Unit 2: Production, cost and revenue

A production function shows the technical relationship between physical inputs and output: Q = f(L, K).

• Short run: at least one factor is fixed (capital); output changes by varying the variable factor (labour).
• Long run: all factors are variable.

Law of variable proportions

• Stage I: TP rises at an increasing rate, then AP reaches maximum — under-use of fixed factor.
• Stage II: MP diminishes but positive; rational stage of production.
• Stage III: MP negative; TP falls — no rational producer operates here.
• Causes of diminishing returns: fixed factor, imperfect substitutability of factors, overcrowding.

An isoquant (equal-product curve) shows combinations of two inputs (L and K) that produce the same output.

• Properties: slope downward, convex to the origin (diminishing MRTS), do not intersect, higher isoquants = higher output.
• MRTS(L,K): units of capital that can be replaced by one unit of labour keeping output constant = MPL/MPK.
• Isocost line: combinations of inputs with the same total cost: w·L + r·K = C.

• Producer's equilibrium (least-cost combination): where an isocost line is tangent to an isoquant — MRTS = w/r, or MPL/w = MPK/r.
• Expansion path: the locus of least-cost combinations as output expands.

Returns to scale describe how output changes when all inputs are increased in the same proportion.

• Causes of increasing returns: internal economies — specialisation, indivisibility of machines, managerial and technical economies.
• Causes of decreasing returns: diseconomies of large scale — coordination and management difficulties.
• Cobb–Douglas production function: Q = A·L^α·K^β; returns to scale increasing if α + β > 1, constant if = 1, decreasing if < 1.

• Normal profit is the minimum profit needed to keep the entrepreneur in the business — included in economic cost.
• Economic profit = Total revenue − (Explicit + Implicit costs).

• AFC falls continuously (rectangular hyperbola).
• AVC, ATC and MC are U-shaped due to the law of variable proportions.
• MC cuts AVC and ATC at their minimum points — when MC < AC, AC falls; when MC > AC, AC rises.

• In the long run all costs are variable; the firm chooses the plant size.
• The long-run average cost (LAC) curve is the envelope of short-run average cost curves — touches each SAC at one point (planning curve).
• LAC is U-shaped (but flatter) due to economies and diseconomies of scale.

• Modern theory: LAC is often L-shaped — after minimum efficient scale, costs remain roughly constant.
• Long-run marginal cost (LMC) cuts LAC at its minimum.

• Short-run AVC is saucer-shaped — flat over a range of output because firms build reserve capacity for flexibility; MC equals AVC over this range.
• Long-run average cost is L-shaped — costs fall up to the minimum efficient scale (MES) and then remain roughly constant, because managerial diseconomies are offset by technical economies and decentralised management.
• Empirical evidence (Johnston, Bain) supports L-shaped LAC curves in many industries.
• Implication: large firms can expand without rising unit costs; barriers to entry for small firms where MES is large (steel, cement, automobiles).

• Under perfect competition, price is constant, so AR = MR — a horizontal line.
• Under imperfect competition, AR slopes downward and MR lies below AR (for a straight-line AR, MR falls twice as fast).
• TR is maximum when MR = 0.