Intermediatemicroeconomics
Average Cost Curves: AFC, AVC, and ATC
Overview
Average costs translate totals into per-unit terms the firm can compare with price. This lesson defines AFC, AVC, and ATC, explains the rectangular hyperbola of AFC, the U-shapes of AVC and ATC, the spreading effect versus diminishing returns, and the vertical relationships among the three curves - including where MC meets each.
Learning objectives
- Define AFC, AVC, and ATC and compute them from total costs.
- Explain why AFC falls continuously as output rises.
- Explain the U-shapes of AVC and ATC.
- Locate the MC crossings and the ATC-AVC gap on the diagram.
From Totals to Averages
Divide each total by output Q: AFC = TFC/Q, AVC = TVC/Q, ATC = TC/Q. Because TC = TFC + TVC, it follows that ATC = AFC + AVC - average total cost is the vertical sum of the other two. Averages answer 'what does each unit cost on average?', the question price must cover in the long run.
AFC: The Rectangular Hyperbola
Spreading a fixed sum over more units means AFC = TFC/Q falls continuously, approaching zero but never reaching it - the curve is a rectangular hyperbola. Doubling output halves AFC: this 'spreading effect' is the only force acting on AFC, so unlike the other averages it has no minimum and no rising portion.
AFC's endless decline is why high-volume production looks so attractive: the rent, licenses, and salaried staff cost less per unit with every extra unit. But spreading alone never justifies output - only the full ATC matters.
AVC: U-Shaped by Diminishing Returns
AVC = TVC/Q first falls as specialization and efficient input use dominate, then rises once diminishing marginal returns make each extra unit need more variable input. The U-shape mirrors the MC curve (recall MC = w/MPL): AVC's minimum sits where MC crosses it from below, at the output where variable inputs are used most efficiently on average.
ATC: The Sum of Both Forces
ATC = AFC + AVC combines spreading (pulling down throughout) with diminishing returns (pushing up eventually). At low output the spreading effect dominates and ATC falls steeply; at high output diminishing returns dominate and ATC rises. ATC is therefore U-shaped with its minimum to the right of AVC's minimum, and MC crosses it exactly at that minimum.
Every point on ATC reflects a tug-of-war: spreading fixed costs pulls average cost down, diminishing returns push it up. The minimum is where the two forces momentarily balance - which is also where MC passes through.
Reading the Vertical Gaps
At any output, the vertical distance between ATC and AVC equals AFC - and that gap shrinks as output grows, so ATC and AVC converge at high output without ever touching. The distance from the horizontal axis to AVC is AVC itself; to ATC, ATC itself. These gaps let you read fixed-cost intensity straight off the diagram: a wide early gap means heavy fixed costs.
Averages in Decision-Making
Averages guide the stay-or-go decisions: produce in the short run only if price covers minimum AVC (the shutdown rule), and stay in the industry in the long run only if price covers minimum ATC (the exit rule). But the how-much decision belongs to marginal cost - a division of labor between average and marginal concepts that runs through all of microeconomics.
Key points
- AFC = TFC/Q falls continuously (rectangular hyperbola); AVC = TVC/Q; ATC = TC/Q = AFC + AVC.
- AVC and ATC are U-shaped due to diminishing marginal returns; AFC never rises.
- ATC's minimum lies to the right of AVC's minimum because of the spreading effect.
- MC crosses AVC and ATC at their respective minimums.
- The vertical gap between ATC and AVC is AFC, shrinking as output rises.
- Shutdown compares P with min AVC; long-run exit compares P with min ATC.
Common misconceptions
✓ Truth: AFC = TFC/Q with constant TFC falls monotonically toward zero - there is no force pushing it up. The U-shape belongs to AVC and ATC, where diminishing returns eventually outweigh spreading.
✓ Truth: They converge but never meet: the gap is AFC, which approaches zero asymptotically without reaching it. Fixed costs are spread thin, never spread away entirely.
✓ Truth: Minimum ATC is the efficient scale, not the profit-maximizing output. A price-taking firm produces where P = MC, which generally differs from min ATC - only in long-run competitive equilibrium do they coincide.
Practice questions
Q1. TFC = $200 and output is 50 units. AFC equals:
- $200
- $4
- $10,000
- $0
AFC = TFC/Q = 200/50 = 2 - the spreading effect in action.
Q2. At 100 units, AVC = $6 and AFC = $2. ATC equals:
- $8
- $4
- $12
- $3
ATC = AFC + AVC = 2 + 6 = 800, the sum of TFC (600).
Q3. Why is ATC's minimum at a higher output than AVC's minimum?
- Because MC crosses ATC first.
- Because falling AFC keeps pulling ATC down after AVC starts rising.
- Because fixed costs rise with output.
- Because TVC is zero at zero output.
ATC = AFC + AVC. After AVC's minimum, AVC rises but AFC still falls; ATC keeps falling until AVC's rise outweighs AFC's fall - necessarily to the right of AVC's minimum.
Q4. A price-taking firm will shut down in the short run if price falls below:
- minimum ATC.
- minimum AVC.
- marginal cost.
- average fixed cost.
If P < min AVC, revenue fails to cover even variable costs, so producing loses more than shutting down (which loses only fixed costs). The min-AVC point, where MC crosses AVC, is the shutdown point.
Click a question to reveal the answer and explanation.
Frequently asked questions
Why is AVC's minimum to the left of ATC's minimum?
AFC keeps falling even after AVC starts rising, so the sum ATC = AFC + AVC keeps falling a while longer - the spreading effect offsets early diminishing returns. Only when AVC's rise overwhelms AFC's fall does ATC turn up.
How do I compute the curves from a TC table?
Read TFC as TC at zero output. Then TVC = TC - TFC; divide each by Q for the averages; take first differences of TC for MC. One TC column generates the entire diagram - a standard exam exercise.
What does a very flat-bottomed ATC curve imply?
A wide range of outputs with near-minimum cost - typical when fixed costs are small relative to variable costs or diminishing returns set in slowly. Firms then have latitude in choosing scale without much cost penalty.
Do these shapes hold in the long run?
The long-run LRAC is also U-shaped but for different reasons: economies of scale (falling) then diseconomies (rising), driven by plant-size choice rather than fixed-input congestion. Same shape, different economics.