# Cost Structures

Business I · Economics of the Firm · https://tryals.app/learn/business-i/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.

| Measure | Formula | Question answered |
|---|---|---|
| Total cost | $TC = FC + VC(q)$ | What does total output cost? |
| Average total | $ATC = TC/q$ | What does each unit cost? |
| Marginal | $MC = \Delta TC / \Delta q$ | What does one more unit cost? |
| Break-even | $q^* = FC/(p-v)$ | When does profit begin? |

## Practice questions

4 of this lesson's 12 practice questions, with answers. The full set is in the app.

### 1. An airline sells a last-minute seat for far less than the average cost per passenger and still improves its profit. How?

A. Because average cost falls as more seats are sold, eventually reaching the low price
B. Because the flight's costs are almost entirely fixed and sunk
C. Because last-minute passengers cost the airline less to serve overall
D. Because the airline is accepting a loss on that seat to build customer loyalty

**Answer:** B. Because the flight's costs are almost entirely fixed and sunk

**Why:** The plane, crew and gate are paid for whether the seat flies empty or full, so the only cost in play is the marginal one, and anything above it is money that would otherwise not exist. Deciding on average cost would leave the seat empty, which is why pricing questions must always ask *marginal to what?*

Page: https://tryals.app/practice/business-i/cost-structures/an-airline-sells-a-last-minute-seat-for-far-less-than-the-average

### 2. Sort each source of falling average cost into its scale-economy driver.

**Answer:**

- Spreading fixed costs: The same factory license covers double the output, R&D spending serves every unit sold
- Specialization: Workers each master one station instead of all tasks
- Purchasing power: Bulk orders earn a 15% supplier discount

**Why:** Three engines of scale economies: dilute the fixed, divide the labor, and squeeze the suppliers.

Page: https://tryals.app/practice/business-i/cost-structures/sort-each-source-of-falling-average-cost-into-its-scale-economy

### 3. Fixed costs are 500€; unit variable cost is 3€. Set the slider to the **average total cost** at 100 units, in €.

**Answer:** 8 (within ±0.5)

**Why:** $ATC = 500/100 + 3 = 8$€. At 500 units it would be just 4€, the fixed-cost share melts as output grows.

Page: https://tryals.app/practice/business-i/cost-structures/fixed-costs-are-500-unit-variable-cost-is-3-set-the-slider-to-the

### 4. A firm doubles output and total cost rises from 100k€ to 180k€. What does this reveal?

A. The firm is below break-even
B. Constant returns to scale
C. Economies of scale: average cost fell
D. Diseconomies of scale: average cost rose

**Answer:** C. Economies of scale: average cost fell

**Why:** Cost per unit fell from 100k/q to 180k/2q = 90k/q, a 10% drop in average cost. Less-than-proportional cost growth is the definition of scale economies.

Page: https://tryals.app/practice/business-i/cost-structures/a-firm-doubles-output-and-total-cost-rises-from-100k-to-180k-what