3.6. Firms’ costs, revenue and objectives

Learning objectives

3.6.1Definitions of costs of production• total cost (TC), average total cost (ATC), fixed cost (FC), average fixed cost (AFC), variable cost (VC), average variable cost (AVC)3.6.2Calculation of costs of production• calculation of TC, ATC, FC, AFC, VC and AVC• drawing and interpretation of diagrams that show how changes in output affect costs of production 3.6.3Definition of revenue• definitions of total revenue (TR) and average revenue (AR)3.6.4Calculation of revenue• calculation of TR and AR• the influence of sales on revenue 3.6.5Objectives of firms• survival, social welfare, profit maximisation and growth

A firm's total cost is built from fixed cost and variable cost. Fixed cost does not change when output changes in the short run and is still paid at zero output; variable cost changes with output. An average cost expresses a total per unit of output.

Measure	Meaning	Typical interpretation
FC	total fixed cost	rent or insurance that remains when output is zero
VC	total variable cost	materials or production labour that changes with output
TC	all production cost	FC plus VC
AFC	fixed cost per unit	the same FC spread across output
AVC	variable cost per unit	VC divided across output
ATC	total cost per unit	TC divided across output; also AFC plus AVC

$TC = FC + VC AFC = FC / Q AVC = VC / Q ATC = TC / Q = AFC + AVC$

Classify a cost by how it behaves as output changes, not just by its name. Wages or electricity may be fixed in one production setting and variable in another; state the relevant time period and output relationship.

For each output level Q, first identify FC and VC, calculate TC = FC + VC, then divide the relevant total by Q for AFC, AVC or ATC. Keep totals and per-unit figures separate and do not divide when output is zero.

| Q | FC ( $) | VC ($ ) | TC ( $) | AFC ($ ) | AVC ( $) | ATC ($ ) |
|---:|---:|---:|---:|---:|---:|---:|
| 20 | 40 | 40 | 80 | 2 | 2 | 4 |

For a total-cost diagram, place cost on the vertical axis and output on the horizontal axis. FC is horizontal above zero. VC normally begins at the origin and rises with output. TC begins at the FC intercept and remains vertically above VC by exactly FC because TC − VC = FC.

For an average-cost diagram, AFC falls as output rises because the same fixed cost is spread over more units. At each output, the vertical gap between ATC and AVC equals AFC. Read a curve value at the chosen output before comparing costs; a falling average can coexist with a rising total.

The height of a total-cost curve is a total amount, while the height of an average-cost curve is cost per unit. Mixing those two scales is the main source of incorrect calculations and diagram readings.

Revenue is the money a firm receives from sales. Total revenue (TR) is the firm's whole sales receipt over a period; average revenue (AR) is sales revenue per unit sold.

$TR = total sales revenue AR = TR / Q sold$

If every unit is sold at one price, AR equals that price. For example, sales of 50 units at $3 each give TR of$ 150 and AR of $3.

Revenue is not profit. Revenue records money from sales before production costs are deducted; high revenue can therefore occur alongside low profit or a loss.

$TR = price × quantity sold AR = TR / quantity sold$

Use quantity actually sold, not merely produced. If price is unchanged, more sales raise TR in direct proportion. If price and sales both change, calculate price × quantity for each situation before deciding the revenue effect.

| Situation | Price ( $) | Sales | TR ($ ) | AR ($) |
|---|---:|---:|---:|---:|
| before | 5 | 1000 | 5000 | 5 |
| after | 10 | 600 | 6000 | 10 |

Here sales fall by 400 units but TR rises by $1000 because the higher price more than offsets the lower quantity sold. AR rises to$ 10 because each sold unit brings in $10.

More sales do not guarantee more revenue when the selling price changes, and a higher price does not guarantee more revenue when sales fall. Compare the two complete TR calculations.

A firm's objective is the outcome guiding its decisions. The priority can change with ownership, competition, finances and time, and a firm may pursue more than one objective while accepting trade-offs.

Objective	Decision rule	Likely emphasis	Possible trade-off
survival	keep operating, especially during start-up or difficult trading	cash flow, retaining customers and covering costs over time	postpone growth or accept lower short-run profit
social welfare	improve outcomes for workers, consumers, communities or the environment	access, working conditions, sustainability or essential services	higher cost or lower financial return
profit maximisation	choose the output where TR minus TC is greatest	revenue growth and cost control	may conflict with welfare or rapid expansion
growth	increase output, sales, market share or business scale	investment, new products, outlets or markets	uses finance and can raise risk or short-run cost

A new small firm may prioritise survival, a state-owned health provider may prioritise social welfare, and an established private firm may emphasise profit or growth. These are plausible priorities, not automatic rules based only on ownership.

Profit maximisation means the greatest possible gap between TR and TC, not the greatest output, revenue or profit compared with last year. Growth can support later profit but is a separate objective.

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3.6. Firms’ costs, revenue and objectives

Learning objectives

Connect fixed, variable and average costs

Calculate and interpret production costs

Distinguish total and average revenue

Calculate how sales change revenue

Compare the objectives of firms

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