Firm Behaviour

Lessons

Senior 4 · Economics

Firm Behaviour

5 lessons

Lesson 3 of 5

Costs of the firm in the short run

30 min

Rent does not care how much you bake

A bakery pays the same rent, the same loan repayments on its ovens and the same manager's salary whether it bakes one loaf or ten thousand. Flour, sugar, packaging and power are different: they rise with every batch. Under Rwanda's electricity tariff in force from 1 October 2025, a small manufacturing plant using between 5,000 and 100,000 kWh a year pays Frw 175 for every kWh, before VAT (REG). A bakery that runs its ovens on 200 kWh a day therefore adds $200 \times 175 = 35{,}000$ francs a day to its costs, but only on the days it bakes.

Separating costs that change with output from costs that do not is the key to every pricing and output decision. This lesson builds the cost curves of a firm in the short run, when its plant is fixed.

Definition

Fixed costs (FC): costs that do not change with output in the short run and must be paid even if nothing is produced: rent, insurance, interest on loans, salaries of permanent staff, depreciation of machines. Also called overheads or supplementary costs.

Variable costs (VC): costs that change with output: raw materials, fuel and power used in production, wages of casual workers, packaging. Also called prime or direct costs.

Total cost (TC) $= T F C + T V C$ .

Example: for a moto taxi rider, the daily licence and insurance are fixed; fuel and tyre wear are variable.

1. Kinds of cost

Pair of terms	Meaning	Example
Explicit and implicit costs	Explicit: money actually paid to others. Implicit: the opportunity cost of the owner's own resources (her time, her building, her savings)	A shop owner who could earn Frw 150,000 a month working for someone else bears that as an implicit cost
Accounting and economic costs	Accounting cost counts explicit costs only; economic cost adds implicit costs	Economic profit is therefore smaller than accounting profit
Private and social costs	Private: borne by the firm. Social: private cost plus external costs borne by others	Smoke from a brick kiln harms neighbours
Sunk costs	Costs already spent that cannot be recovered	Money paid for a market study; it should not affect future decisions

2. Total, average and marginal costs

A bakery's costs follow $T F C = 256$ and $T V C = 60 Q - 12 Q^{2} + Q^{3}$ , with Q in hundreds of loaves a day and costs in thousands of francs a day (illustrative).

AFC = \frac{TFC}{Q}, \qquad AVC = \frac{TVC}{Q}, \qquad ATC = \frac{TC}{Q} = AFC + AVC, \qquad MC = \frac{\Delta TC}{\Delta Q} = \frac{\Delta TVC}{\Delta Q}

Q	TFC	TVC	TC	AFC	AVC	ATC	MC
0	256	0	256	–	–	–	–
1	256	49	305	256	49	305	49
2	256	80	336	128	40	168	31
3	256	99	355	85.3	33	118.3	19
4	256	112	368	64	28	92	13
5	256	125	381	51.2	25	76.2	13
6	256	144	400	42.7	24	66.7	19
7	256	175	431	36.6	25	61.6	31
8	256	224	480	32	28	60	49
9	256	297	553	28.4	33	61.4	73
10	256	400	656	25.6	40	65.6	103

Reading the total-cost diagram. TFC is flat: it is the same at every output. TVC starts at zero. TC is TVC lifted up by 256 at every output, so the two curves are parallel in the vertical direction. Both rise slowly at first and then steeply, because of the law of diminishing returns.

Reading the per-unit diagram. (1) AFC falls all the time, because a fixed sum is spread over more units. (2) MC falls at first, reaches its lowest point at $Q = 4$ , then rises. (3) AVC and ATC are U-shaped. (4) MC passes through the lowest points of AVC (Q = 6, Frw 24 thousand) and ATC (Q = 8, Frw 60 thousand). (5) The vertical gap between ATC and AVC is AFC, so it narrows as output grows. (The marginal costs in the table are whole-unit steps; the smooth MC curve is drawn from the equation.)

Worked example 1: reading the cost schedule

(a) At Q = 5: $T V C = 300 - 300 + 125 = 125$ ; $T C = 256 + 125 = 381$ ; $AFC = \frac{256}{5} = 51.2$ ; $AVC = \frac{125}{5} = 25$ ; $ATC = \frac{381}{5} = 76.2$ . Check: $51.2 + 25 = 76.2$ ✔.

(b) Marginal cost of the 9th hundred loaves: $M C = T C_{9} - T C_{8} = 553 - 480 = 73$ .

(c) Why does ATC rise after Q = 8? The 9th unit costs 73, more than the average of 60 at Q = 8, so it pulls the average up to $\frac{553}{9} \approx 61.4$ .

(d) Lowest cost per loaf: 60 thousand francs per hundred loaves at Q = 8, that is Frw 600 a loaf.

3. Why the short-run curves have these shapes

The link with production. Suppose labour is the only variable input, paid a wage $w$ . Then

MC = \frac{w}{MP_L} \qquad\text{and}\qquad AVC = \frac{w}{AP_L}

When extra workers are more and more productive (MP rising), each extra unit of output needs less labour, so MC falls. Once diminishing returns set in, MP falls and MC rises. The same logic links AVC to AP: AVC is lowest where AP is highest. So the U-shape of the short-run cost curves is the law of diminishing returns (unit 6) seen from the cost side.

Why MC cuts the averages at their lowest points. If the cost of the next unit is below the average, it pulls the average down; if above, it pulls the average up. So the average is lowest exactly where MC equals it, the same "newcomer" rule as MP and AP.

