From production to cost
In Topic 3.1 you measured what a firm can produce. Every input it uses has to be paid for: workers need wages, buildings need rent, machines need finance and materials need buying. A firm’s costs of production are the money value of the inputs it uses. Because production in the short run shows diminishing marginal returns, costs in the short run follow a matching pattern.
Remember that in the short run at least one input is fixed. That splits a firm’s costs into two kinds.
Fixed and variable costs
| Cost | Meaning | Examples |
|---|---|---|
| Total fixed cost (TFC) | Costs of the fixed inputs. They do not change with output and must be paid even if output is zero | rent on a lease, insurance, loan repayments on machinery, a yearly licence |
| Total variable cost (TVC) | Costs of the variable inputs. They rise as output rises and are zero at zero output | wages of hourly workers, raw materials, energy used by machines |
| Total cost (TC) | All costs of producing a given output | TC = TFC + TVC |
So at zero output, TC = TFC. If a bakery bakes nothing this week, it still owes the rent.
The seven cost measures
From TFC and TVC you can build every other short-run cost. Q is output.
| Measure | Formula | What it tells you |
|---|---|---|
| Total fixed cost (TFC) | given | fixed, at every Q |
| Total variable cost (TVC) | given | rises with Q |
| Total cost (TC) | TFC + TVC | everything |
| Marginal cost (MC) | ΔTC ÷ ΔQ = ΔTVC ÷ ΔQ | cost of producing one more unit |
| Average fixed cost (AFC) | TFC ÷ Q | fixed cost per unit |
| Average variable cost (AVC) | TVC ÷ Q | variable cost per unit |
| Average total cost (ATC) | TC ÷ Q = AFC + AVC | total cost per unit |
Marginal cost uses ΔTC or ΔTVC: they give the same answer, because TFC does not change.
Throughout this guide we use Ashgrove Cycles, a fictional workshop that builds custom bicycle frames. Its workshop lease and equipment cost $600 per week (TFC). Q is frames per week.
| Q | TFC ($) | TVC ($) | TC ($) | MC ($) | AFC ($) | AVC ($) | ATC ($) |
|---|---|---|---|---|---|---|---|
| 0 | 600 | 0 | 600 | – | – | – | – |
| 1 | 600 | 300 | 900 | 300 | 600 | 300 | 900 |
| 2 | 600 | 500 | 1,100 | 200 | 300 | 250 | 550 |
| 3 | 600 | 660 | 1,260 | 160 | 200 | 220 | 420 |
| 4 | 600 | 880 | 1,480 | 220 | 150 | 220 | 370 |
| 5 | 600 | 1,200 | 1,800 | 320 | 120 | 240 | 360 |
| 6 | 600 | 1,680 | 2,280 | 480 | 100 | 280 | 380 |
Like marginal product, MC sits between two rows: the $220 in the Q = 4 row is the cost of the fourth frame, as output goes from 3 to 4. On a graph, plot MC halfway between the outputs.
Why the cost curves have their shapes
Average fixed cost always falls. The same $600 is spread over more and more frames: $600, $300, $200 … $100. AFC gets closer to zero but never reaches it. This is “spreading the overhead”.
Marginal cost falls at first, then rises. Marginal cost is the mirror image of marginal product. If the only variable input is labour paid a wage w, then each extra worker costs w and adds MP units of output, so:
MC = w ÷ MP
- At low output, adding workers allows specialisation and the division of labour: each worker focuses on one task and gets faster. MP rises, so MC falls (Ashgrove: $300, $200, $160).
- Then diminishing marginal returns set in: each extra worker has less of the fixed capital to work with, MP falls, so MC rises ($220, $320, $480).
The output where MP is at its maximum is the output where MC is at its minimum. A production function with diminishing marginal returns gives an upward-sloping marginal cost curve.
AVC and ATC are U-shaped. In the same way, AVC = w ÷ AP. AVC falls while AP rises and rises once AP falls. ATC = AFC + AVC: at low output, both parts are falling, so ATC falls steeply. Later, rising AVC outweighs the shrinking fall in AFC, and ATC turns up.
MC cuts AVC and ATC at their lowest points. This is the same average–marginal rule as in Topic 3.1:
- when MC is below an average, the average falls;
- when MC is above an average, the average rises;
- so MC crosses each average at that average’s minimum.
At Ashgrove, AVC is lowest at $220 (3 and 4 frames), and the fourth frame’s MC is exactly $220. ATC is lowest at $360 (5 frames): the fifth frame’s MC of $320 is below the ATC of $370, so ATC falls; the sixth frame’s MC of $480 is above $360, so ATC rises.
The gap between ATC and AVC is AFC, so the two curves get closer as output rises (Ashgrove: a gap of $300 at 2 frames, $100 at 6). The minimum of ATC is at a larger output than the minimum of AVC (Q₂ > Q₁ in Figure 2), because AFC is still falling there.
What shifts the cost curves
The cost table holds input prices and technology constant. If they change, the curves shift.
| Change | TFC, AFC | TVC, AVC, MC | TC, ATC |
|---|---|---|---|
| Wage or raw-material price rises (variable input) | no change | shift up | shift up |
| Rent, insurance or a yearly licence fee rises (fixed input) | shift up | no change | shift up |
| Productivity rises (better technology or training, at no extra fixed cost) so MP and AP rise | no change in TFC | shift down | shift down |
| A fall in a variable input’s price | no change | shift down | shift down |
The second row is a favourite exam trap. A rise in a fixed cost does not change marginal cost, because it does not change the cost of producing one more unit.
