Producer Behaviour: Production Function, Returns and Equilibrium
This domain tests production relationships - total, average and marginal product, the law of variable proportions, returns to scale, and least-cost input choice.
Core rules
- A production function maps inputs to output; the short run has at least one fixed input, the long run has all inputs variable.
- TP = ΣMP; AP = TP/L; MP = ΔTP/ΔL. MP cuts AP at the maximum of AP.
- Law of variable proportions has three stages. Stage I: MP and AP rise, MP > AP. Stage II: MP falls but stays positive, AP falls and AP > MP, ending where MP = 0. Stage III: MP is negative and TP falls. A rational producer operates in Stage II.
- Returns to scale describe output when all inputs change proportionally - increasing, constant, decreasing - and arise from economies and diseconomies of scale, not factor proportions.
- An isoquant shows input combinations giving the same output; MRTS = MPL/MPK and diminishes along it.
- Least-cost equilibrium: MRTS = w/r, equivalently MPL/w = MPK/r. For output choice the rule is MR = MC.
- Supply rises with price; it shifts with input prices, technology, taxes and subsidies, and the number of firms.
Worked example
Labour 1, 2, 3, 4 gives TP = 10, 24, 33, 36. Then MP = 10, 14, 9, 3 and AP = 10, 12, 11, 9. MP rises up to L = 2 (Stage I), then falls but remains positive while AP also falls and exceeds MP - Stage II. A fifth worker with MP = –2 would cut TP to 34 and begin Stage III, so employment stops at four.
Traps
Writing AP = TP × L. Calling Stage III 'diminishing returns' - diminishing returns is Stage II. Treating returns to scale as the same law as variable proportions. Confusing a movement along the supply curve with a shift.