Cost concepts: TFC, TVC and TC
Cost = money spent on inputs to produce output. In the short run some costs are fixed.
- Total fixed cost (TFC): does not change with output and is paid even at zero output (rent, salary of permanent staff, interest). Its curve is a horizontal line.
- Total variable cost (TVC): changes with output; zero at zero output (raw material, daily wages, power). It rises first at a falling rate, then at a rising rate (inverse-S), because of returns to a factor.
- Total cost (TC) = TFC + TVC. TC starts at TFC (not at zero) and has the same shape as TVC; the vertical gap is always TFC.
Average and marginal costs
- AFC = TFC ÷ q: keeps falling but never touches the axis (a rectangular hyperbola, since AFC × q is constant).
- AVC = TVC ÷ q: U-shaped.
- AC (ATC) = TC ÷ q = AFC + AVC: U-shaped. The gap AC − AVC = AFC shrinks as output rises, so AVC reaches its minimum before AC.
- MC = TCn − TCn−1 = TVCn − TVCn−1: U-shaped. Fixed cost does not affect MC. Also TVC = ΣMC.
| q | TFC | TVC | TC | AFC | AVC | AC | MC |
|---|---|---|---|---|---|---|---|
| 0 | 60 | 0 | 60 | – | – | – | – |
| 1 | 60 | 40 | 100 | 60 | 40 | 100 | 40 |
| 2 | 60 | 70 | 130 | 30 | 35 | 65 | 30 |
| 3 | 60 | 90 | 150 | 20 | 30 | 50 | 20 |
| 4 | 60 | 120 | 180 | 15 | 30 | 45 | 30 |
| 5 | 60 | 170 | 230 | 12 | 34 | 46 | 50 |
| 6 | 60 | 240 | 300 | 10 | 40 | 50 | 70 |
Why are the curves U-shaped?
Because of the law of variable proportions: when MP of labour rises, each extra unit needs less labour, so MC falls; when MP falls, MC rises. AC falls first because fixed cost is spread and MC is low, then rises when MC climbs.
Relationship between AC and MC
- MC < AC → AC falls.
- MC = AC → AC is at its minimum.
- MC > AC → AC rises.
MC cuts AVC and AC from below at their lowest points. MC falls and rises faster than AC.
Revenue: TR, AR and MR
Revenue = money a firm receives from selling its output.
- Total revenue (TR) = P × q.
- Average revenue (AR) = TR ÷ q = P. So the AR curve is the firm's demand curve.
- Marginal revenue (MR) = TRn − TRn−1 = ΔTR/Δq. TR = ΣMR.
When price stays the same (perfect competition)
The firm can sell any amount at the market price. AR = MR = P, a horizontal line. TR is a straight line from the origin whose slope equals the price.
| q | P = AR | TR | MR |
|---|---|---|---|
| 1 | 5 | 5 | 5 |
| 2 | 5 | 10 | 5 |
| 3 | 5 | 15 | 5 |
| 4 | 5 | 20 | 5 |
When price falls as more is sold (monopoly, monopolistic competition)
AR slopes downward. MR falls faster and lies below AR (for a straight-line AR, MR falls twice as fast). MR can become negative.
| q | AR | TR | MR |
|---|---|---|---|
| 1 | 9 | 9 | 9 |
| 2 | 8 | 16 | 7 |
| 3 | 7 | 21 | 5 |
| 4 | 6 | 24 | 3 |
| 5 | 5 | 25 | 1 |
| 6 | 4 | 24 | −1 |
Relationships
- MR > 0 → TR rises; MR = 0 → TR is maximum; MR < 0 → TR falls.
- MR < AR → AR falls; MR = AR → AR constant.
Try it at home
Plan a lemonade stall: table rent ₹60 (fixed), each glass needs ₹10 of lemon and sugar, and after 4 glasses you pay a helper ₹20 more per glass. Make a TC, AC and MC table for 1 to 6 glasses. Where is AC lowest? Then use the free-play slider to check a similar table.
Key formulas and definitions
- TC = TFC + TVC
- AFC = TFC/q; AVC = TVC/q; AC = TC/q = AFC + AVC
- MC = TCn − TCn−1 = TVCn − TVCn−1; TVC = ΣMC
- TR = P × q; AR = TR/q = P
- MR = TRn − TRn−1; TR = ΣMR
- Price constant ⇒ AR = MR; MR = 0 ⇒ TR max
Worked examples
1. TFC = ₹60, TVC at 3 units = ₹90. Find TC, AFC, AVC and AC.
TC = 150; AFC = 60/3 = 20; AVC = 90/3 = 30; AC = 150/3 = 50.
2. TC at 4 units = 180 and at 5 units = 230. Find MC of the 5th unit.
MC = 230 − 180 = ₹50.
3. AC of 4 units = ₹45 and AVC = ₹30. Find TFC.
AFC = 45 − 30 = 15; TFC = 15 × 4 = ₹60.
4. TC at 0 output is ₹60. MC of units 1 to 3 is 40, 30, 20. Find TC and TVC at 3.
TVC = 40 + 30 + 20 = 90; TC = 60 + 90 = 150.
5. A firm sells 10 units at ₹8 each; to sell 11 it must cut price to ₹7.60. Find MR of the 11th unit.
TR10 = 80; TR11 = 11 × 7.60 = 83.6. MR = 3.6.
6. TR at 4 units = 24 and at 5 units = 25; at 6 units = 24. What happens to TR and why?
MR5 = 1 (TR still rises); MR6 = −1 (TR falls). TR is maximum close to 5 units where MR is about 0.
Common mistakes
- Starting the TC curve from the origin. It starts at TFC.
- Adding fixed cost to MC. MC depends only on variable cost.
- Thinking AFC can become zero. It keeps falling but never touches the x-axis.
- Saying MR = AR always. That is true only when the price stays the same.