Production and Costs

2.1 Core concepts

• Production is the process by which inputs (labour, machines, land, raw materials) are transformed into output, carried out by producers or firms; production is assumed instantaneous, and "production" and "supply" are used synonymously (NCERT §3 intro, p. 36).
• Cost, revenue, profit: to acquire inputs a firm pays the cost of production; selling output earns revenue; profit = revenue − cost; the firm's objective is maximum profit (NCERT §3 intro, p. 36).
• Production function q = f(L, K) gives the maximum output q for given inputs L and K — it deals only with the efficient use of inputs, and is defined for a given technology; improved technology means a new production function (NCERT §3.1, pp. 37–38).
• Factors of production are the inputs a firm uses; analysis here is restricted to two factors — labour (L) and capital (K) (NCERT §3.1, p. 37).
• Isoquant is the set of all input combinations that yield the same maximum output level; when marginal products are positive, isoquants are negatively sloped (NCERT §3.1 box "Isoquant", p. 38).
• Short run = at least one factor (here capital) cannot be varied and remains the fixed factor; the other is the variable factor. Long run = all factors can be varied; there is no fixed factor. The distinction is not defined in calendar terms but by whether all inputs can be varied (NCERT §3.2, pp. 38–39).
• Total Product (TP): the relationship between a variable input and output when all other inputs are held constant; also called total return or total physical product of the variable input (NCERT §3.3.1, p. 39).
• Average Product: APL = TPL / L — output per unit of variable input (NCERT §3.3.2, eq. 3.2, p. 39).
• Marginal Product: MPL = ΔTPL / ΔL — change in output per unit change in input, holding other inputs constant; MP is undefined at zero level of input; total product equals the sum of marginal products of every preceding unit (NCERT §3.3.3, eq. 3.3–3.4, pp. 39–40).
• Law of Variable Proportions / Diminishing Marginal Product: as a variable input is increased (holding the other fixed), MP first rises, then falls — because factor proportions first become more suitable for production, then the process becomes "too crowded" with the variable input (NCERT §3.4, pp. 40–41).
• Shapes of TP, MP, AP curves: TP is positively sloped; MP curve is inverse-U-shaped; AP curve is also inverse-U-shaped; MP cuts AP from above at AP's maximum — when AP rises, MP > AP; when AP falls, MP < AP (NCERT §3.5, pp. 41–42, Fig. 3.1, Fig. 3.2).
• Returns to scale (long run, both factors scaled by t > 1): CRS if f(tx1, tx2) = t·f(x1,x2); IRS if f(tx1, tx2) > t·f(x1,x2); DRS if f(tx1, tx2) < t·f(x1,x2). If doubling all inputs doubles output → CRS; more than doubles → IRS; less than doubles → DRS (NCERT §3.6, pp. 42–43).
• Cost function gives the least cost of producing each level of output, given factor prices and technology — for every output level the firm chooses the least-cost input combination (NCERT §3.7, p. 43).
• Short-run costs: TC = TVC + TFC (eq. 3.6); SAC = TC/q (eq. 3.7); AVC = TVC/q (eq. 3.8); AFC = TFC/q (eq. 3.9); SAC = AVC + AFC (eq. 3.10); SMC = ΔTC/Δq (eq. 3.11). At zero output, SAC, AVC, AFC and SMC are all undefined; only TFC equals a positive constant and TVC = 0 (NCERT §3.7.1, pp. 43–45, Table 3.3).
• Shapes of short-run cost curves: TFC is a horizontal straight line; AFC is a rectangular hyperbola (AFC × q = TFC, constant); SMC, AVC, and SAC are all U-shaped; SMC cuts AVC from below at AVC's minimum; SMC cuts SAC from below at SAC's minimum; minimum of SAC lies to the right of minimum of AVC because AFC keeps falling even after AVC starts rising (NCERT §3.7.1, pp. 45–48, Fig. 3.3–3.8).
• Long-run costs: all inputs variable → no fixed cost; TC = TVC in the long run; LRAC = TC/q (eq. 3.13); LRMC = (TC at q1) − (TC at q1 − 1) (eq. 3.14) (NCERT §3.7.2, pp. 48–49).
• Shapes of long-run cost curves and link to returns to scale: IRS → LRAC falls; CRS → LRAC constant; DRS → LRAC rises. A typical firm shows IRS, then CRS, then DRS, so LRAC is U-shaped; LRMC is also U-shaped and cuts LRAC from below at LRAC's minimum (NCERT §3.7.2, p. 49, Fig. 3.9).
• Cobb-Douglas: for q = x1^α · x2^β, scaling inputs by t gives output scaled by t^(α+β); so α+β = 1 ⇒ CRS, α+β > 1 ⇒ IRS, α+β < 1 ⇒ DRS (NCERT §3.7 box "Cobb-Douglas Production Function", p. 43).

