Cost Theory

Cost Theory

🟢 Lite — Quick Review (1h–1d)

Cost Theory studies how a firm’s production costs change as output varies. Total Fixed Cost (TFC) stays constant regardless of output (rent, salaries), while Total Variable Cost (TVC) rises with production (raw materials, direct labour). The foundational equation is TC = TFC + TVC, where TC = Total Cost. For per-unit analysis: AC = TC / Q (Average Cost per unit) and MC = ΔTC / ΔQ (Marginal Cost — extra cost of one more unit). Average Fixed Cost = TFC / Q always falls as output grows. Average Variable Cost = TVC / Q first falls, then rises — the classic U-shape driven by the Law of Variable Proportions. A critical inverse link: when Marginal Product (MP) peaks, Marginal Cost (MC) bottoms out. The MC curve cuts the AC curve at its minimum. Memorise these six formulas: TC = TFC + TVC; AC = TC/Q; MC = ΔTC/ΔQ; AFC = TFC/Q; AVC = TVC/Q; AC = AFC + AVC. CMA Foundation typically allocates 4–6 marks from this topic — expect MCQs or short numericals requiring curve relationship identification or cost calculation from a production table.

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🟡 Standard — Regular Study (2d–2mo)

Short-Run Cost Classification

In the short run, at least one input (typically capital) is fixed. TFC includes rent, insurance, and management salaries — it does not change with output level. TVC includes raw materials, direct labour, and power — it rises as production increases. Total Cost (TC) is simply TFC + TVC.

Average and Marginal Cost Measures

Average Fixed Cost (AFC = TFC/Q) continuously declines because the fixed-cost total is spread over more units. Average Variable Cost (AVC = TVC/Q) falls initially due to increasing returns, then rises as diminishing returns set in. Average Cost (AC = TC/Q) is the sum AC = AFC + AVC and follows a U-shaped path. Marginal Cost (MC = ΔTC/ΔQ) measures the change in total cost from producing one additional unit — it depends only on the variable-cost change, never on fixed costs.

The MP–MC Inverse Relationship

The Law of Variable Proportions drives the MP–MC link. When additional units of a variable input (labour) raise Total Product (TP) at an increasing rate, each extra unit of output costs less to produce — MC falls. Once TP increases at a decreasing rate, MC begins to rise. The point where MP is maximum coincides with the point where MC is minimum.

Exam Question Patterns

CMA Foundation questions often provide a table of output (Q) and labour units (L) with wage rate, then ask you to compute TVC, TC, AC, AVC, AFC, and MC. The second common pattern: identify which cost curve is cut by MC at its minimum, or select the correct AC/MC shape from a diagram.

Cost Type	Formula	Behaviour
TFC	Fixed	Constant
TVC	Variable	Rises with Q
AFC	TFC/Q	Always falls
AVC	TVC/Q	Falls then rises
AC	TC/Q	U-shaped
MC	ΔTC/ΔQ	U-shaped, cuts AC minimum

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🔴 Extended — Deep Study (3mo+)

Long-Run Cost Dynamics

In the long run, all inputs are variable — the firm can change its scale of production freely. Long-Run Average Cost (LAC) is U-shaped, but the driver is Returns to Scale rather than variable proportions. When output grows faster than the increase in all inputs, increasing returns to scale cause LAC to fall (economies of scale: specialisation, bulk purchasing, managerial division of labour). When inputs must grow proportionally more than output, decreasing returns to scale push LAC upward (coordination costs, communication bottlenecks). The LAC curve envelopes all possible short-run AC curves.

Marginal Cost in Long-Run Decisions

A firm selecting its optimal plant size in the long run uses the long-run MC curve alongside LAC. The firm chooses the output level where LAC is minimised, which coincides with where long-run MC equals long-run AC. Any short-run plant chosen must be the one whose short-run AC curve is tangent to the LAC curve at the desired output — a tangency condition that CMA Foundation numericals sometimes test.

Common Mistakes to Avoid

1. Confusing MC with AC: MC is the cost of the next unit; AC is the cost per unit of all units produced. They are numerically equal only at AC’s minimum.
2. Treating TFC as variable in short-run analysis: Fixed costs are sunk in the short run — they should not influence marginal decisions about whether to produce an additional unit.
3. Applying Law of Variable Proportions to long-run analysis: That law governs one variable input with fixed capital — it does not apply when all inputs are adjustable.
4. Forgetting the MP–MC inverse link: If a question gives you a TP table, calculate MP first (ΔTP/ΔL) — MC = wage/MP. A high MP means a low MC, and vice versa.

Practice Prompts

1. A firm has TFC = ₹50,000. Labour costs ₹300 per unit. At Q = 0, 10, 20, 30, 40, 50 units, the TP values are 0, 10, 22, 30, 35, 38 respectively. Compute TVC, TC, AVC, AC, MC at each output level and identify where MC is minimum.
2. With the same data, draw the MP curve and explain why the point of maximum MP corresponds to the minimum point of the MC curve, referencing the wage rate explicitly in your derivation.

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