Cost concepts and cost curves: fixed, variable, average, marginal, explicit, implicit; short-run and long-run cost

1. Cost of production

Cost of production is the total expenditure a firm incurs on the inputs used to produce a given output. The cost function shows cost as a function of output: C = f(Q), for given input prices and technology.

2. Cost concepts

• Explicit costs are actual money payments to outsiders: wages, rent of hired premises, interest on borrowed capital, raw materials, power, taxes. They are recorded in the books (accounting costs).
• Implicit (imputed) costs are the costs of the owner’s own resources, for which no payment is made: rent of his own building, interest on his own capital, salary for his own work. They are opportunity costs and are not in the books. Economic cost = explicit + implicit cost. Accounting profit = revenue − explicit cost; economic profit = revenue − explicit − implicit cost.
• Fixed costs do not change with output in the short run and are incurred even at zero output: rent, salaries of permanent staff, insurance, depreciation by time, interest on loans. Also called supplementary or overhead costs.
• Variable costs change directly with output: raw materials, casual wages, power, packing. Also called prime costs.
• Total, average and marginal cost — see the formulae below.
• Sunk cost (already incurred and irrecoverable) versus incremental cost (the change caused by a decision). Only the second is relevant to decisions.
• Private cost (borne by the firm) versus social cost (borne by society, including pollution).
• Historical cost (original price) versus replacement cost (present price of the same asset).

3. Formulae

4. Problem (February 2025)

From the following data find TFC, TVC, AFC, AVC, MC and AC. Output 0 to 70 in steps of 10; total cost Rs. 600, 700, 900, 1,050, 1,200, 1,500, 1,900, 2,400.

TFC is the cost at zero output: Rs. 600, the same at every level. Output rises by 10 units at a time, so MC = ΔTC ÷ 10.

Reading the result. AFC falls continuously (600 spread over more units). AVC falls to Rs. 15 between 20 and 40 units and then rises. AC is lowest at Rs. 30 between 40 and 50 units; that is the optimum output range of this plant. MC (per unit over each interval of 10) is below AC while AC falls and above it once AC rises. Check one row: at 70 units, AFC 8.57 + AVC 25.71 = 34.28, which equals AC 34.29 apart from rounding.

5. Short-run cost curves

• TFC is a horizontal straight line; TVC starts at the origin and rises, first at a decreasing and then at an increasing rate; TC has the same shape as TVC but starts at the level of TFC.
• AFC falls continuously and approaches the X-axis without touching it (a rectangular hyperbola: AFC × Q is constant).
• AVC, AC and MC are U-shaped. They fall at first because of increasing returns to the variable factor and rise later because of diminishing returns (the law of variable proportions). AC is U-shaped also because the fall in AFC is eventually outweighed by the rise in AVC.
• The AC–MC relation. When MC is below AC, AC falls; when MC is above AC, AC rises; MC cuts AC (and AVC) from below at its minimum point. MC reaches its minimum before AC and AVC do.
• The gap between AC and AVC is AFC, which narrows as output rises.

The diagram, in words. Output on the X-axis, cost per unit on the Y-axis. Draw a falling AFC near the bottom, then U-shaped AVC, and above it U-shaped AC whose minimum lies to the right of AVC’s minimum. Draw a steeper U-shaped MC rising through the lowest points of AVC and then AC.

6. Long-run cost

In the long run all inputs are variable, so there are no fixed costs and the firm can choose the size of plant. For each plant size there is a short-run average cost curve (SAC). The long-run average cost curve (LAC) is the curve tangent to all the SACs: for each output it shows the lowest average cost at which that output can be produced when the plant can be chosen freely. It is therefore called the envelope curve or the planning curve (Jacob Viner, 1931).

• LAC is U-shaped, but flatter than the SACs. It falls at first because of economies of scale (increasing returns to scale), is flat over a range of constant returns, and rises because of diseconomies (diminishing returns to scale).
• On the falling part, LAC touches each SAC to the left of the SAC’s minimum (a plant under-used); on the rising part, to the right (a plant over-used). Only at the minimum of LAC does it touch the minimum of an SAC: that plant is the optimum plant.
• Long-run marginal cost (LMC) cuts LAC at its minimum.
• Empirical studies often find an L-shaped LAC: costs fall and then stay nearly constant over a wide range of output.

How this is examined

February 2025: “Find out TFC, TVC, AFC, AVC, MC, AC” (6 marks) or “Explicit and implicit cost” (6 marks). August 2024: “What is cost of production? Explain the short run cost conditions of a firm with a suitable diagram” (10 marks) and “Explicit and implicit costs”. January 2026: short notes on “Short run cost” or “Long run cost”. In the sum, write the formulae first, then the full table, then two lines of interpretation.