Producer Behaviour and Supply: Production, Costs and the Law of Supply
Questions here move from the short-run production function and the law of variable proportions, through cost and revenue curves, to the law of supply and elasticity of supply.
Production in the short run
Q = f(L, K), with capital fixed in the short run. TP is total output, AP = TP/L, MP = ΔTP/ΔL. The law of variable proportions has three stages: Stage I, AP rising with MP > AP; Stage II, AP falling but MP positive, ending where MP = 0 and TP is maximum; Stage III, MP negative and TP falling. A rational producer operates in Stage II. MP cuts AP at AP's maximum.
Cost and revenue
TFC is constant, TVC starts from the origin, TC = TFC + TVC. AC = AFC + AVC, and AFC falls continuously. MC = ΔTC/ΔQ = ΔTVC/ΔQ, since fixed cost does not change; MC cuts AC at its minimum from below, and AC falls only while MC < AC. AR = TR/Q = price, MR = ΔTR/ΔQ. Under perfect competition AR = MR; generally MR = AR(1 − 1/e).
Supply
The law of supply: other things equal, quantity supplied rises with price. Es = (% change in quantity supplied) ÷ (% change in price).
Worked example
Labour 1–5 gives TP = 10, 22, 30, 34, 35, so AP = 10, 11, 10, 8.5, 7 and MP = 10, 12, 8, 4, 1. At 2 workers MP (12) > AP (11), so AP rises; AP peaks at 11 where MP cuts it between 2 and 3 workers; after that MP < AP and AP falls. MP is positive throughout, so the firm is in Stage II.
Traps
MC does not depend on fixed cost. AC can fall while MC is rising, provided MC < AC. The law of variable proportions is a short-run law; returns to scale are long-run. A price rise causes extension of supply, not an increase in supply - an increase means a rightward shift from changed input prices, technology or taxes.