Worked example 1: reading a short-run cost table
Question. Use the Ashgrove Cycles table. (a) Show how the TC, MC, AFC, AVC and ATC entries for 5 frames are calculated. (b) Show that ATC = AFC + AVC at 5 frames. (c) The landlord raises the weekly lease from $600 to $750. What happens to MC, AVC and ATC at 5 frames? (d) Explain why ATC at 6 frames is higher than at 5, even though AFC is lower.
(a)
- TC = TFC + TVC = 600 + 1,200 = $1,800.
- MC of the fifth frame = ΔTC ÷ ΔQ = (1,800 − 1,480) ÷ 1 = $320. (Check with TVC: 1,200 − 880 = 320.)
- AFC = 600 ÷ 5 = $120.
- AVC = 1,200 ÷ 5 = $240.
- ATC = 1,800 ÷ 5 = $360.
(b) AFC + AVC = 120 + 240 = 360 = ATC. ✓
(c) The lease is a fixed cost.
- MC does not change: still $320, because TVC is unchanged.
- AVC does not change: still $240.
- ATC rises: TC = 750 + 1,200 = 1,950, so ATC = 1,950 ÷ 5 = $390. (AFC rises from $120 to $150, and ATC rises by the same $30.)
(d) From 5 to 6 frames, AFC falls by only $20 (120 → 100), but AVC rises by $40 (240 → 280). The rise in AVC is bigger, so ATC rises from $360 to $380. Equivalently, the sixth frame’s MC ($480) is above the ATC of $360, so it pulls the average up.
Check. Every cost is in dollars; per-unit costs are dollars per frame. MC is a change; the averages are ratios.
Worked example 2: from production to cost
Question. Larchmont Pottery is a fictional firm. It rents a kiln for $200 per day (fixed) and hires potters at $120 per day each (variable). Total product, in mugs per day, is:
| Potters | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Total product (mugs per day) | 0 | 10 | 30 | 60 | 84 | 96 |
(a) Find the marginal product of each potter and the marginal cost per mug. (b) Find AVC and ATC at each level of output. (c) Explain the pattern in marginal cost. (d) The daily wage rises to $150. What happens to MC for the mugs made by the fourth potter, and to AVC at 84 mugs?
(a) Each potter adds $120 to cost and MP mugs to output, so MC per mug = 120 ÷ MP.
| Potter | MP (mugs) | MC per mug ($) |
|---|---|---|
| 1st | 10 | 120 ÷ 10 = 12.00 |
| 2nd | 20 | 120 ÷ 20 = 6.00 |
| 3rd | 30 | 120 ÷ 30 = 4.00 |
| 4th | 24 | 120 ÷ 24 = 5.00 |
| 5th | 12 | 120 ÷ 12 = 10.00 |
(b) TVC = 120 × potters; TC = 200 + TVC.
| Q (mugs) | TVC ($) | TC ($) | AVC ($) | ATC ($) |
|---|---|---|---|---|
| 10 | 120 | 320 | 12.00 | 32.00 |
| 30 | 240 | 440 | 8.00 | 14.67 |
| 60 | 360 | 560 | 6.00 | 9.33 |
| 84 | 480 | 680 | 5.71 | 8.10 |
| 96 | 600 | 800 | 6.25 | 8.33 |
(c) MC falls from $12 to $4 while MP rises (the potters specialise: one throws, one glazes, one loads the kiln). MC is lowest ($4) exactly where MP is highest (the third potter, who adds 30 mugs). From the fourth potter, diminishing marginal returns set in: MP falls, so MC rises to $5 and then $10. AVC is lowest at 84 mugs, where AP is highest (84 ÷ 4 = 21 mugs per potter, and 120 ÷ 21 = $5.71).
(d) MC for the fourth potter’s mugs = 150 ÷ 24 = $6.25 (up from $5.00). AVC at 84 mugs = (150 × 4) ÷ 84 = $7.14 (up from $5.71). A higher price of a variable input shifts MC, AVC and ATC up. AFC does not change, because the kiln rent is the same.
Interpretation. Cost curves are production curves turned upside down. When output per worker rises, cost per unit falls, and the other way round.
Common misconceptions
- “Fixed costs are zero when the firm produces nothing.” TFC must be paid at every output, including zero. Only TVC is zero at zero output.
- “A rise in rent raises marginal cost.” Rent is fixed, so it raises AFC and ATC only. MC and AVC do not change.
- “MC rises because the firm buys worse inputs.” In the short run, MC rises because of diminishing marginal returns to the variable input working with fixed capital.
- “MC cuts ATC wherever it likes.” MC always cuts AVC and ATC at their minimum points, from below.
- “AFC is U-shaped.” AFC falls at every output.
- “The minimum of ATC and the minimum of AVC are at the same output.” ATC’s minimum is at a larger output, because AFC is still falling.
- “Producing more always lowers average total cost, because overhead is spread.” Spreading overhead lowers AFC, but beyond the minimum of ATC rising AVC outweighs it.
Where this leads
These are short-run costs: at least one input is fixed. In Topic 3.3 every input can change, and you will see how long-run production costs produce economies and diseconomies of scale. Later, marginal cost becomes the key to the firm’s profit-maximising output. For the production side, look back at the production function. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate.
Quick questions
Why does marginal cost not depend on fixed cost?
Fixed cost is the same whatever the firm produces, so it does not change when output rises by one unit. Only variable cost changes, so marginal cost is the change in variable cost.
Why is the lowest point of ATC to the right of the lowest point of AVC?
Past the minimum of AVC, average fixed cost is still falling. For a while that fall outweighs the rise in AVC, so ATC keeps falling until marginal cost reaches it.