Difficulty: Intermediate | Prerequisites: Section 7.1 (Measuring Costs), Chapter 6 concepts (production function, marginal product of labour, average product of labour, diminishing marginal returns).
The short run is where most day-to-day business decisions happen: capital is locked in, and the firm can only adjust labour and materials. This section builds the cost curves (total, average, marginal) that drive every output and pricing decision in the rest of the course. If you understand why marginal cost first falls then rises, and why it cuts the average cost curves at their minimums, you have the core mechanics for Chapters 8 through 12. You should already be comfortable with marginal and average product from Chapter 6, because the cost curves are essentially mirror images of those product curves.
In the short run, a firm has fixed costs (which do not change with output) and variable costs (which do). Marginal cost is the extra cost of one more unit of output, and it equals the wage divided by the marginal product of labour. The shapes of all the cost curves trace back to the production function, specifically to diminishing marginal returns.
Fixed cost (F)
A cost that does not vary with the level of output. Includes expenditures on land, office space, production facilities and other overhead. Think of it as the bill you pay whether you produce one unit or a thousand.
Variable cost (VC)
The production expense that changes with the quantity of output produced. This is the cost of the inputs the firm can adjust, such as labour and materials.
Total cost (C)
The sum of fixed cost and variable cost: C = VC + F. Because variable cost changes with output, total cost also changes with output.
Marginal cost (MC)
The amount by which a firm's cost changes if it produces one more unit of output: MC = dC(q)/dq. In simple terms, it is the price tag on the next unit. Because fixed cost does not change, MC also equals dVC(q)/dq.
Average fixed cost (AFC)
Fixed cost divided by units of output: AFC = F/q. It falls continuously as output rises because the same fixed cost is spread over more units.
Average variable cost (AVC)
Variable cost divided by units of output: AVC = VC/q. It typically forms a U-shape, first falling then rising.
Average cost / average total cost (AC)
Total cost divided by units of output: AC = C/q = AVC + AFC. This tells the firm whether it is making a profit (if price exceeds AC) or a loss.
Avoidable cost
A fixed cost that the firm can escape by shutting down. A month-to-month lease is a fixed cost but not sunk: the firm can cancel next month. In simple terms, it is a fixed cost you can walk away from.
In the short run, capital is fixed and labour is variable. Fixed costs include rent, equipment and other overhead. Variable costs cover labour and materials.
C = VC + F. The total cost curve is a vertical shift of the variable cost curve, always F dollars above it.
Fixed costs can be sunk (already paid, cannot be recovered this period) or avoidable (can be cancelled, e.g. a month-to-month lease for next month).
MC = dC(q)/dq = dVC(q)/dq (fixed cost drops out).
Because the only way to increase output in the short run is to hire more labour, MC = w / MP_L (Equation 7.3).
MC moves in the opposite direction to the marginal product of labour. When MP_L rises (workers specialise, use equipment better), MC falls. When diminishing marginal returns set in and MP_L falls, MC rises.
Result: the MC curve typically falls first and then rises, forming a check-mark or swoosh shape.
AFC = F/q. Strictly falling, approaches zero as q grows. This is sometimes called "spreading the overhead."
AVC = VC/q = w / AP_L (Equation 7.4). Moves opposite to the average product of labour, so it is typically U-shaped.
AC = AVC + AFC. Also U-shaped. At low output, the falling AFC pulls AC down steeply. At high output, AVC dominates and AC rises.
The MC curve cuts the AVC curve at its minimum. When MC < AVC, average variable cost is falling. When MC > AVC, it is rising.
The MC curve cuts the AC curve at its minimum. Same logic: if the marginal unit costs less than the average, it pulls the average down, and vice versa.
These minimum-crossing relationships are tested frequently.
Cost function: C(q) = 100q - 4q² + 0.2q³ + 450
Fixed cost: F = 450 (the part that does not depend on q)
Variable cost: VC(q) = 100q - 4q² + 0.2q³
MC = 100 - 8q + 0.6q²
AVC = 100 - 4q + 0.2q²
AFC = 450/q
AC = AVC + AFC = 100 - 4q + 0.2q² + 450/q
The production function determines the shape of every cost curve. If input prices are constant, the variable cost curve is the inverse of the production function.
VC = wL and L = g⁻¹(q), so VC(q) = w × g⁻¹(q).
Diminishing marginal returns to labour cause VC to rise more than proportionally with output, which makes MC and AVC eventually rise.
Specific (per-unit) tax: Shifts MC, AVC and AC upward by the amount of the tax. Does not affect AFC. The minimum of AC stays at the same output level.
Franchise tax / lump-sum business licence fee: Increases fixed costs only. Shifts AFC and AC upward but does not affect MC or AVC. This changes the output at which AC is minimised.
