AP® Microeconomics review sheet from Aim for Five (aimforfive.com/micro/units/3/3-2)
Unit 3 · Topic 3.2
3.2 Short-Run Production Costs
A firm's short-run costs split into fixed costs, which don't change with output, and variable costs, which do. From those you get average and marginal cost curves with predictable shapes. Reading, calculating and shifting these curves is central to Units 3 and 4.
Key terms
- fixed cost
- variable cost
- marginal cost
- average total cost
- average variable cost
- average fixed cost
Fixed, variable and total cost
Fixed cost (FC) is the same at every level of output, even zero: rent, insurance, the loan payment on equipment. Variable cost (VC) changes with output: raw materials, hourly wages, electricity for the machines. Total cost (TC) = FC + VC. At zero output, TC equals FC.
| Measure | Formula | Shape on the graph |
|---|---|---|
| Marginal cost (MC) | change in TC ÷ change in Q (also change in VC ÷ change in Q) | falls briefly, then rises |
| Average fixed cost (AFC) | FC ÷ Q | falls continuously as output rises |
| Average variable cost (AVC) | VC ÷ Q | U-shaped |
| Average total cost (ATC) | TC ÷ Q, or AFC + AVC | U-shaped, above AVC |
Why marginal cost eventually rises
Marginal cost mirrors marginal product. If a worker costs a wage W and adds MP units, the cost of each extra unit is about W ÷ MP. While MP is rising (increasing marginal returns, often thanks to specialization and the division of labor), MC falls. Once diminishing marginal returns set in and MP falls, MC rises. That's why MC is shaped like a check mark (or a 'swoosh'): down a little, then up steeply.
How the curves fit together
Draw cost in dollars on the vertical axis and output on the horizontal axis. The same grade rule from topic 3.1 applies: when MC is below an average, the average falls; when MC is above it, the average rises. So the MC curve crosses both AVC and ATC at their lowest points, from below.
The vertical gap between ATC and AVC is AFC. Since AFC keeps falling as output grows (the fixed cost is spread over more units), ATC and AVC get closer together as output rises, but they never touch. The lowest point of ATC sits to the right of the lowest point of AVC.
What shifts the cost curves
The rule to remember: marginal cost only reacts to costs that change with output. A one-time fee is the same whether you make 1 unit or 1,000, so it can't change the cost of one more unit.
| Change | Curves that shift | Curves that don't |
|---|---|---|
| Fixed cost rises (rent, a lump-sum tax or license fee) | AFC and ATC up | MC and AVC |
| Variable cost rises (wages, materials, a per-unit tax) | MC, AVC and ATC up | AFC |
| Productivity improves (better technology or training) | MC, AVC and ATC down | AFC |
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Completing a cost table
A firm's fixed cost is $60. Its total cost for 0 to 6 units is $60, $100, $130, $150, $180, $230, $300. Find MC, AFC, AVC and ATC for each unit, and identify where AVC and ATC are lowest.
Show the solutionHide the solution
- Step 1: MC is the change in TC: $40, $30, $20, $30, $50, $70 for units 1 through 6.
- Step 2: VC = TC − $60: $40, $70, $90, $120, $170, $240. AVC = VC ÷ Q: $40, $35, $30, $30, $34, $40.
- Step 3: AFC = $60 ÷ Q: $60, $30, $20, $15, $12, $10.
- Step 4: ATC = TC ÷ Q: $100, $65, $50, $45, $46, $50.
- Step 5: AVC bottoms out at $30 (units 3 and 4); ATC bottoms out at $45 (unit 4). MC of the 5th unit ($50) is above $45, so ATC starts rising after unit 4, as the grade rule predicts.
Answer: MC: 40, 30, 20, 30, 50, 70. AFC: 60, 30, 20, 15, 12, 10. AVC: 40, 35, 30, 30, 34, 40. ATC: 100, 65, 50, 45, 46, 50. Minimum AVC is $30 (Q = 3–4); minimum ATC is $45 (Q = 4).
- Example 2Calculator allowed
Marginal cost from marginal product
Each worker at a bakery is paid $120 per shift. The marginal products of workers 1 through 5 are 10, 15, 11, 8 and 4 loaves. What is the marginal cost of a loaf produced by each worker? Explain the pattern.
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- Step 1: MC ≈ wage ÷ MP. Worker 1: $120 ÷ 10 = $12 per loaf. Worker 2: $120 ÷ 15 = $8.
- Step 2: Worker 3: $120 ÷ 11 ≈ $10.91. Worker 4: $120 ÷ 8 = $15. Worker 5: $120 ÷ 4 = $30.
- Step 3: MC falls while MP rises (worker 2), then rises as MP falls. Diminishing marginal returns cause rising marginal cost.
Answer: $12, $8, about $10.91, $15 and $30 per loaf; MC rises because of diminishing marginal returns.
- Example 3
Which curves shift? (classic trap)
The firm's landlord raises its monthly rent by $500. Which of the firm's cost curves shift? Would the firm's profit-maximizing output change?
Show the solutionHide the solution
- Step 1: Rent is the same at every output level, so it's a fixed cost.
- Step 2: A higher fixed cost raises AFC and ATC. It doesn't change MC or AVC, because it doesn't change the cost of making one more unit.
- Step 3: Firms choose output where MR = MC (topic 3.5). Since MC and MR haven't changed, output doesn't change; profit just falls by $500. The trap is shifting MC.
Answer: Only AFC and ATC shift up; MC and AVC don't move, so the profit-maximizing output stays the same.
Common mistakes
- Shifting MC when a fixed cost changes. Only AFC and ATC move.
- Drawing MC crossing ATC and AVC anywhere other than their lowest points.
- Forgetting that the gap between ATC and AVC is AFC, which shrinks as output grows.
- Calculating MC as TC ÷ Q. That's ATC; MC is the change in TC from one more unit.
On the exam
- Free-response questions often ask you to describe a correctly labeled cost graph: cost on the vertical axis, quantity on the horizontal, MC crossing AVC and ATC at their minimums.
- Expect questions like 'a lump-sum tax is imposed; what happens to MC, ATC and output?' Lump-sum costs move ATC only; per-unit costs move MC, AVC and ATC.
Connected topics
Videos
Check yourself
5 questions on 3.2 Short-Run Production Costs. Pick an answer to see if you got it, and why.
| Output (units) | Total cost |
|---|---|
| 0 | $40 |
| 1 | $70 |
| 2 | $90 |
| 3 | $105 |
| 4 | $125 |
| 5 | $155 |
| 6 | $195 |
| 7 | $245 |
Hypothetical short-run costs for a perfectly competitive firm
What is the firm's total fixed cost?
What is the marginal cost of the third unit?
What is the average total cost of producing 4 units?
At what level of output is average total cost at its minimum?
As output rises from 1 unit to 7 units, what happens to average fixed cost?
0 of 5 answered