Cost concepts: cost function, fixed, variable, sunk and marginal cost

Detail

1. The cost function

• Cost function: it gives the least cost of producing each level of output. Two things are taken as given:
• factor prices (the wage of labour, the rent of capital);

• technology (the production function, i.e. which input mixes can produce which output).

• A firm can often make the same output with different mixes of labour and capital. The cost function records only the cheapest mix, the least-cost combination from Section 5.

• Example: a firm can make 50 units in three ways, costing ₹500, ₹450 and ₹520. Only ₹450 goes into the cost function as C(50).

• So the cost function already assumes the firm is technically efficient (no inputs wasted) and economically efficient (the cheapest mix is used).

• Link to the Class 8 idea of factors of production: land, labour, capital and entrepreneurship are combined to produce goods. The cost function is the money cost of the best such combination at each output.

2. Explicit vs implicit costs (beyond NCERT)

• Explicit costs: money actually paid out to others. Examples: wages, rent, raw materials, interest on loans.
• Implicit (imputed) costs: the value of inputs the owner supplies personally, valued at their opportunity cost (the best income they could have earned elsewhere).

• Examples: the owner's own capital (lost interest), own building (lost rent), own labour (lost salary).

• Accounting cost = explicit costs only.

• Economic cost = explicit + implicit costs.
• Worked example: a shop owner pays ₹6 lakh a year for rent, stock and a helper (explicit). They also put in ₹10 lakh of their own savings, which could earn 7% interest (₹70,000), and give up a job paying ₹4 lakh a year.
• Accounting cost = ₹6 lakh.

• Economic cost = ₹6 lakh + ₹0.7 lakh + ₹4 lakh = ₹10.7 lakh.

• Indian policy use: CACP cost concepts for MSP

• The Commission for Agricultural Costs and Prices (CACP) looks at two cost measures when it recommends Minimum Support Prices (MSP): A2+FL and C2 [5].
• Its cost of production covers paid-out costs such as hired human labour, bullock and machine labour, rent paid for leased-in land, seeds, fertilisers, manures, irrigation charges, depreciation on implements and farm buildings, interest on working capital, and diesel or electricity for pump sets. It also counts the imputed value of family labour [5].
  • A2 is the explicit cost. A2+FL adds family labour, which is an implicit cost.
• CACP calculates the return on A2+FL only. It uses C2 mainly as a benchmark reference cost (opportunity cost), to check that the MSP covers C2 in major producing States [5].
  • C2 is the closest match to "economic cost", because it also values the farmer's owned land and capital.

• CACP recommends MSP with a margin of at least 50% over the cost of production. It also weighs demand and supply, domestic and world prices, inter-crop price parity and the terms of trade [5].

• Normal profit is covered in firm-supply-perfect-competition. Opportunity cost as a concept is covered in economic-problem-systems.

3. Short-run cost components

• Short run: at least one input (for example plant or machinery) is fixed. Only some inputs can change. Because of this, costs split into fixed and variable parts.

(a) Total Fixed Cost (TFC)

• TFC: the cost of fixed inputs. It must be paid even at zero output.
• Examples: rent, interest on loans, salaries of permanent staff, insurance, licence fees, depreciation.
• In economics, fixed costs stay the same when output rises or falls in the short term. Examples are leasing a building and maintaining heavy machinery [2].

• Depreciation (wear and tear of machines and buildings) appears in MoSPI's national accounts as "consumption of fixed capital" [6].

• TFC is the same at every output level, so its curve is a horizontal line parallel to the output axis.

(b) Total Variable Cost (TVC)

• TVC: the cost of variable inputs, which change with output.
• Examples: raw materials, power and fuel, wages of casual labour.

• Variable costs rise or fall with the quantity of output. Labour and raw materials are the standard examples [3].

• TVC is zero at zero output (no production means no raw material). It rises as output rises.

(c) Total Cost (TC)

• Formula: TC = TVC + TFC.
• The TC curve is the TVC curve shifted up by TFC. The vertical gap between them is always equal to TFC.
• TC starts at TFC on the vertical axis, not at the origin. TVC starts at the origin.
• Why TVC and TC have an inverse-S shape (Law of Variable Proportions, LVP):
• At first, the marginal product of the variable input rises. Each extra unit of output needs less extra input, so costs rise at a falling rate.
• Later, marginal product falls (diminishing returns). Each extra unit of output needs more extra input, so costs rise at a rising rate.
• Result: the curve is first concave, then convex (the inverse-S).

(d) Average cost

• Average cost (AC or ATC) = TC / q.
• It can be split into two parts:
• AFC = TFC / q (falls steadily as output rises, because a fixed amount is spread over more units);
• AVC = TVC / q;
• AC = AFC + AVC.

(e) Marginal cost (MC)

• MC = ΔTC / Δq: the addition to total cost from producing one more unit of output.
• In the short run TFC does not change, so ΔTC = ΔTVC. Hence MC = ΔTVC / Δq.

