Cost Structures

The Anatomy of Costs

Every cost a firm pays is one of two kinds:

• Fixed costs (FC): paid regardless of output — rent, insurance, salaried staff. At zero production they are still due.
• Variable costs (VC): grow with output — materials, energy, piece-rate labor.

$$TC(q) = FC + VC(q)$$

From total cost, three derived measures do the analytical work:

$$ATC(q) = \frac{TC(q)}{q} \qquad AVC(q) = \frac{VC(q)}{q} \qquad MC(q) = \frac{\Delta TC}{\Delta q}$$

Marginal cost — the cost of one more unit — is the decision-maker's number: produce another unit whenever its price exceeds its marginal cost.

Break-even: with price $p$ and unit variable cost $v$, each sale contributes $p - v$ toward covering fixed costs. The firm breaks even at

$$q^* = \frac{FC}{p - v}$$

A café with 3,000€ monthly fixed costs, selling coffee at 2.50€ with 1.00€ variable cost, needs $3000 / 1.50 = 2000$ coffees a month before the first cent of profit.

Economies of scale: when doubling output less than doubles cost, average cost falls with size — driven by spreading fixed costs, specialization, and volume discounts. Diseconomies appear when coordination costs of size overwhelm those gains.

The cost toolkit

Common pitfall: Fixed is not the same as sunk. Rent next year is fixed but avoidable (close the shop); last year's failed ad campaign is sunk — and sunk costs must never drive decisions.