demand, safety obligations, or liquidity limits. These can change feasible choices without invalidating subtraction. The table establishes the best row under its assumptions; it does not establish what an actual firm ought to prioritize or what its managers will choose.
Work through the mechanism
Profit at each feasible output
P is currency per unit, Q units per period, VC variable cost at that output, and F the unavoidable fixed cost for the period. All costs are stated in currency units.
Choose among all feasible outputs
Units
Revenue
Variable cost
Total cost
Profit
0
0
0
18
-18
1
15
12
30
-15
2
30
22
40
-10
3
45
30
48
-3
4
60
40
58
2
5 · best
75
54
72
3
6
90
74
92
-2
Best output in this capacity-limited model: 5. Profit: 3. Shutdown loses 18 because fixed cost is unavoidable.
Currency units per period; at most six units can be produced. Fixed cost is 18. Every output is compared, with the smaller output selected if profits tie. Presets and the slider reprice the same cost schedule immediately. This does not model entry, demand feedback, financing, or a long-run exit decision.
At price 11
Output
Revenue
Total cost
Profit
Shut down
0
0
18
−18
Operate
4
44
58
−14
The fixed cost is unavoidable this period. The operating option contributes 4 toward it but still makes a total loss.
Read the presets as separate operating decisions
Begin with Cover all costs, which sets price fifteen. Revenue at outputs zero through six is zero, fifteen, thirty, forty-five, sixty, seventy-five, and ninety. Adding fixed eighteen to the variable schedule gives total costs eighteen, thirty, forty, forty-eight, fifty-eight, seventy-two, and ninety-two. Subtraction produces profits of negative eighteen, negative fifteen, negative ten, negative three, two, three, and negative two. Five units are best with profit three. Six units generate more sales but lower profit because the sixth adds fifteen of revenue while adding twenty of cost. Maximizing revenue would select a different row from maximizing profit.
Next choose Shut down at price eight. Revenue becomes zero, eight, sixteen, twenty-four, thirty-two, forty, and forty-eight across the seven outputs. The total costs do not change. Profits are negative eighteen, negative twenty-two, negative twenty-four, negative twenty-four, negative twenty-six, negative thirty-two, and negative forty-four. Zero is best because every positive output worsens the loss relative to leaving the equipment idle. The label describes the best decision for this preset within the current period. It does not liquidate assets, dismiss workers in a simulated future, or remove the fixed obligation from subsequent rows.
More output need not mean more profit
Return to the price-fifteen case for every bar; do not carry over the price-eight shutdown preset. Five units earn three, while six lose two because the final unit adds twenty of cost but only fifteen of revenue. Shutdown still loses eighteen. These selected alternatives illustrate the reversal; the full model checks all seven feasible outputs.
The price slider explores between six and twenty-two currency units per unit and immediately reprices the same cost schedule. For a revealing comparison, set fourteen. Four units bring revenue fifty-six against total cost fifty-eight, giving loss two. Five bring seventy against seventy-two, also loss two. Both dominate shutdown's loss eighteen. The interface selects four because it chooses the smaller output when profits tie. This is an explicit selection convention, not an economic proof that four is uniquely optimal. A different tie rule could highlight five without changing the maximum achievable profit at that price.
For a second slider case, set twenty. Five units bring revenue one hundred and cost seventy-two, giving profit twenty-eight. Six bring revenue 120 and cost ninety-two, also giving twenty-eight. The model highlights five under the same tie convention. At twenty-two, the sixth unit adds twenty-two of revenue against twenty of cost, so six becomes best with revenue 132, cost ninety-two, and profit forty. The capacity limit prevents exploring a seventh unit. It would be wrong to extend the last marginal cost mechanically and claim that still more production is profitable; the model supplies no such cost or capacity.
The table preserves every alternative, so inspect the profit column rather than only the highlighted row. Presets and slider changes replace the price assumption and do not accumulate sales, cash, inventories, or losses from earlier clicks. There is no playback to reset, and selecting a preset restores that preset's price rather than a simulated business history. The default price is fifteen. The fixed cost and capacity cannot be changed through the controls. A calculation involving another fixed cost, extra financing, or a lease renewal belongs on paper and should not be described as another available experiment.
A tie can end when the sixth unit pays its cost
In the invented cost schedule, price twenty leaves five and six units tied at twenty-eight; highlighting five merely applies the smaller-output convention. At price twenty-two, six earns forty because its final unit now adds more revenue than cost. These are separate price assumptions, not accumulated earnings. No seventh-unit cost is supplied, so the comparison stops at capacity.
Operating at a loss can be rational temporarily
With an unavoidable fixed cost of 18, shutting down still loses 18. At price 11, producing four units gives revenue 44 and variable cost 40, leaving 4 toward the fixed cost. Profit is negative 14, which is better than negative 18. This is a short-run comparison, not a claim that the firm is healthy or should operate forever.