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 3.1 — Total Product curve: positively sloped curve in the L–output plane; with L units of labour, the firm produces at most q1 (p. 41).
• Fig. 3.2 — AP and MP curves: both inverse-U-shaped; MP cuts AP from above at AP's maximum (point L on horizontal axis); to the left of L, MP > AP and AP is rising; to the right of L, MP < AP and AP is falling (p. 42).
• Fig. 3.3 — TFC, TVC, TC curves: TFC is a horizontal line at c1; TC is the vertical sum of TFC and TVC (p. 45).
• Fig. 3.4 — AFC curve: rectangular hyperbola; area of rectangle OFCq1 = TFC (p. 46).
• Fig. 3.5 — TFC curve geometry: slope of ∠AOq0 (tan θ) gives AFC at q0 (p. 46).
• Fig. 3.6 — AVC curve: U-shaped; area of rectangle OVBq0 = TVC at q0 (p. 47).
• Fig. 3.7 — TVC curve geometry: slope of ∠EOq0 (tan θ) gives AVC at q0 (p. 47).
• Fig. 3.8 — SMC, AVC, SAC curves: all U-shaped; SMC cuts AVC at P (minimum of AVC) and SAC at S (minimum of SAC); q1 < q2, so AVC reaches its minimum before SAC does (p. 48).
• Fig. 3.9 — LRAC and LRMC curves: both U-shaped; LRMC cuts LRAC from below at LRAC's minimum (p. 49).
• Table 3.1 — Production function: L on rows (0–6), K on columns (0–6), entries are q; with L = K = 0 output is 0; with L = 1, K = 1, q = 1; with L = K = 2, q = 10 (p. 37).
• Table 3.2 — TP, MP, AP schedule with K fixed at 4: TP rises from 0 to 57 as L goes 0 to 6; MP rises to 16 (at L = 3), then falls; AP peaks at 13.33 (at L = 3) (p. 40).
• Table 3.3 — Cost schedule: TFC fixed at Rs 20; minimum AVC = 6.5 at q = 6; minimum SAC = 9.57 at q = 7; SMC at q = 5 equals (53 − 49)/1 = 4 (p. 45).

2.5 Key formulas

2.4 Common confusions / NTA trap points

• MP-AP relationship. Students confuse "MP = AP" (AP at its maximum) with "MP = 0" (TP at its maximum). NCERT says MP cuts AP at AP's maximum from above (p. 42).
• Law of Variable Proportions vs Returns to Scale. Variable proportions is a short-run phenomenon (one factor fixed); returns to scale is a long-run phenomenon (all factors scaled proportionally). NCERT explicitly contrasts these in §3.6 (p. 42).
• AFC curve. AFC is a rectangular hyperbola — it falls continuously toward zero but never touches the axis; AFC × q is always equal to TFC (p. 46). Students wrongly say AFC is U-shaped or horizontal.
• Position of minimum AVC vs minimum SAC. Minimum SAC lies to the right of minimum AVC because, after AVC begins to rise, AFC is still falling and initially dominates (p. 48).
• At q = 0. TFC > 0 but TVC = 0, TC = TFC, and AFC/AVC/SAC/SMC are all undefined (Table 3.3, p. 45). A common trap is to take SAC = TFC at q = 0.
• Cobb-Douglas test. For q = x1^α · x2^β, the returns-to-scale verdict depends on (α + β) — not on α and β individually (p. 43).