Total and unit cost from the cost function
The linear cost function separates fixed and variable costs. Cost per unit falls with output because fixed costs are spread over more units.
Worked example
A firm's cost function is C(x) = 48000 + 21.5x. Work out total cost and cost per unit at 3,350 units.
Worked solution
- 1.C = fixed + variable × x = £48,000.00 + £21.50 × 3,350 = £120,025.00
- 2.Cost per unit = £120,025.00 / 3,350 = £35.83
- 3.Cost per unit falls as quantity rises because fixed costs are spread over more units.
Typical mistake: Giving the variable cost per unit as the cost per unit; the fixed cost share is missing.
Your turn
Three problems of exactly this type, each time with new numbers. Amounts with or without thousands separators.
Task
A firm's cost function is C(x) = 25000 + 37x. Work out total cost and cost per unit at 3,750 units.
Total cost in £
Cost per unit (average cost) in £
Amounts like 12,500 or 12500.50; percentages as a number (12.5). Round to the penny or 2 decimal places.
Formulas for this topic
- Total cost = fixed + variable × x
- Cost per unit = total cost / x
- High-low: variable = (C₂ − C₁) / (x₂ − x₁), then fixed = C₁ − variable × x₁
Typical mistake: Giving the variable cost per unit as the cost per unit; the fixed cost share is missing.
Frequently asked questions
What is the typical mistake in "Total and unit cost from the cost function"?
Giving the variable cost per unit as the cost per unit; the fixed cost share is missing.
Why does cost per unit fall with output?
Fixed costs are spread over more units.