Short-Run Costs (Cambridge International A-Level Economics)

Types of short-run costs

• In the short run, some factors of production such as factory space or machinery are fixed, while others, such as labour or raw materials can be varied

• This creates two types of costs:

  • Fixed costs, which do not change with output
  • Variable costs, which change as production increases

• These together form the short-run cost structure of a firm

Fixed and variable costs

1. Fixed costs (FC)

• Fixed costs are expenses that do not change with the level of output. They must be paid even if the firm produces nothing

  • Examples include rent for premises, insurance premiums, and salaries of permanent staff
  • A cinema pays rent and licensing fees whether it screens films or not
  • On a graph, total fixed costs appear as a horizontal line, since they remain constant regardless of output

• Firms operating in industries with high fixed costs such as hotels or airlines often aim to maximise output

• This helps to spread these costs over more units, thereby reducing the average fixed cost per unit

2. Variable costs (VC)

• Variable costs change directly with the level of production

  • These include expenses such as wages for temporary staff, electricity used in production, and the cost of raw materials
  • For example, a bakery’s flour and sugar costs rise as more cakes are baked.
  • Variable costs increase with output and are crucial for calculating total cost

3. Total cost (TC)

• Total cost represents the overall cost of producing a given level of output
• It is the sum of fixed and variable costs

$\mathrm{TC}=\mathrm{TFC}+\mathrm{TVC}$

• Where:

  • TFC = total fixed costs
  • TVC = total variable costs

• As output increases, total cost rises because variable costs increase

Average costs

• Average costs measure the cost per unit of output

1. Average total cost (ATC)

• Average total cost shows the total cost of producing each unit of output

$\mathrm{ATC}=\frac{\mathrm{TC}}{Q}$

• Where:

  • TC = total cost
  • Q = quantity of output

2. Average fixed cost (AFC)

• Average fixed cost measures the fixed cost per unit of output

$\mathrm{AFC}=\frac{\mathrm{TFC}}{Q}$

• As output increases, average fixed cost falls because the fixed costs are spread across more units

  • This is sometimes called 'spreading overheads' or 'fixed cost spreading'

3. Average variable cost (AVC)

• Average variable cost measures the variable cost per unit of output

$\mathrm{AVC}=\frac{\mathrm{TVC}}{Q}$

• AVC may initially fall due to better use of variable inputs, but eventually rises due to the law of diminishing returns

Marginal cost (MC)

• Marginal cost is the increase in total cost caused by producing one more unit of output

$\mathrm{MC}=\frac{\mathrm{ΔTC}}{\mathrm{ΔQ}}$

• Because fixed costs do not change with output in the short run, marginal cost can also be calculated using:

$\mathrm{MC}=\frac{\mathrm{ΔTVC}}{\mathrm{ΔQ}}$

• Marginal cost typically:

  • Falls at first, due to increasing productivity
  • Then rises as diminishing returns occur

• This creates the U-shaped marginal cost curve

• The MC curve intersects the ATC and AVC curves at their minimum points

Worked Example Cost calculations using the above formulas

Assume:

• Total fixed cost (TFC) = $200
• Variable costs rise at an increasing rate as output increases
• This reflects the law of diminishing returns, where additional workers become less productive and production becomes more expensive

This means:

• Total variable cost (TVC) increases at an increasing rate
• Marginal cost (MC) eventually rises

Short-run cost calculations example

Output (Q)	TFC	TVC	TC =$\mathrm{TFC}+\mathrm{TVC}$	MC = $\frac{\Delta\mathrm{TC}}{\Delta Q}$	AFC =$\frac{\mathrm{TFC}}{Q}$	AVC =$\frac{\mathrm{TVC}}{Q}$	ATC =$\frac{\mathrm{TC}}{Q}$
0	200	0	200	–	–	–	–
1	200	50	250	50	200	50	250
2	200	90	290	40	100	45	145
3	200	140	340	50	66.67	46.67	113.33
4	200	200	400	60	50	50	100
5	200	280	480	80	40	56	96
6	200	380	580	100	33.33	63.33	96.67
7	200	520	720	140	28.57	74.29	102.86
8	200	700	900	180	25	87.5	112.5

What this table demonstrates

• TFC remains constant at $200 because fixed costs do not change with output
• TVC increases at an increasing rate due to the law of diminishing returns
• MC initially falls, then rises as diminishing returns begin
• AFC always falls as fixed costs are spread over more output
• ATC falls initially, then rises as increasing marginal costs dominate

Drawing and interpreting cost diagrams

Fixed costs (FC)

• The firm must pay its fixed costs even if output is zero
• Fixed costs do not change with the level of output

Variable costs (VC)

• Initially, variable costs may increase slowly as labour becomes more productive
• As more variable factors are added to fixed factors, the law of diminishing returns causes variable costs to rise at an increasing rate

Total cost (TC)

• The total cost is the sum of the variable and fixed costs
• The total costs cannot be 0, as all firms have some level of fixed costs

Average fixed cost (AFC)

• If the fixed costs of a firm are $1,000 and it produces 1 unit of output, then its **AFC is $1,000 **($1,000/1)
• If the firm increases its output to 1000 units, then the** AFC is $1 per unit **($1000/1,000)
• The more units a firm produces, the lower its AFC will be
• This is one reasons why large levels of output help to increase the profit per unit

Average total cost (ATC)

• As a firm grows, it is able to increases its scale of output generating efficiencies that lower its average total costs (AC) of production

• As a firm continues increasing its scale of output, it will reach a point where its average total costs (AC) start to increase

• ATC is U-shaped mainly because of:

  • increasing returns initially
  • diminishing returns later

Marginal costs (MC)

• The distance between the AVC and AC = the AFC

  • AVC converges towards AC as the AFC continuously decreases with an increase in output
  • AVC decreases as additional workers are added and each worker produces additional product

• Marginal costs (MC) decrease initially as additional workers are added and the marginal product is increasing

• Diminishing returns begin when the MC starts to increase

• MC will cross the AVC and AC curves at their lowest point

  • As long as the cost of producing the next unit (MC) is lower than the average, it will pull down the average
  • When the cost of producing the next unit (MC) is higher than the average, it will pull up the average