Cost Theory

Cost Theory

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Cost in economics is the monetary value of resources sacrificed to produce a good or service. The accounting view records only explicit costs (wages, rent, materials paid in cash), while the economist adds implicit costs — the opportunity cost of owner-owned inputs (own labour, own capital) — to obtain economic cost. The core six formulas carry every ICAN numerical: TC = FC + VC, AC = TC/Q, AFC = FC/Q, AVC = VC/Q, MC = ΔTC/ΔQ, and Break-even (units) = FC ÷ (Price − AVC). Three points to lock down: (1) MC intersects AC and AVC at their minimum points, not their maximum; (2) short run = at least one fixed factor (commonly capital), NOT a calendar period; (3) a loss-making firm continues in the short run if Price ≥ AVC, otherwise it shuts down.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Cost Categories and Components

Economists split total cost into fixed cost (FC) — outlays that do not vary with output (rent, insurance, salaries of permanent staff, depreciation of plant) — and variable cost (VC), which rises and falls with the quantity produced (raw materials, piece-rate wages, electricity for machines). Total cost is the simple identity TC = FC + VC. Fixed costs exist even when output is zero, so TC starts above the origin on a graph; VC starts at zero. Economic cost goes further: it equals accounting cost (explicit) + implicit cost, where implicit cost is the value of foregone alternatives, e.g. an entrepreneur’s own time that could earn a salary elsewhere, or own capital that could earn interest.

Per-Unit Cost Curves

Dividing totals by quantity gives average measures: AC = TC/Q, AFC = FC/Q, AVC = VC/Q. Because AFC falls continuously as Q rises (a fixed sum spread over more units), the gap between AC and AVC narrows with output but never closes. The marginal cost MC = ΔTC/ΔQ is the extra cost of producing one more unit. ICAN frequently tests the geometric rule that the MC curve cuts both AVC and AC at their respective minima: when MC < AC, AC is falling; when MC > AC, AC is rising; AC is stationary exactly where MC = AC.

Short-Run Behaviour and the Law of Variable Proportions

In the short run at least one factor (capital) is fixed, so adding more of the variable factor (labour) first yields increasing marginal returns (specialisation, better use of the fixed capital), then diminishing marginal returns once the fixed factor becomes overstretched. This produces the characteristic U-shape of MC, AVC and AC: MC dips, reaches a minimum, then rises sharply; AVC and AC lag behind MC and share the U-shape at a flatter level.

Typical ICAN Question Patterns

Candidates should expect MCQ items on (a) identifying which cost is fixed, (b) computing AC/MC from a cost schedule, and (c) interpreting a diagram where MC crosses AVC and AC. Numerical questions frequently supply a table of TC and Q and ask for AC, AVC, AFC and the profit-maximising output where MC equals a given price.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Long-Run Cost Curves and Returns to Scale

In the long run all factors are variable, so the firm can vary plant size. The long-run average cost (LAC) curve is the envelope of all possible short-run average cost (SAC) curves — each SAC corresponds to a different plant size, and LAC touches but never crosses any SAC. The U-shape of LAC reflects first economies of scale (bulk buying, specialisation, indivisibilities, financial discounts, marketing spreads) and later diseconomies of scale (managerial inefficiency, coordination failure, principal–agent problems, input bottlenecks) as the firm grows too large. Returns to scale (long run) is distinct from diminishing returns (short run): the former describes scaling all inputs together, the latter describes holding one input fixed.

The Dual Relationship with Production

A precise microeconomic link ties cost theory to production theory. If w is the price of the variable input (labour) and MPP its marginal physical product, then MC of output = w ÷ MPP. As MPP first rises (specialisation) and then falls (diminishing returns), MC first falls and then rises — confirming why the short-run MC curve is U-shaped. The minimum of MC occurs exactly at the maximum of MPP.

Shut-Down, Break-Even and Exit Rules

The shut-down point is the minimum of AVC: below this price the firm cannot even cover its variable costs and should cease production in the short run, even though FC remains unpaid. The break-even point is where Price = AC, the firm earning only normal profit (zero economic profit). If price falls persistently below AC, the firm exits in the long run, recovering nothing of its avoidable fixed cost; if price stays between AVC and AC, it operates at a loss in the short run but covers variable cost and part of fixed cost — preferable to shutting down and losing all of FC.

Common Mistakes

Students routinely (1) treat the “short run” as 6 or 12 months instead of defining it by fixity of a factor; (2) confuse AC with MC and so wrongly state that AC is rising whenever MC is rising; (3) ignore implicit cost when computing profit, double-counting owner’s salary as both expense and income; (4) claim a loss-making firm must shut down, forgetting the AVC test.

Practice Prompts

1. A firm has FC = ₦200,000, AVC = ₦150 at Q = 1,000 units, and price = ₦180. Should it operate in the short run? Calculate the break-even output.
2. Explain, with reference to the envelope curve, why a firm’s LAC is lower than the highest of its SACs but tangent to the minimum of each chosen SAC.

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