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Class 12 Production and Costs: cheat sheet
CBSE Social Science. The production function: total, average and marginal product, the law of variable proportions, returns to scale, and short-run costs (TFC, TVC, AFC, AVC, AC, MC).
Key ideas
- In the short run at least one input is fixed; in the long run all inputs can vary.
- Law of variable proportions: adding a variable input to fixed inputs first raises its marginal product, which then falls.
- AP rises while MP is above it and falls once MP is below it, so MP cuts AP at the maximum of AP.
- Returns to scale ask what happens when ALL inputs rise in the same proportion: output rising by more, the same or less gives increasing, constant or decreasing returns.
- Fixed costs (rent, permanent salaries) do not change with output; variable costs (raw materials, daily wages) do.
- AFC falls all the way; AVC, AC and MC are U-shaped, and MC cuts AVC and AC at their minimum points.
- The gap between AC and AVC is AFC, so it narrows as output rises.
Remember
| Marginal product | MPₙ = TPₙ − TPₙ₋₁ for the nth worker (TP = sum of MPs) |
| Average product | AP = TP ÷ units of the variable input |
| Total cost | TC = TFC + TVC |
| Average costs | AFC = TFC ÷ q; AVC = TVC ÷ q; AC = TC ÷ q = AFC + AVC |
| Marginal cost | MC = TCₙ − TCₙ₋₁ = TVCₙ − TVCₙ₋₁ (TVC = sum of MCs) |
| Returns to scale | inputs × t: output more than t times = increasing; t times = constant; less = decreasing |
Watch out
- Mixing up diminishing marginal product (one input varied) with decreasing returns to scale (all inputs varied).
- Including TFC when finding MC from TVC, or forgetting that MC is the same from TC or TVC.
- Dividing by the previous output instead of the current one for an average.
Worked example
A firm’s TFC is ₹80 and its TVC for 1 to 6 units is 24, 40, 48, 62, 88, 120 rupees. (a) Find AVC and AC for each output. (b) Find MC for each unit. (c) What happens to the gap between AC and AVC, and why?
Working: AVC = TVC ÷ q; AC = (TFC + TVC) ÷ q; MC = change in TVC
Answer: (a) AVC 24, 20, 16, 15.5, 17.6, 20; AC 104, 60, 42.67, 35.5, 33.6, 33.33 (b) MC 24, 16, 8, 14, 26, 32 (c) it narrows, because the gap is AFC, which falls as output rises
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