Production, Cost and Revenue
This domain links inputs to output and output to cost and revenue. Expect questions on the law of variable proportions, the shape of short-run cost curves, and the relationship between AR, MR and elasticity.
Core rules
- Production function: Q = f(L, K). The short run has fixed factors; in the long run all factors vary.
- Law of variable proportions: with one variable input, MP first rises, then falls, then turns negative - increasing returns, diminishing returns, negative returns.
- TP, AP, MP: AP = TP/L; MP = ΔTP/ΔL. MP cuts AP at AP's maximum.
- Costs: TC = TFC + TVC; AC = AFC + AVC; MC = ΔTC/ΔQ. MC cuts AC at AC's minimum.
- Revenue: TR = P × Q; AR = TR/Q = price; MR = ΔTR/ΔQ. Under perfect competition AR = MR; under monopoly MR < AR.
Worked example
A firm's TFC is ₹100; its TVC at 5 units of output is ₹150. TC = 100 + 150 = ₹250. AC = 250/5 = ₹50. AVC = 150/5 = ₹30. AFC = 100/5 = ₹20. Check: AFC + AVC = 20 + 30 = ₹50 = AC. If TVC at 6 units were ₹186, MC = 186 − 150 = ₹36, which is above AVC, so AVC rises.
Traps that cost marks
- Calling fixed cost "fixed per unit" - TFC is fixed in total, so AFC falls continuously as output rises.
- Saying MC is the cost of all units; MC is the addition to total cost of one more unit.
- Drawing AC and MC without MC cutting AC at the minimum point.
- Forgetting that in the long run there are no fixed costs and no fixed factors.