Production, costs and feasible profit

A workshop can produce more chairs yet earn less if additional chairs sell cheaply or require costly overtime. It can also earn money while imposing a cost on people outside the transaction. Keep three questions separate: what can be produced, what the producer gains, and what happens to everyone affected. We begin with the technical relationship between inputs and output, then add prices and opportunity costs. This sequence makes it easier to see which conclusions arise from technology and which depend on markets, alternatives and values.

Imagine a workshop with one cutting machine and different numbers of workers. Adding a worker can change how effectively the machine is used, but adding a second machine is outside this particular short-run choice. A different business may adjust equipment much faster or slower. The distinction is about available adjustment, not a fixed calendar rule. The production relationship also assumes comparable worker hours, skill and material quality. If those change across observations, a higher output cannot automatically be attributed to worker numbers alone.

Subtract each output from the next one. The first worker adds 12 minus zero. The second adds 28 minus 12, or 16. The third adds 39 minus 28, or 11. The fourth adds seven and the fifth adds four. Early specialisation can explain an initial rise in marginal product; crowding around fixed equipment can explain a later decline. These are possible mechanisms, not facts established merely by the table. Diminishing marginal product means smaller additions to output, not necessarily falling total output or a judgement about any worker’s individual worth.

At two workers, output of 28 gives an average of fourteen. The third worker adds eleven units, below fourteen, so the new average falls to thirteen. This is a general property of averages. A new observation below an existing average lowers that average when weights are comparable. Average product and marginal product answer different questions: output per worker across the whole team versus output added by a change in team size. Neither alone determines the profit-maximising workforce, because we also need output prices, labour costs and any other costs caused by expansion.

Do not use fixed and sunk as synonyms. Suppose a workshop can cancel next month’s room hire at no charge. The hire is fixed over the month’s feasible production range, but avoiding it is relevant to whether the workshop opens. A non-refundable design payment made last year is sunk for today’s decision. A machine already owned may still have a resale or rental alternative, creating an opportunity cost even if no new cash payment is needed. Classify costs for the specific decision and period rather than attaching permanent labels without context.

If an owner could earn money elsewhere during the same hours, business receipts alone do not show whether operating improves their position. One method subtracts forgone alternative earnings from the business cash surplus. Another adds remaining alternative earnings to business receipts and compares that full allocation with working elsewhere throughout. Both should agree when they include the same costs and time. An accounting allocation may or may not reflect a relevant sacrifice. Ask whether the decision changes cash spending, resource use or the value of an available alternative.

Begin with consistent time units. Divide twelve minutes by sixty to obtain 0.2 hours. Multiply by the available alternative hourly return of fifteen pounds, giving a three-pound opportunity cost per unit. Subtract both the seven-pound cash cost and this time cost from the selling price. Eight pounds remains to cover the costs that do not vary with unit volume and then provide an economic surplus. This contribution assumes each extra sale leaves other sales unchanged, uses the stated resources and fits within capacity. It is not yet the profit on an entire month.

Check the result by two routes. The contribution route gives 30 times eight, or £240, less fixed economic costs of £90 plus four times £15, yielding £90. The cash route begins with 30 times £18 revenue, or £540. Subtract £210 variable cash costs and £90 monthly cash costs to get £240. Production takes thirty times 0.2 hours, or six hours, and maintenance takes four more. Ten hours valued at £15 cost £150 in forgone earnings. Subtracting that from cash surplus gives the same £90 economic result.

Write economic surplus as eight times quantity minus 150. Set it equal to zero, add 150 to both sides and divide by eight. The result is 18.75, which is a planning boundary rather than a possible whole-unit sale count. At eighteen units, contribution is £144 and the business is six pounds short. At nineteen, contribution is £152 and the surplus is two pounds. This threshold assumes unchanged prices, costs and product mix. If contribution were zero or negative, increasing volume alone would not cover positive fixed costs within this linear model.

A project can have been disappointing overall and still be worth continuing from today, or have done well historically and now be worth stopping. The relevant question is what each available decision changes. Sunk-cost reasoning does not require forgetting the past: past results can inform forecasts and reveal mistakes. It requires separating information from an unrecoverable payment. Also check whether something described as sunk really is unrecoverable. If the design could be licensed to someone else only when unused by this business, that alternative would create a current opportunity cost.

Subtract fixed time before dividing by time per unit: twenty minus four is sixteen, and sixteen divided by 0.2 is eighty. At full capacity, an extra order cannot simply consume another otherwise unused twelve minutes. It may displace an existing order, require overtime or require someone else’s help. Its opportunity cost must reflect that actual alternative. A constant-contribution formula is useful only while its resource and pricing assumptions hold. Always check a proposed break-even or switching threshold against capacity before presenting it as a feasible business plan.

Multiply each output by twelve, then subtract one hundred pounds per worker and the committed sixty pounds. For three workers, revenue is 39 times twelve, or £468; costs are £300 plus £60, leaving £108. The fourth adds seven units worth £84 but costs £100, reducing the result by £16. The fifth also reduces it. The first three additions increase the result, even though the one-worker total remains negative after the committed cost. This example shows why marginal contributions and complete-plan comparisons work together. The conclusion assumes all listed staffing options are feasible.

A business may discover a useful way to serve customers, or it may benefit from restricted entry, misleading information or costs imposed on others. The same accounting label cannot distinguish those cases by itself. A liberty-oriented approach values experimentation and voluntary cooperation, while a careful analysis asks how rights, liability and competition shape the available opportunities. Long-run entry can reduce some excess returns, but barriers, innovation and uncertainty can sustain differences. Avoid turning a useful tendency into a promise that all markets instantly reach identical returns or perfectly reward social value.

A good business calculation should be reproducible by someone who knows only the assumptions and arithmetic. Label pounds per unit, hours per month and total pounds distinctly. Show intermediate values before rounding and explain whether an average represents expected product mix or actual sales. Then test the assumptions most likely to reverse the choice, such as demand, service time or the availability of alternative work. The numerical exercises check specified calculations. Their ungraded reflection fields ask you to identify what the arithmetic leaves unresolved rather than pretending that an automatic marker can fully assess business judgement.