C = VC + FMC = \frac{dC(q)}{dq} = \frac{dVC(q)}{dq} = \frac{w}{MP_L}AFC = \frac{F}{q}, \quad AVC = \frac{VC}{q} = \frac{w}{AP_L}, \quad AC = \frac{C}{q} = AVC + AFCFigure 7.1 (Short-Run Cost Curves): Two panels. Top panel shows F (horizontal line), VC (rising curve starting at origin), and C (VC shifted up by F, parallel to VC). Bottom panel shows AFC (falling), U-shaped AVC, U-shaped AC, and MC. MC crosses AVC at AVC's minimum and crosses AC at AC's minimum.
Figure 7.2 (Effect of a Specific Tax): A per-unit tax of $10 shifts both MC and AC upward by exactly $10 at every quantity. The minimum of AC stays at the same output. AFC is unaffected.
Japanese beer manufacturer (Cobb-Douglas): With q = 1.52L^0.6 K^0.4 and K fixed at 100, the short-run cost curves are derived step by step. VC(q) ≈ 0.55q^1.67, AVC = 0.55q^0.67, MC ≈ 0.92q^0.67. The AVC curve is strictly rising (no U-shape) because the production function has diminishing returns for all positive output. The MC curve lies above AVC everywhere and cuts AC at its minimum at q = 100.
The sharing economy and the short run: Companies like Yard Club let construction firms rent heavy equipment on demand, turning what used to be a fixed cost (owning a bulldozer) into a variable cost. When all inputs are variable, the distinction between the short run and the long run disappears.
"Fixed costs are always sunk costs." They are not. A month-to-month lease is fixed (it does not vary with output) but avoidable (the firm can cancel next month). Only costs already paid and non-recoverable are sunk.
Confusing where MC crosses AC versus AVC. MC crosses both curves at their respective minimums, but these occur at different output levels. MC crosses AVC first (at a lower output) and AC second (at a higher output).
Thinking a per-unit tax shifts the AC minimum to a different output. It does not. A specific tax shifts AC upward in parallel, so the minimum stays at the same quantity.
Ignoring the link between product curves and cost curves. MC = w/MP_L and AVC = w/AP_L are not just formulas to memorise. They mean that cost curves are the mirror image of the production function's product curves. If you can draw MP_L and AP_L, you can sketch MC and AVC.
⚠️ You will almost certainly be asked to derive MC, AVC and AC from a given cost function, and to identify fixed and variable components.
⚠️ Be ready to explain why MC = w/MP_L and AVC = w/AP_L, and to sketch cost curves from a production function.
⚠️ The rule "MC cuts AC and AVC at their minimums" is a top exam question. Know the intuition (the marginal pulls the average up or down) and be able to prove it with calculus.
⚠️ Tax-shifting questions (specific tax vs franchise tax) test whether you know which curves move and which stay put.
True or False: Marginal cost depends on fixed cost.
False. MC = dVC/dq; fixed cost drops out of the derivative.
Fill in the blank: AVC = w / ____.
AP_L (average product of labour).
True or False: A franchise tax (lump-sum business licence) shifts the MC curve upward.
False. It only increases fixed costs, which shifts AFC and AC but not MC or AVC.
Fill in the blank: The MC curve crosses the AC curve at AC's ____.
Minimum.
True or False: If MP_L is rising, MC is falling.
True. MC = w/MP_L, so they move in opposite directions.
Q: A firm has the cost function C(q) = 100q - 4q² + 0.2q³ + 450. What are the fixed cost, variable cost, and marginal cost functions?
A: Fixed cost F = 450. Variable cost VC(q) = 100q - 4q² + 0.2q³. Marginal cost MC = dC/dq = 100 - 8q + 0.6q².
Q: If the wage is $10 per hour and it takes four extra hours of labour to produce one more unit of output, what is the marginal cost of that unit?
A: The marginal product of labour is 1/4 (one unit of output per four hours). MC = w/MP_L = $10/(1/4) = $40.
Q: A government imposes a $10 per-unit tax on a beer manufacturer whose pre-tax MC is 0.92q^0.67. What is the new MC? What happens to AFC?
A: New MC = 0.92q^0.67 + 10. AFC is unaffected because a per-unit tax changes variable cost, not fixed cost.
Q: Explain why the short-run AC curve is U-shaped, referring to AFC and AVC.
A: At low output, the rapidly falling AFC dominates, pulling AC down. At high output, AFC is negligible and the rising AVC (driven by diminishing marginal returns) pushes AC up. The combination produces a U shape.
Short-run cost curves feed directly into the firm's output decision in Chapter 8: MC = Price is the profit-maximising rule for a competitive firm, and the firm shuts down if price falls below AVC. The relationship between cost curves and product curves (MC = w/MP_L) ties this chapter back to Chapter 6. Long-run costs in Section 7.3 relax the fixed-capital constraint, and the LRAC is built as the envelope of the SRAC curves introduced here.
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