Costs, scale of production and break-even
Costs, revenue and profit
- fixed costs don't change with output (rent); variable costs do (materials).
$$\text{total cost} = \text{fixed costs} + \text{variable costs}$$
$$\text{total revenue} = \text{price} \times \text{quantity sold}$$
$$\text{profit} = \text{total revenue} - \text{total cost}$$
Practice
Total revenue is 9,000 and total cost is 6,500. What is the profit (in dollars)?
Profit = total revenue − total cost = 9,000 − 6,500 = 2,500.
Break-even
- Break-even is the output where total revenue = total cost (no profit, no loss).
$$\text{break-even output} = \frac{\text{fixed costs}}{\text{price per unit} - \text{variable cost per unit}}$$
- The margin of safety = actual output − break-even output. A bigger margin is safer.
- Limits: it assumes all output is sold and that price and costs stay the same.
Practice
Fixed costs are 3,000; each unit sells for 10 with a variable cost of 4. What is the break-even output (in units)?
Break-even = fixed costs ÷ (price − variable cost) = 3,000 ÷ (10 − 4) = 3,000 ÷ 6 = 500 units.
Practice
Actual output is 700 units and break-even is 500. What is the margin of safety (in units)?
Margin of safety = actual − break-even = 700 − 500 = 200 units.
You've got it
Key idea
- total cost = fixed + variable; profit = total revenue − total cost
- break-even = fixed costs ÷ (price − variable cost per unit)
- margin of safety = actual − break-even output (bigger = safer)