• Marginal cost is roughly the rise in variable cost when output goes up by one unit [4].

• ΣMC = TVC: adding up the MC of every unit produced gives total variable cost. Fixed cost is never part of MC.

4. Worked example (NCERT Table 3.3)

q	TFC (₹)	TVC (₹)	TC (₹)	MC (₹)	AFC (₹)	AVC (₹)	AC (₹)
0	20	0	20	–	–	–	–
1	20	10	30	10	20	10	30
2	20	18	38	8	10	9	19
3	20	24	44	6	6.67	8	14.67

• TFC stays at ₹20 at every output, including zero.
• MC: 30 − 20 = 10; 38 − 30 = 8; 44 − 38 = 6. MC is falling here because the firm is in the stage of increasing returns to the variable input.
• Check ΣMC = TVC: 10 + 8 + 6 = 24 = TVC at q = 3.
• AFC falls from 20 to 10 to 6.67 as the ₹20 is spread over more units.

5. Sunk cost

• Sunk cost: money already spent that cannot be recovered in any way, whether by selling the asset, by exiting, or by stopping production.

• Examples: specialised machinery with no resale value, research and development (R&D), non-refundable licence or spectrum fees.

• Decision rule: a rational firm ignores sunk costs when it makes forward-looking decisions. Only future (avoidable) costs and benefits matter.

• The past spending is lost whether the firm continues or stops, so it cannot change which option is better.

• Sunk-cost (Concorde) fallacy: continuing a project only because "we have already spent so much".

• The name comes from the Anglo-French Concorde supersonic jet, which was kept going long after it was clearly unprofitable.

• Worked example: a firm has spent ₹5 crore (sunk) on a project. Finishing it needs ₹3 crore more and will bring in ₹2 crore.

• Right decision: compare ₹3 crore of future cost with ₹2 crore of future benefit, and stop.
• The ₹5 crore is gone either way.

6. Fixed ≠ sunk

• Fixed cost does not vary with output. It may still be avoidable in the long run or on exit. For example, rent stops when the lease ends.
• Sunk cost is gone for good, whatever the firm does next.
• A cost can be fixed but not sunk (monthly rent on a lease the firm can end). It can also be both fixed and sunk (a non-refundable licence fee already paid).
• In the long run, all costs are variable. There is no TFC in the long run, but costs already sunk stay sunk.

Cost	Varies with output?	Recoverable?
Rent	No (fixed)	Avoidable when the lease ends
Raw materials	Yes (variable)	Not incurred if output is not produced
R&D already spent	–	No (sunk)

Prelims Hooks

• Cost function = the minimum cost of producing each output, given factor prices and technology. It does not include every possible cost.
• TC = TFC + TVC. At zero output, TC = TFC and TVC = 0.
• TFC curve is horizontal. TVC starts from the origin. TC starts from the vertical axis at the level of TFC.
• Short-run MC = ΔTVC / Δq. TFC has no effect on MC. ΣMC = TVC, not TC.
• TVC and TC have an inverse-S shape because of the Law of Variable Proportions, not because of returns to scale.
• Trap: all sunk costs are fixed in character, but not all fixed costs are sunk (lease rent can be avoided on exit).
• Accounting cost = explicit costs only. Economic cost = explicit + implicit costs. So economic profit ≤ accounting profit.
• CACP calculates the return for MSP on A2+FL (paid-out costs plus the imputed value of family labour). It uses C2 only as a benchmark opportunity cost. The margin is at least 50% over the cost of production [5].
• In national accounts, depreciation is called consumption of fixed capital [6].

Mains Points

• Which cost to use for MSP: A2+FL or C2 (GS-III, agriculture)
• CACP calculates the return on A2+FL. That base leaves out the rental value of owned land and the interest on owned capital, which are implicit costs [5].
• Farmer groups ask for the margin over C2, which is closer to the full economic cost.

• Trade-off: a C2-based MSP gives farmers a better real income. But it raises the fiscal cost of procurement, pushes up food inflation and makes cropping patterns worse (more paddy and wheat).

• Sunk costs and public projects (GS-III, infrastructure and investment)

• Stalled projects are often kept going because "₹X crore is already spent". This is the Concorde fallacy.

• Appraisal should look only at the remaining cost against the remaining benefit. This matters for reviving stalled infrastructure and for PSU disinvestment decisions.

• High sunk costs are entry barriers (GS-III, competition and regulation)

• Examples: telecom spectrum, R&D in pharmaceuticals, rail and power networks.
• Firms will not enter if they cannot recover these costs on exit. So markets end up with few firms, and regulation of prices and access is needed.

• The same logic explains why governments sometimes share project risk, as in viability gap funding.

• High fixed costs and small firms (GS-III, MSMEs)

• AFC falls as output rises. So small firms with high fixed costs (rent, licences, compliance) face high average costs.
• This is why lower compliance and fixed costs (such as through single-window clearance) matter for MSME competitiveness.