Intermediatemicroeconomics
Marginal Cost: The Cost of One More Unit
Overview
Marginal cost - the extra cost of one more unit - is the single most important cost concept in microeconomics: it drives pricing, supply, and profit maximization. This lesson defines MC, derives its U-shape from diminishing marginal returns, proves it crosses AVC and ATC at their minimums, and shows the inverse link between MC and marginal product.
Learning objectives
- Define marginal cost and compute it from total cost data.
- Explain the U-shape of MC via diminishing marginal returns.
- Prove that MC crosses AVC and ATC at their minimum points.
- Relate MC to marginal product through MC = w / MPL.
Defining Marginal Cost
Marginal cost is the change in total cost from producing one more unit: MC = ΔTC/ΔQ. If raising output from 10 to 11 units lifts total cost from 162, the marginal cost of the 11th unit is $12. Because fixed costs never change, MC can equally be computed from variable cost: MC = ΔTVC/ΔQ. It is a marginal concept - about the next unit, never the average over all units.
Why MC Is U-Shaped
At low output, adding workers to an underused plant raises marginal product, so each extra unit needs less additional labor - MC falls. But diminishing marginal returns eventually set in: marginal product falls, each unit needs more labor, and MC rises. The falling-then-rising pattern is the U-shape, and its turning point mirrors the peak of the marginal product curve.
With wage w per worker, MC = w / MPL: the cost of one more unit equals the wage divided by the extra output one more worker produces. When MPL is high, MC is low - and vice versa. Diminishing MPL is literally rising MC.
MC Crosses AVC and ATC at Their Minimums
This is the marginal-average rule from the product lesson applied to costs. While MC lies below AVC, producing one more unit pulls average variable cost down; while MC lies above AVC, it pulls AVC up. AVC therefore falls until MC meets it, then rises after - the crossing is exactly AVC's minimum. Identical logic puts the MC/ATC crossing at ATC's minimum.
MC intersects AVC and ATC at their minimum points - always, by arithmetic. If a diagram shows otherwise, the diagram is wrong. This single fact unlocks the shutdown point, the supply curve, and long-run equilibrium.
The Order of the Minimums
Because ATC = AVC + AFC and AFC always falls, ATC's minimum occurs at a higher output than AVC's minimum: the MC curve meets AVC first, then ATC. The vertical gap between ATC and AVC at any output is AFC, which shrinks as output grows - so the two average curves converge at high output while MC cuts through both minimums.
MC and the Firm's Supply Decision
For a price-taking firm, producing an extra unit is worthwhile whenever its price exceeds its marginal cost - so the firm expands output until P = MC. That makes the rising portion of MC (above minimum AVC) the firm's short-run supply curve. Marginal cost is thus the bridge from cost theory to market supply: the supply curve is MC in disguise.
Common MC Mistakes
Three errors recur: treating MC as the cost of the last unit on average (it is the cost of the next unit at the margin); thinking fixed costs shift MC (they cannot - ΔTFC is always zero); and reading MC off the ATC curve (MC is its own curve, steeper, crossing the averages at their floors). Keeping marginal and average mentally separate prevents all three.
Key points
- MC = ΔTC/ΔQ = ΔTVC/ΔQ: the extra cost of one more unit.
- MC is U-shaped because marginal product first rises then falls (diminishing returns).
- MC = w / MPL: marginal cost is the wage divided by marginal product.
- MC crosses AVC and ATC exactly at their minimum points (marginal-average rule).
- The MC/AVC crossing is the shutdown point; the rising MC above it is the firm's supply curve.
- Fixed costs never affect marginal cost.
Common misconceptions
✓ Truth: MC is the cost of the next unit at the margin - the increment. The 'last unit on average' confuses marginal with average; the two differ everywhere except at the minimum points of the average curves.
✓ Truth: ΔTFC is identically zero, so MC = ΔTVC/ΔQ is untouched by fixed costs. Rent hikes shift ATC up but leave MC - and hence the profit-maximizing output - unchanged in the short run.
✓ Truth: MC typically falls at first as specialization raises marginal product, then rises once diminishing returns dominate. The U-shape, not a monotonic rise, is the standard case.
Practice questions
Q1. Total cost for 4, 5, 6 units is $200, $240, $290. The marginal cost of the 6th unit is:
- $50
- $48.33
- $40
- $90
MC = TC(6) - TC(5) = 290 - 240 = 48.33 figure is ATC at 6 units - a different concept, illustrating why marginal and average must not be confused.)
Q2. The wage is $20/hour and the marginal product of labor is 5 units/hour. Marginal cost is:
- $100
- $4
- $25
- $15
MC = w/MPL = 20/5 = 20/5 = $4 - the mirror relationship between productivity and cost.
Q3. On a standard cost diagram, the MC curve crosses the AVC curve:
- at AVC's maximum.
- at AVC's minimum.
- to the left of AVC's minimum.
- only if fixed costs are zero.
By the marginal-average rule, AVC falls while MC < AVC and rises while MC > AVC, so the crossing must be AVC's minimum point. This holds regardless of fixed costs.
Q4. A price-taking firm should produce the quantity where:
- MC is minimized.
- P = MC on the rising portion of MC.
- ATC is minimized.
- MC = AVC.
Each unit with P > MC adds to profit, so expand until P = MC. The relevant segment is MC's rising portion above minimum AVC - that is the firm's short-run supply curve.
Click a question to reveal the answer and explanation.
Frequently asked questions
How do I compute MC from a total cost table?
Take first differences: MC of the nth unit = TC(n) - TC(n-1). If TC is 100, 130, 170, 220 for 0-3 units, MCs are 30, 40, 50. Note TC at zero output equals fixed cost - the intercept reminds you fixed costs are in the data but drop out of MC.
Why does MC = w/MPL hold?
Producing ΔQ extra units needs ΔL = ΔQ/MPL extra workers (each worker adds MPL units). The extra wage bill is w·ΔL = w·ΔQ/MPL, so cost per extra unit is w/MPL. It assumes labor is the only variable input and the wage is constant.
Does MC cross AFC at its minimum too?
No - AFC has no minimum; it falls forever as fixed cost spreads over more units (a rectangular hyperbola). The crossing rule applies to AVC and ATC, the U-shaped averages.
If MC is below ATC, should the firm expand output?
For a price taker, expand while P > MC; the ATC comparison is irrelevant to the output choice. MC below ATC merely tells you average cost is falling - useful for the shutdown check, not for the quantity decision.