Cost Theory

Cost Theory

🟢 Lite — Quick Review (1h–1d)

Cost Theory examines how total cost changes as a firm varies its output level, distinguishing between the short run (at least one fixed input) and the long run (all inputs variable). The core relationships are:

• TC = TFC + TVC — Total Cost equals Fixed Cost plus Variable Cost
• AC = TC / Q — Average Cost per unit of output
• MC = ΔTC / ΔQ — Marginal Cost; the cost of producing one additional unit
• AFC = TFC / Q — Average Fixed Cost falls continuously as output rises
• AVC = TVC / Q — Average Variable Cost first falls, then rises (U-shaped)

Three high-yield pointers for RPSC RAS:

1. MC intersects AVC and AC at their minimum points — this is a perennial MCQ trap. If MC lies below AVC, AVC is falling; when MC rises above AVC, AVC begins rising.
2. AFC is always declining — TFC is spread over more units as Q increases, so AFC hyperbolically approaches the horizontal axis.
3. LAC is the envelope of SAC curves — the Long-Run Average Cost curve touches each Short-Run Average Cost curve at the output level where the chosen plant size is exactly optimal. LMC crosses LAC at its minimum point.

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🟡 Standard — Regular Study (2d–2mo)

Short-Run Cost Behaviour

In the short run, the Total Fixed Cost (TFC) curve is a horizontal line at the level of the fixed input’s cost — it does not change regardless of output. Total Variable Cost (TVC) follows the shape of the marginal product curve: it rises at a decreasing rate while marginal returns are increasing, then rises at an increasing rate once diminishing marginal returns set in.

The Law of Variable Proportions drives this. As the firm adds more units of the variable input to a fixed quantity of other inputs, marginal product (MP) first rises (reducing MC), then falls (increasing MC). Consequently, the MC curve is U-shaped — it slopes downward while MP is rising, then turns upward as MP declines.

Cost Concept	Formula	Behaviour in SR
TFC	Fixed inputs × their prices	Constant at all Q
TVC	Variable inputs × their prices	Rises; rate changes at inflection
AFC	TFC / Q	Continuously falls
AVC	TVC / Q	Falls then rises (U-shaped)
AC	TC / Q	Falls then rises (U-shaped)
MC	ΔTC / ΔQ	Falls then rises; intersects AVC and AC at their minima

Long-Run Cost Curves

In the long run, all inputs are variable. The firm can choose any scale of plant. The Long-Run Average Cost (LAC) curve is derived by joining the minimum points of all possible Short-Run Average Cost (SAC) curves — this is the Envelope Theorem. The firm expands along the output level where LAC is tangent to the relevant SAC.

LAC is U-shaped because economies of scale (specialisation, indivisibilities, managerial efficiency) initially cause LAC to fall, while diseconomies of scale (coordination problems, communication breakdowns) eventually cause it to rise. The output level at the minimum point of LAC is the minimum efficient scale.

The Long-Run Marginal Cost (LMC) curve passes through the minimum point of LAC. Cost minimisation requires the firm to produce where the isoquant is tangent to the iso-cost line: MPL / w = MPK / r, where w is the wage rate and r is the rental rate of capital.

Opportunity Cost and Profit Concepts

Explicit costs are direct monetary payments (wages, rent, materials). Implicit costs are the opportunity costs of resources owned by the firm (owner’s time, capital invested). Economic cost = Explicit + Implicit cost. Normal profit is the minimum return required to keep the entrepreneur in this industry — it is an implicit cost included in TC. Economic profit = Total Revenue − Economic Cost.

A sunk cost is an irrecoverable fixed cost — once paid, it should not influence future output decisions. Rational decision-making requires ignoring sunk costs.

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🔴 Extended — Deep Study (3mo+)

The MC–MP Relationship

A fundamental link connects production theory and cost theory. The marginal cost of the variable input is: MC = w / MPL, where w is the price of the variable input. When the marginal product of labour (MPL) rises, MC falls; when MPL falls due to diminishing returns, MC rises. This explains the U-shape of MC mechanistically — it is not arbitrary but derived directly from the production function. In RPSC RAS papers, numerical questions frequently ask students to calculate MC given wage rate and MPL, or to identify the output level where MC equals a given price.

Envelope Theorem — Why LAC is Never Above SAC

The Envelope Theorem states that the LAC curve is the lower-bound envelope of all attainable SAC curves. At any output level Q*, the firm selects the SAC curve corresponding to the plant size that minimises cost at exactly Q*. For output levels left or right of Q*, the firm incurs higher average cost on that same plant — hence SAC lies above LAC except at the tangency point. Students frequently err by assuming LAC is simply the average of SAC curves; it is actually the outer boundary (lower envelope) of the family.

Returns to Scale and LAC Shape

The behaviour of LAC reflects returns to scale in production. If production exhibits increasing returns to scale (output grows faster than all inputs), LAC falls. If constant returns to scale prevail, LAC is flat. If decreasing returns to scale set in, LAC rises. Diseconomies of scale arise from managerial complexity — as firm size grows, monitoring efficiency drops, communication lags, and bureaucratic costs increase. This is a common RPSC RAS question angle: distinguishing internal economies (firm-specific) from external economies (industry-wide).

Common Mistakes to Avoid

1. Treating AFC as variable — AFC falls with every unit increase in Q but never becomes zero; TFC is paid regardless of output level.
2. Forgetting that MC = ΔTVC / ΔQ — in the short run, MC depends only on the change in variable cost, not on TFC, because TFC is constant.
3. Confusing economic profit with accounting profit — accounting profit ignores implicit costs; economic profit subtracts both explicit and implicit costs, including normal profit.
4. Assuming LAC is always U-shaped — some industries exhibit L-shaped LAC (constant returns followed by diseconomies) or downward-sloping LAC (persistent economies). The shape depends on the underlying technology.

Practice Prompts

1. A firm pays ₹500/day as wage to labour. At the current output level, the marginal product of labour is 25 units/day. Calculate the marginal cost. If the firm faces a product price of ₹30, should it increase or decrease output to maximise profit? (Hint: MC = w/MPL = 500/25 = ₹20; since P > MC, expand output.)

2. In the long run, a firm can choose between three plant sizes with SAC curves whose minimum points are at outputs 100, 200, and 300 units with AC values of ₹40, ₹35, and ₹38 respectively. Draw the LAC envelope and identify the minimum efficient scale. (Hint: the minimum point of LAC is at output 200 units with AC = ₹35, which is the MES.)

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