Worked example 2: costs from productivity

A farm in unit 6 harvested 250 bags with 5 workers and 324 bags with 6; each worker is paid Frw 3,000 a day for the harvest.

(a) MC of a bag from the 6th worker: his marginal product is $324 - 250 = 74$ bags, so $MC = \frac{3{,}000}{74} \approx 40.5$ francs a bag.

(b) AVC with 6 workers: $AP = \frac{324}{6} = 54$ bags, so $AVC = \frac{3{,}000}{54} \approx 55.6$ francs a bag.

(c) Interpretation: MC is below AVC, so AVC is still falling: the farm is in the range of rising average product. When the marginal product of labour falls below its average product, MC will rise above AVC.

Warning

Do not confuse average and marginal cost. MC is the cost of the next unit; ATC is the cost per unit of all units so far. MC can rise while ATC is still falling (between Q = 4 and Q = 8 here). And fixed costs do not affect MC at all: $MC = \frac{\Delta TVC}{\Delta Q}$ .

Tip

Draw the per-unit diagram in this order: AFC sloping down; a U-shaped AVC; a U-shaped ATC above it with the gap shrinking; then MC as a "Nike tick" that rises through the bottom of AVC first and then the bottom of ATC.

Important

Discuss. A bakery's electricity tariff rises. Is this a fixed or a variable cost? Which of the curves AFC, AVC, ATC and MC shift, and in which direction? What if, instead, its rent rises?

Jacob Clifford, "Short-Run Cost Curves (Part 3)". Watch his explanation of why marginal cost falls and then rises, and why the MC curve crosses ATC at its lowest point; then find the same features on the bakery diagram above.

✦

Practice

Distinguish between fixed and variable costs, with two examples of each for a maize mill.
Explain the difference between explicit and implicit costs, and between private and social costs.
A firm's TFC is Frw 120 thousand and its TVC for outputs 1 to 6 is 50, 90, 120, 160, 220, 300 (Frw thousand). Calculate TC, AFC, AVC, ATC and MC at each output.
From question 3, at what output is ATC lowest? Use MC to explain why ATC falls before that output and rises after it.
Explain why the AFC curve falls continuously and why the gap between ATC and AVC narrows.
Using the law of diminishing returns, explain why the short-run MC and AVC curves are U-shaped.
If the wage is Frw 4,000 a day and the 3rd worker adds 50 units of output, what is the marginal cost of a unit of output? If 3 workers produce 120 units in total, what is AVC?
A firm's rent rises. Explain, with a diagram, what happens to its AFC, AVC, ATC and MC.

Show answersHide answers

Fixed costs do not change with output (rent of the building, loan interest on the mill, the guard's salary); variable costs do (maize grain, electricity for milling, casual workers, sacks).
Explicit costs are payments to others; implicit costs are the opportunity cost of the owner's own resources. Private costs fall on the firm; social costs add external costs on others (pollution, noise, congestion).
TC: 170, 210, 240, 280, 340, 420. AFC: 120, 60, 40, 30, 24, 20. AVC: 50, 45, 40, 40, 44, 50. ATC: 170, 105, 80, 70, 68, 70. MC: 50, 40, 30, 40, 60, 80.
ATC is lowest at output 5 (68). The 5th unit costs 60, less than the average of 70 before it, so it pulls ATC down; the 6th unit costs 80, more than 68, so it pulls ATC up to 70. MC rises through ATC at its lowest point.
AFC = TFC ÷ Q: a fixed sum spread over more and more units. ATC − AVC = AFC, which keeps falling, so the gap narrows (but never reaches zero).
$MC = \frac{w}{MP_L}$ and $AVC = \frac{w}{AP_L}$ . While MP and AP rise, MC and AVC fall; once diminishing returns make MP and AP fall, MC and AVC rise: a U-shape.
$MC = \frac{4{,}000}{50} = 80$ francs. $AP = \frac{120}{3} = 40$ , so $AVC = \frac{4{,}000}{40} = 100$ francs.
Rent is fixed: AFC and ATC shift upwards; AVC and MC do not change, because they depend only on variable costs.

Quick check

Match each cost of a maize mill with its type.

Tap one on the left, then its partner on the right.

Key points

In the short run, $T C = T F C + T V C$ ; fixed costs are paid even at zero output.
$AFC = \frac{TFC}{Q}$ falls continuously; AVC, ATC and MC are U-shaped because of diminishing returns ( $MC = \frac{w}{MP_L}$ , $AVC = \frac{w}{AP_L}$ ).
MC cuts AVC and ATC at their minimum points; the gap between ATC and AVC is AFC.
Economic costs include implicit (opportunity) costs; social costs add external costs to private costs.

Sources and credits

Electricity tariff for small industries: The Electricity End-User tariff has been revised, effective as of 1 October 2025, Rwanda Energy Group (REG), under RURA. Daily cost calculated by Ganzaa.
Photo: Bread making during class practices in Rwanda, Claude Nizeyimana, Wikimedia Commons, CC BY-SA 4.0.
Video: Short-Run Cost Curves (Part 3), Jacob Clifford, embedded from YouTube.

Written by Ganzaa: the text, the cost diagrams (drawn to scale from $T F C = 256$ and $T V C = 60 Q - 12 Q^{2} + Q^{3}$ ), the tables, the worked examples and the practice items. The bakery's costs and its 200 kWh a day are illustrative.

This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1Rent does not care how much you bake

21. Kinds of cost

32. Total, average and marginal costs

43. Why the short-run curves have these shapes

Rent does not care how much you bake

1. Kinds of cost

2. Total, average and marginal costs

3. Why the short-run curves have these shapes