Cost Theory

Cost Theory

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Cost Theory maps how a firm’s output level drives its production costs. In the short run, Total Fixed Cost (TFC) stays constant regardless of output (rent, salaries), while Total Variable Cost (TVC) rises with quantity (raw materials, labor). Total Cost (TC) = TFC + TVC.

Four per-unit formulas to memorize: AFC = TFC/Q (falls continuously as Q increases), AVC = TVC/Q (U-shaped), AC = TC/Q (U-shaped, AC = AFC + AVC), and MC = ΔTC/ΔQ (also U-shaped, crosses AC at its minimum). When MC < AC, AC falls; when MC > AC, AC rises. This intersection is the single most-tested relationship in CA Foundation.

The shut-down point occurs where Price = minimum AVC — if P falls below this, the firm should cease production in the short run.

Key exam pointers: (1) MC always crosses AC at AC’s lowest point — this is non-negotiable geometry, (2) In the long run, TFC disappears because all inputs become variable, (3) LAC envelopes all possible SAC curves as a Planning Curve.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Short-Run Cost Behavior

The short-run cost function holds at least one input fixed (typically capital). TFC remains flat at every output level — it exists even at Q = 0. TVC starts at zero when Q = 0 and increases, initially at a decreasing rate (due to increasing returns to the variable factor), then at an increasing rate (due to diminishing returns).

The Law of Variable Proportions drives this: as a firm adds more units of a variable input to a fixed input, marginal product first rises (causing MC to fall), then falls (causing MC to rise). This creates the characteristic U-shape of both MC and AVC curves.

Deriving MC from TC

MC = dTC/dQ (continuous) or ΔTC/ΔQ (discrete). Since TFC is constant, MC = ΔTVC/ΔQ in the short run. The slope of the TC curve at any point equals MC at that output level.

The MC–AC Relationship

This relationship flows from basic arithmetic, not theory: when adding a new unit costs less than the current average, the average must fall. Formally:

• If MC < AC, the last unit was cheaper than the average → AC falls
• If MC > AC, the last unit was more expensive than the average → AC rises
• Therefore MC = AC at AC’s minimum point

Shut-Down Condition

A firm should continue production in the short run if P ≥ minimum AVC. Below this price, total revenue cannot cover variable costs, so losses from shutting down (equal to TFC) are smaller than losses from producing.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Long-Run Cost Curves: The Envelope Relationship

In the long run, all inputs are variable and no input is permanently fixed. The Long-Run Average Cost (LAC) curve represents the lowest possible average cost at each output level when the firm can choose its optimal factory size. It is the Planning Curve — it tells the firm what scale to build.

Technically, the LAC curve is the envelope of all Short-Run Average Cost (SAC) curves. Each SAC corresponds to a specific plant size. The LAC touches each SAC at exactly one point — the output level where that particular plant size is optimal.

LAC Shape: Economies and Diseconomies of Scale

The U-shape of the LAC arises from two opposing forces:

• Economies of Scale (LAC falling): specialization of labor, managerial division of labor, bulk purchasing, technological adoption
• Diseconomies of Scale (LAC rising): coordination costs, communication breakdowns, loss of entrepreneurial control

Between these zones, constant returns to scale produce a flat segment of LAC.

Long-Run Marginal Cost (LMC)

LMC = ΔLTC/ΔQ. The relationship between LMC and LAC mirrors the short-run MC–AC relationship: LMC crosses LAC at LAC’s minimum. Critically, when LMC < LAC, the firm should increase output (building a larger plant is worthwhile); when LMC > LAC, the firm should reduce output.

Common Mistakes to Avoid

1. TFC in the long run: Students often forget that TFC is a short-run concept. In the long-run, all costs are variable — there is no fixed cost.
2. MC always falling: MC first falls (increasing returns), reaches a minimum, then rises (diminishing returns). It never simply declines with output.
3. AVC at zero output: At Q = 0, TVC = 0 so AVC = 0/0 is undefined, but remember TC = TFC at zero output.
4. SAC–LAC tangency: The LAC envelope touches each SAC at only one point, and the SAC lies above LAC everywhere else.

Worked Example

Suppose TFC = ₹20,000. At Q = 100, TVC = ₹30,000.

• TC = 20,000 + 30,000 = ₹50,000
• AFC = 20,000/100 = ₹200
• AVC = 30,000/100 = ₹300
• AC = 50,000/100 = ₹500 (equals AFC + AVC = 200 + 300 ✓)

If output rises to Q = 200 and TVC becomes ₹50,000:

• MC = (50,000 − 30,000)/(200 − 100) = ₹200 per unit

If P = ₹400, the firm earns ₹80,000 revenue against TC ₹70,000 (profit ₹10,000), so it should produce in the short run since P > minimum AVC.

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