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Costs, Revenue and Objectives » Costs of Production

What you'll learn this session

Study time: 30 minutes

Cambridge spec: 3.6.1, 3.6.2

Define fixed, variable, total and average costs
Calculate TC, ATC, FC, AFC, VC and AVC
Draw and interpret cost diagrams
Explain why average total cost is U-shaped

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The six costs of production

Every firm has to pay for the resources it uses. Economists split these costs into types, because each type behaves differently when the firm makes more or fewer goods.

Key terms:

Fixed cost (FC): a cost that does not change when output changes, such as rent, insurance or a loan repayment.
Variable cost (VC): a cost that changes when output changes, such as raw materials, packaging or electricity used by machines.
Total cost (TC): all the costs of producing a given output. TC = FC + VC.
Average fixed cost (AFC): the fixed cost for each unit produced. AFC = FC / output.
Average variable cost (AVC): the variable cost for each unit produced. AVC = VC / output.
Average total cost (ATC): the total cost for each unit produced. ATC = TC / output.

Fixed and variable costs

🏡 Fixed cost

Ravel Kites rents a workshop for $240 a week. It pays $240 whether it makes 10 kites or 60 kites. That rent is a fixed cost.

📦 Variable cost

Each kite needs cloth, string and wooden rods. Make more kites and the firm pays more for these. They are variable costs.

Add the two together and you get total cost. Dividing any of the three by output gives the "average" version, which is the cost per kite.

Calculating the costs

Here is a made-up cost table for Ravel Kites, a firm in Pomara. Fixed cost is $240 a week. Output is kites per week.

Output	FC ($)	VC ($)	TC ($)	AFC ($)	AVC ($)	ATC ($)
10	240	80	320	24.00	8.00	32.00
20	240	140	380	12.00	7.00	19.00
30	240	210	450	8.00	7.00	15.00
40	240	320	560	6.00	8.00	14.00
50	240	500	740	4.80	10.00	14.80
60	240	780	1,020	4.00	13.00	17.00

Worked example 1: output of 40 kites

TC = FC + VC = 240 + 320 = $560.
ATC = TC / output = 560 / 40 = $14.
AFC = 240 / 40 = $6.
AVC = 320 / 40 = $8.
Check: AFC + AVC = 6 + 8 = $14, which equals ATC.

That check is useful in the exam. ATC always equals AFC + AVC.

Worked example 2: working backwards

Pomara Juice makes 500 litres. Its total cost is $1,500 and its variable cost is $1,100. Find FC, AFC, AVC and ATC.
FC = TC - VC = 1,500 - 1,100 = $400.
AFC = 400 / 500 = $0.80.
AVC = 1,100 / 500 = $2.20.
ATC = 1,500 / 500 = $3.00.

Worked example 3: starting from the average

A firm makes 150 units. Its ATC is $12 and its FC is $900. Find TC, VC and AVC.
TC = ATC x output = 12 x 150 = $1,800.
VC = TC - FC = 1,800 - 900 = $900.
AVC = 900 / 150 = $6.

Drawing and reading the cost diagrams

You can draw the table as a diagram. Follow these steps in the exam.

📈 Diagram 1: total costs

Put Output on the horizontal axis and Costs ($) on the vertical axis. Draw FC as a flat horizontal line, because it does not change. Draw VC starting at the origin and rising, because no output means no variable cost. Draw TC starting on the vertical axis at the level of FC and rising. TC is always FC above VC, so the TC line is the VC line lifted up by the same amount.

📉 Diagram 2: average costs

Use the same axes, but label the vertical axis Cost per unit ($). Draw AFC as a curve that slopes down and gets flatter, never touching the horizontal axis. Draw AVC as a U-shape. Draw ATC as a U-shape above AVC. The gap between ATC and AVC is AFC, and it gets smaller as output rises.

Why is ATC U-shaped?

Two things pull ATC in opposite directions.

Falling AFC: as output rises, the fixed cost is shared over more units. At 10 kites each carries $24 of rent. At 60 kites each carries only $4.
Rising AVC: at high output, variable costs per unit go up. Workers get in each other's way, machines are overworked and extra materials cost more.

At first, falling AFC wins and ATC falls. Later, rising AVC wins and ATC rises. The lowest point of ATC is at 40 kites, where ATC is $14. This U-shape is for a firm of one fixed size. The long-run ATC diagram, where the firm changes its size, is covered in the lesson on economies and diseconomies of scale.

Common mistakes

Saying that fixed cost per unit is fixed. FC stays the same in total, but AFC falls as output rises.
Dividing by the wrong number. Always divide by output, never by another cost.
Forgetting that TC does not start at zero. Even at zero output the firm still pays its fixed costs.
Drawing ATC as a straight line. It must curve into a U-shape.

Exam-style question

Lantana Lamps is a small firm in Corvedo. Its fixed cost is $600 a month. The variable cost of making 100 lamps is $400, of making 200 lamps is $700 and of making 300 lamps is $1,200.

(a) Define fixed cost. [2 marks]
(b) Calculate the total cost of making 200 lamps. [2 marks]
(c) Calculate the average total cost of making 300 lamps. [2 marks]
(d) Explain why average fixed cost falls as output rises. [4 marks]

Model answer

(a) A cost that does not change when output changes (1), such as rent or insurance (1).
(b) TC = FC + VC (1) = 600 + 700 = $1,300 (1).
(c) TC = 600 + 1,200 = $1,800 (1). ATC = 1,800 / 300 = $6 (1).
(d) AFC = FC / output (1). Fixed cost stays the same however much is produced (1). As output rises, the same fixed cost is shared between more units (1). For example, $600 / 100 lamps is $6 each, but $600 / 300 lamps is only $2 each (1).

Paper 1 style item: A firm has a total cost of $900 when it makes 30 units. Its fixed cost is $300. What is its average variable cost?
A $10 B $20 C $30 D $40

Answer

B. VC = 900 - 300 = $600, and 600 / 30 = $20. A is AFC and C is ATC.

Exam tip

In a "Calculate" question, write the formula first and then the numbers. Even if you slip on the arithmetic, you can still earn the method mark.

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