Long-run survival requires covering relevant opportunity costs, including the owner's time and the return available on alternative uses of capital. Accounting profit may omit some of those implicit costs. Economic profit subtracts them. Zero economic profit can therefore include normal compensation for work and investment. Positive accounting profit is not necessarily an exceptional return, while persistently high returns may reflect innovation, scarcity, risk, or market power.
Separate current operation from renewal and ownership returns
A short-run operating decision compares avoidable consequences from now onward. Under the widget's price-eleven assumptions, four units create a contribution of four after variable costs, reducing the loss on the unavoidable obligation. This does not establish that renewing the arrangement is sensible. For a separate paper decision, suppose the same output opportunities will recur next period but a new eighteen-unit lease payment can be avoided entirely by not renewing. With no other consequences, operating four yields negative fourteen and declining renewal yields zero. The better short-run operating choice and the better renewal choice differ because the available alternatives differ.
Cash timing adds a constraint not represented by period profit. Suppose a workshop expects sixty in customer receipts at the end of the month and must pay forty for materials now plus eighteen for the lease before production. Expected accounting profit is two under those costs. If it begins with only fifty in cash and cannot borrow, it lacks eight to pay the fifty-eight due before receipts arrive. A positive expected profit does not fund that gap automatically. Assuming credit of eight would make payment feasible but would add a liability and possibly interest. The widget assumes away this timing problem rather than solving it.
Later profit cannot pay an earlier bill
The invented workshop owes forty for materials plus eighteen for the lease before producing, but has only fifty available now. Its eight-unit funding gap persists despite sixty expected at month-end and an expected profit of two. These bars compare payment timing, not simultaneous balances. Borrowing could bridge the gap but introduces repayment obligations and possibly interest.
Long-run comparisons also require implicit opportunity costs. In a paper business, suppose revenue is 240 and recorded costs are 180 over a year. Accounting profit is sixty. The owner supplies work that could earn forty-five elsewhere and uses capital that could earn twelve in a comparable alternative. After subtracting both forgone returns, economic profit is three. If recorded costs rise to 185 with the alternatives unchanged, accounting profit is fifty-five but economic profit becomes negative two. The calculation assumes the alternatives are available and measured over the same year, with comparable risk and no double counting of costs already recorded.
Profit also differs from the seller surplus used in a competitive market diagram. If revenue is sixty and variable opportunity costs are forty, seller surplus before fixed costs is twenty. Subtract an unavoidable fixed cost eighteen and the remaining profit is two, assuming the accounts contain all other relevant costs. That profit is not Marxian surplus value. Marx's category concerns surplus labor within his theory of value and class relations, not simply receipts minus the cost entries in this table. Using the same word surplus for both without specifying the theory would erase differences in definitions rather than explain them.
Finally, the firm's private optimum is not a complete appraisal of the activity. If the best output causes an uncompensated cost of seven to neighbors, a recorded profit of three does not establish a positive combined gain. The neighbors bear a cost omitted from the firm's objective. Under a simple additive comparison, three less seven is negative four, though a full assessment would also include customer gains and other affected parties. Costs, rights, and distribution require their own evidence. The output table answers a narrow conditional choice question well precisely because it leaves those broader questions explicit rather than claiming that the best profit row settles them.
Exercises
A fixed-cost change
A firm's unavoidable fixed cost rises by 20, with prices, feasible outputs, and variable costs unchanged. Does its profit-maximizing short-run output necessarily change?
Hint
Compare the same subtraction from every option, including zero output.
Worked answer
Option
Old profit
New profit
A
8
−12
B
3
−17
Shutdown
−10
−30
Option A remains best even though it now loses money.
No. Every option's profit falls by 20, so their ranking stays the same. Long-run entry, exit, or a decision about an avoidable future lease can change. The conclusion relies on the cost being unavoidable for the current comparison.
Account for an owner's alternative
A business has accounting profit 50 after recorded costs. The owner could earn 35 working elsewhere and 10 from an alternative use of invested capital. Ignore double counting and other differences. What is economic profit?
Hint
Subtract the two unrecorded opportunity costs.
Worked answer
Reconciliation
Amount
Accounting profit
50
Alternative labor income
−35
Alternative capital return
−10
Economic profit
5
The numerical residual is not a moral verdict about the owner's entitlement.
Economic profit is 5. The accounting residual of 50 includes compensation for the owner's labor and capital opportunity costs. The comparison depends on those alternatives being genuinely available and measured on a comparable risk and time basis.
Sources and further reading
The lessons and answers stand alone. These optional references identify underlying models, evidence, and perspectives. All numerical examples here are invented unless explicitly attributed; none is a forecast or a personal investment recommendation.
Ownership, organizational authority, incomplete employment contracts, and worker incentives. Our wage-sharing formula is an illustrative bargaining rule, not an estimated wage equation.
Competitive schedules, surplus, taxation, and limits of equilibrium reasoning. All numerical curves in these lessons are separately constructed teaching examples.