Cost Structures

The Anatomy of Costs

Every firm's expenditure splits into two core types:

• Fixed costs (FC): paid regardless of output, like rent or salaries. They remain due even at zero production.
• Variable costs (VC): grow with output, like materials and energy.

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

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

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

Marginal cost ($MC$), the cost of one more unit, is the ultimate decision-maker's number: produce another unit whenever price exceeds its marginal cost.

Common pitfall: Fixed is not the same as sunk. Rent next year is fixed but avoidable if you close; last year's failed ad spend is sunk and must never drive decisions.

Scale and Break-Even

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

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

Worked example: A café with 3,000 euros monthly fixed costs, selling coffee at 2.50 euros with 1.00 euro variable cost, needs $3000 / 1.50 = 2000$ coffees a month before profit begins.

Economies of scale occur when doubling output less than doubles cost, driving average cost down through specialization and volume discounts. Diseconomies appear when coordination costs overwhelm those gains.