Foundationsmicroeconomics
Fixed vs Variable Costs: The Short-Run Split
Overview
Every short-run cost analysis begins by splitting total cost into fixed costs, which do not change with output, and variable costs, which do. This lesson defines each with concrete examples, traces the shapes of the TFC, TVC, and TC curves, explains why the split exists only in the short run, and introduces sunk costs - the fixed costs that should never influence decisions.
Learning objectives
- Define fixed, variable, and total cost and state the TC identity.
- Give real examples of fixed and variable costs for a firm.
- Sketch and interpret the TFC, TVC, and TC curves.
- Explain sunk costs and why they are irrelevant to decisions.
The Short-Run Cost Split
In the short run, some inputs are fixed, so their costs do not vary with output - these are fixed costs (FC): factory rent, insurance, salaried managers. Costs of variable inputs move with output - variable costs (VC): hourly wages, raw materials, electricity for machines. Total cost is simply their sum: TC = TFC + TVC, the master identity of short-run cost.
Fixed Costs: Concrete Examples
A bakery's oven lease, business license, and property insurance cost the same whether it bakes 100 or 1,000 loaves this month. Fixed costs are inescapable in the short run: produce nothing and you still pay them. Their defining feature is not that they never change - the lease can rise next year - but that they do not respond to this period's output.
A cost is fixed if it stays constant when output changes, even if it changes for other reasons. Annual software subscriptions are fixed with respect to daily output but may jump at renewal - still fixed in the short-run analysis.
Variable Costs: Concrete Examples
Flour, yeast, packaging, hourly baker wages, and delivery fuel all rise with loaves baked - these are variable costs. TVC is zero at zero output (produce nothing, buy no flour) and typically rises slowly at first, then faster as diminishing returns set in. Because variable inputs drive production, TVC's shape mirrors the production function: its increasing steepness reflects falling marginal product.
The Three Curves: TFC, TVC, TC
Total fixed cost is a horizontal line - constant at every output. Total variable cost rises from the origin, flattening then steepening. Total cost is TVC shifted up by the fixed amount: TC and TVC are parallel, separated everywhere by the vertical distance TFC. The gap between them never changes, which is why marginal cost depends only on variable cost.
Because TFC is constant, ΔTC = ΔTVC: marginal cost can be computed from variable cost alone. Fixed costs shift total and average cost but never marginal cost - a fact the shutdown lesson exploits.
Sunk Costs: Fixed Costs You Can't Recover
A sunk cost is a fixed cost already incurred and unrecoverable - last year's nonrefundable advertising, a specialized machine with no resale value. Rational decisions ignore sunk costs because no current choice can change them; only forward-looking (avoidable) costs matter. 'We must continue - look what we spent' is the sunk-cost fallacy, and good managers train themselves out of it.
Why the Split Vanishes in the Long Run
The fixed/variable distinction exists only because some inputs are fixed - a short-run condition. In the long run every input is variable, so every cost is variable and the split dissolves. This is why long-run analysis uses total cost directly and asks which plant size minimizes it, rather than decomposing a given plant's costs.
Key points
- TC = TFC + TVC: total cost is the sum of fixed and variable cost.
- Fixed costs are constant with respect to output; variable costs rise with output.
- TFC graphs as a horizontal line; TC is TVC shifted up by TFC, parallel to it.
- Marginal cost depends only on variable cost, since fixed cost never changes.
- Sunk costs are unrecoverable and must be ignored in rational decisions.
- In the long run all costs are variable, so the split disappears.
Common misconceptions
✓ Truth: Fixed means unresponsive to output in the period analyzed. Leases renew, insurance re-prices, and managers get raises - fixed costs change across periods while remaining fixed with respect to output within a period.
✓ Truth: Pricing and output decisions follow marginal cost and marginal revenue. Fixed costs affect whether the firm stays open (the shutdown and exit decisions) but not how much to produce while open.
✓ Truth: The money is gone regardless of what the firm does next. Only costs that differ between the options - avoidable, forward-looking costs - can rationally affect the choice.
Practice questions
Q1. A firm's total cost at 100 units is $5,000, of which $2,000 does not vary with output. Its TVC at 100 units is:
- $2,000
- $3,000
- $5,000
- $7,000
TC = TFC + TVC, so TVC = TC - TFC = 5,000 - 2,000 = 2,000 fixed component is paid regardless of output.
Q2. Which of the following is a fixed cost for a restaurant in the short run?
- Hourly wages of servers.
- Monthly rent on the building.
- Food ingredients.
- Credit-card processing fees.
Rent is owed regardless of meals served this month - it does not vary with output. Wages, ingredients, and processing fees all rise with the number of customers.
Q3. A company spent $1M on advertising last year with no resale value. This year it decides whether to continue a product line. The $1M is:
- a variable cost.
- a sunk cost, irrelevant to the decision.
- a marginal cost.
- an implicit cost.
The spending is unrecoverable - no current decision changes it - so it is sunk. Only forward-looking costs (future production, marketing, opportunity costs) should enter the continue-or-drop analysis.
Q4. If a firm's fixed costs rise (e.g., higher rent), what happens to its marginal cost curve?
- It shifts up.
- It shifts down.
- It does not move.
- It becomes steeper.
MC = ΔTC/ΔQ = ΔTVC/ΔQ because fixed costs never change with output. A higher rent shifts TC, ATC, and AFC up but leaves MC exactly where it was.
Click a question to reveal the answer and explanation.
Frequently asked questions
Is labor a fixed or variable cost?
Usually variable - hours adjust with output. But salaried staff, union-guaranteed hours, or specialized crews hired for the season are fixed or quasi-fixed in the short run. Classify by actual adjustability, not by the label 'labor'.
Can a cost be fixed for one firm and variable for another?
Yes. Delivery trucks are fixed for a bakery that owns them but variable for one that rents by the day. Fixity depends on contracts and technology, not on the input's name.
Why is TVC zero at zero output but TFC positive?
Producing nothing requires no variable inputs - no flour, no hourly wages - so TVC is zero. But the lease and insurance are owed anyway, so TFC (and hence TC) is positive at zero output. That vertical intercept is the firm's short-run loss if it shuts down.
What is a quasi-fixed cost?
A cost that is fixed over a range of output but jumps at thresholds - adding a supervisor when output passes a certain level, or opening a second shift. It behaves as fixed within each range and steps up between ranges.