Cost Curves
Cost is the monetary expenditure incurred by a firm in producing goods. In the short run, some factors are fixed (giving Total Fixed Cost — a horizontal line) and some are variable (giving Total Variable Cost — an inverse-S shape). Total Cost = TFC + TVC. Dividing by output gives Average Fixed Cost (rectangular hyperbola), Average Variable Cost (U-shaped), and Average Total Cost (U-shaped). Marginal Cost is U-shaped and cuts both AVC and ATC at their minimum points from below.
In this chapter
Meaning and Types of Cost
- by who is paid* — explicit cost (paid to outsiders: wages, rent, raw materials, electricity bill) vs implicit cost (cost of self-owned factors: owner's own land, own capital, own labour — not paid in cash but still a real cost); *
- by behaviour with output* — fixed cost (does not change with output: rent of factory, salary of manager, interest on loan) vs variable cost* (changes with output: raw material, fuel, daily wages)
Types of cost — explicit/implicit vs fixed/variable
| Basis | Type | Definition | Nepal Example |
|---|---|---|---|
| By payment | Explicit cost | Paid to outsiders; recorded in books | Wages to workers in Wai Wai factory |
| By payment | Implicit cost | Cost of self-owned factors; not paid in cash | Owner's own land used as factory site |
| By behaviour | Fixed cost (FC) | Does not change with output | Rs 50,000 monthly rent of tea shop in Patan |
| By behaviour | Variable cost (VC) | Changes with output | Milk, sugar, tea leaves used per cup |
| Total | Total Cost (TC) | TC = TFC + TVC | Sum of all expenses to run a factory |
Short-Run Cost Curves: TFC, TVC, TC
In the short run, at least one factor is fixed — usually capital (machines, building). Total Fixed Cost (TFC) is constant regardless of output — its curve is a horizontal line parallel to the output axis. Even if the noodle factory produces zero packets, it still pays rent. Total Variable Cost (TVC) rises with output — its shape is inverse-S (first rises at a decreasing rate due to increasing returns, then at an increasing rate due to diminishing returns). Total Cost (TC) = TFC + TVC — TC has the same inverse-S shape as TVC but starts at the TFC level when output is zero (not at the origin).
Short-run total and average cost formulas
Marginal cost formula
Discrete MC and useful cost identities
Average and Marginal Cost Curves
- Average Fixed Cost (AFC) = TFC/Q — as output rises, the same fixed cost is spread over more units, so AFC falls continuously. Its curve is a rectangular hyperbola (TFC = AFC × Q is constant for every point on the curve). Average Variable Cost (AVC) = TVC/Q and Average Total Cost (ATC) = TC/Q — both are U-shaped: first fall due to increasing returns and spreading of fixed cost, then rise due to diminishing returns. Marginal Cost (MC) is the cost of one extra unit — also U-shaped. The crucial rule: MC cuts AVC and ATC at their minimum points from below. When MC < AVC, AVC is falling
- when MC > AVC, AVC is rising
- when MC = AVC, AVC is at its minimum. Same logic for ATC.
Why MC cuts AVC and ATC at their minima
When MC is below AVC, the new unit costs less than the average, so the average falls. When MC is above AVC, the new unit costs more than the average, so the average rises. The average stops falling (and starts rising) exactly where MC = AVC — that is the minimum of AVC. Same reasoning applies to ATC. This is why MC always passes through the minimum points of AVC and ATC from below.
Cost schedule for a hypothetical Kathmandu tea shop (Rs)
| Q (cups) | TFC | TVC | TC | AFC | AVC | ATC | MC |
|---|---|---|---|---|---|---|---|
| 0 | 100 | 0 | 100 | — | — | — | — |
| 1 | 100 | 20 | 120 | 100.0 | 20.0 | 120.0 | 20 |
| 2 | 100 | 36 | 136 | 50.0 | 18.0 | 68.0 | 16 |
| 3 | 100 | 48 | 148 | 33.3 | 16.0 | 49.3 | 12 |
| 4 | 100 | 56 | 156 | 25.0 | 14.0 | 39.0 | 8 |
| 5 | 100 | 70 | 170 | 20.0 | 14.0 | 34.0 | 14 |
| 6 | 100 | 90 | 190 | 16.7 | 15.0 | 31.7 | 20 |
| 7 | 100 | 120 | 220 | 14.3 | 17.1 | 31.4 | 30 |
| 8 | 100 | 160 | 260 | 12.5 | 20.0 | 32.5 | 40 |
Reading the table
TFC is constant at Rs 100. TC = TFC + TVC. AFC falls continuously. AVC is minimum at Q = 4 and Q = 5 (= Rs 14). ATC is minimum at Q = 7 (= Rs 31.4). Notice that MC = AVC = Rs 14 around Q = 4–5 (the AVC minimum), and MC = ATC = Rs 30 ≈ Rs 31.4 around Q = 7 (the ATC minimum) — confirming the "MC cuts AVC and ATC at their minima from below" rule.
Practice Problem
A small noodle factory in Kathmandu has TFC = Rs 5,000 per day. The total variable cost schedule is given below. Compute TC, AFC, AVC, ATC, and MC for each output level. | Q (cartons) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | | TVC (Rs) | 0 | 1,500 | 2,800 | 3,900 | 4,800 | 5,800 | 7,200 |
Practice Problem
A firm's total cost function is TC = 100 + 50Q − 20Q² + 5Q³ (Rs). (a) Write TFC, TVC, AFC, AVC, ATC, MC. (b) Find the output at which AVC is minimum. (c) Find the output at which ATC is minimum. (d) Verify that MC = AVC at the AVC-minimising output.
Practice Problem
A Patan tea shop sells tea at Rs 25 per cup. Its cost function is TC = 200 + 10Q + 2Q² (Rs). (a) Find the profit-maximising output where MC = MR = P. (b) Calculate total revenue, total cost, and profit at that output. (c) At what price would the shop break even (P = ATC)?
Quick Revision
- Cost = monetary expenditure to produce; explicit vs implicit, fixed vs variable.
- Short run: TFC (horizontal), TVC (inverse-S), TC = TFC + TVC (inverse-S shifted up).
- AFC = TFC/Q (rectangular hyperbola); falls continuously.
- AVC = TVC/Q, ATC = TC/Q — both U-shaped; ATC > AVC always.
- MC = ΔTC/ΔQ = dTC/dQ — U-shaped.
- Rule: MC cuts AVC and ATC at their minimum points from below.
- If MC < AVC, AVC falls; if MC > AVC, AVC rises; if MC = AVC, AVC minimum.