3.1.4.4 - Calculating production costs

Which costs change with output?

A firm's costs of production are the costs of the resources it uses to produce output. A fixed cost does not change with output over the relevant short-run period; a variable cost changes as output changes.

A workshop's contracted rent may be £120 per day whether it makes zero or 40 units. Its spending on materials changes with the number produced. Fixed means fixed with respect to output in that period, not fixed forever: the next rent negotiation could change the amount. Variable does not necessarily mean proportional: overtime rates, bulk discounts and productivity can change the cost of extra production.

Classify the payment, not simply the resource. A salaried employee's daily wage may be fixed over the relevant output range; hourly labour that can be hired as needed is variable. A machine's lease payment can be fixed while its energy use varies with output. State the period and contractual assumptions.

Here $TC$ is total cost, $TFC$ total fixed cost and $TVC$ total variable cost. In the original illustrative table below, the workshop pays its rent even at zero output. No variable inputs are used at zero output.

At 30 units, total cost is $£120+£240=£360$. At zero output it is £120, not zero. A fixed payment does not disappear simply because the firm produces nothing that day.

Cost per unit of output

Average cost is cost per unit of output. Divide a total cost by the output that generated it; do not divide by the number of workers or by the change in output.

$Q$ means output. $AFC$, $AVC$ and $ATC$ are average fixed, average variable and average total cost. “Average cost”, or $AC$, normally means ATC unless a different measure is specified.

For 20 units in the workshop table, $AFC=£120/20=£6$, $AVC=£160/20=£8$, and $ATC=£280/20=£14$ per unit. Check that $£6+£8=£14$.

AFC falls as the same £120 is spread across more output. AVC can move differently: it falls initially, stays at £8 between 20 and 30 units, then rises. From 30 to 40 units, falling AFC exactly offsets rising AVC, so ATC stays at £12. “Spreading fixed costs” does not prove that ATC must fall at every output.

At zero output, the totals are defined but these averages are not: a positive fixed cost divided by zero does not give a meaningful finite cost per unit. Units help prevent mistakes. TC is pounds per day, while ATC is pounds per unit.

The cost of additional output

Marginal cost (MC) is the extra total cost of producing extra output.

If one additional unit raises total cost from £100 to £107, its MC is £7. If the data give blocks of ten units, the calculation gives additional cost per unit over that block; it does not reveal the separate cost of the last individual unit.

In the workshop, raising output from 10 to 20 increases TC from £220 to £280. MC over this interval is $(£280-£220)/(20-10)=£6$ per additional unit. The following intervals give £8 and £12 per additional unit. MC is different from ATC: at 20 units, ATC is £14, but the extra units between 10 and 20 cost £6 each on average.

When fixed cost is unchanged, $\Delta TC=\Delta TVC$, so the same MC follows from variable-cost changes. Dividing the entire £280 by the extra ten units would be wrong: MC uses the change in cost. Changing rent by a fixed amount raises total and average fixed cost, but does not change short-run MC if it leaves the variable-cost schedule unchanged.

Cost data alone do not establish which output maximises profit. A firm must also consider what additional output can earn; producing more to reduce an average may be unwise if the products cannot be sold.

Costs and choices over different periods

Short-run costs reflect at least one fixed input; long-run costs reflect the ability to choose all inputs. In the long run a firm can change its plant and method, so no input is inherently fixed. That does not mean rent or equipment becomes free. After choosing a new plant and signing a contract, a firm can again face fixed payments in its next short-run period.

The following original illustrative options are prospective production methods. Each can produce the stated outputs with identical quality. Constant variable cost per unit is assumed over this range to isolate the choice between fixed and variable costs.

At 40 units, A costs $£120+40(£6)=£360$, £60 less than B. At 80 units, B costs £540, £60 less than A. Their costs are equal when $120+6Q=300+3Q$, giving $Q=60$, with TC £480. B's larger fixed cost is worthwhile only if its variable-cost saving is spread across sufficiently much output, under these assumptions.

An existing short-run plant may prevent switching immediately. A long-run decision can compare both options, allowing for expected demand, quality, reliability and any transition costs omitted from this simple table. The cheapest method is not automatically the most profitable scale of output.

Economists also count opportunity costs of resources owned by the business. Suppose daily revenue is £1,000 and paid costs are £800. The owner's enterprise has a £200 opportunity cost: the minimum reward required to keep the entrepreneur in this activity. Accounting profit before this imputed cost is £200, but economic cost is $£800+£200=£1{,}000$, so economic profit is zero. This minimum entrepreneurial reward, called normal profit, is included in economic costs; zero economic profit does not imply the owner earns nothing. Detailed revenue and profit analysis builds on this cost measurement.

Quick recap

Add fixed and variable costs to obtain TC. Divide totals by output to obtain averages; divide the change in cost by the change in output to obtain MC. State the period and units, and include relevant opportunity costs when using economic profit.