Theory of Production and Cost
Domain 5 tests production functions, the law of variable proportions, returns to scale, and short-run and long-run cost curves. Numerical questions on total, average, and marginal product and on cost are common.
Core rules and concepts
- In the short run at least one factor is fixed; in the long run all factors can vary.
- Total product, average product (TP/L), and marginal product (ΔTP/ΔL) follow the law of variable proportions: increasing, diminishing, and negative returns.
- Marginal product cuts average product at the maximum of average product.
- Returns to scale describe output response when all inputs change proportionally.
- Cost: TC = TFC + TVC; AC = TC/Q; MC = ΔTC/ΔQ. MC cuts AC at AC's minimum. Fixed costs do not affect marginal cost.
Worked example
Labour units 1 to 4 give TP = 10, 24, 36, 40. MP is 10, 14, 12, 4; AP is 10, 12, 12, 10. AP is highest at 3 units, where MP equals AP at 12. Diminishing returns set in after the second unit, because MP falls from 14 to 12. If TC rises from ₹500 to ₹560 when output rises from 20 to 30, MC = ₹60/10 = ₹6.
Traps that cost marks
Do not confuse diminishing returns with negative returns. Do not say MC cuts AC at AC's maximum; it cuts at the minimum. Do not include fixed cost in marginal cost. Do not treat accounting cost as economic cost, which includes implicit costs.