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Short-run costs curves

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Short-run Cost Curves

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In the Fraser of Allander Institute Economic Commentary Volume 47 No.3 it was stated that “more than 8 in 10 businesses have seen their costs increase in the past year (2023), with over two-thirds of firms absorbing these costs to avoid passing them on to consumers.” in response to Scotland’s weak economic growth and high inflation

fraserofallander.org

These costs include:

Wage costs

typically considered variable costs

Operating costs

often have both fixed and variable components

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We will look at the different types of production costs and what charting them can tell us about firm behaviour in the short and long run to answer this question!

👉 This will help show why companies might change their prices or production levels, and how they plan for the future.

Fixed, variable, total, average, and marginal costs

Fixed Cost

What is a fixed cost?

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A fixed cost is a cost that does not depend on the quantity of output produced. This is commonly known as overhead cost in industry.

What are examples of fixed costs?

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Rent is a classic example of a short-run fixed cost. In the short-run rent payments for an office space will need to be made whether the firm is servicing 10, 100, or 1000 customers. Other examples could include types of equipment or services like insurance.

What is the average fixed cost (AFC)?

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The average fixed cost (AFC) is the fixed cost per unit of output produced by a business.

Since the cost is consistent regardless of the level of output produced, AFC decreases as more is produced. This leads to a downward-sloping AFC.

\text{AFC} = \frac{\text{Fixed Cost}}{\text{Quantity of Output}}

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Let’s illustrate this in a table and a graph:

Output	Fixed cost	Average fixed cost
0	50	–
1	50	50
2	50	25
3	50	16.7
4	50	12.5
5	50	10
6	50	8.3
7	50	7.1
8	50	6.3
9	50	5.6
10	50	5

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This graph plots both the fixed cost and average fixed cost:

Fixed cost

Regardless of weather a firm produces 2 outputs or 10 outputs, they will still incur a cost of £50 hence why the fixed cost line is a horizontal line.

Average fixed cost (AFC)

Say a firm produces 2 outputs, the AFC will be 50/2=25
if a firm produces 10 outputs, the AFC will be 50/10 =5

Therefore, the AFC decreases as a firm produces more because fixed costs are spread over a larger number of units of output
AFC therefore falls rapidly at first but can never quite reach the x-axis because fixed costs are always positive and never completely vanish.

Variable Cost

What is a variable cost?

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A variable cost is a cost that does depend on the quantity of output produced.

Example:

Output	Fixed cost	Variable cost
0	50	0
1	50	40
2	50	70
3	50	90
4	50	100
5	50	120
6	50	150
7	50	190
8	50	240
9	50	300
10	50	370

We can see that regardless of a firm’s output, the fixed cost stays the same at 50 throughout
However, if we go to the the variable cost column, we see that as a firm produces more, the variable costs increases

What are examples of variable costs?

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Raw materials: Costs that increase with the quantity of goods produced, like ingredients for baking cookies.

Labour: Wages paid to workers that vary with production levels, such as paying hourly workers in a factory.

Utilities: Costs like electricity and water that go up or down depending on how much is used, similar to how your family's electric bill changes each month

What is the Average variable cost (AVC)?

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The average variable cost (AVC) is the variable cost per unit of output produced by a business.

\text{AVC} = \frac{\text{Variable Cost}}{\text{Quantity of Output}}

Let’s add in the AVC column:

Output	Variable cost	Average variable cost (AVC)
0	0	–
1	40	40
2	70	35
3	90	30
4	100	25
5	120	24
6	150	25
7	190	27.1
8	240	30
9	300	33.3
10	370	37

At Output 2, the variable cost is 70. To calculate the AVC: 70/2 = 35
At Output 6, the variable cost is 150. To calculate the AVC: 150/6 = 25

Notice in the Average variable cost column, AVC decreases till output reaches 4 units, and then starts to increase afterwards when output increases over 6 units. Why is this the case? 👇

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remember the Law of diminishing returns?

The law of diminishing marginal returns states that as one factor of production (like labour) is increased while others are held constant, the additional output or returns will eventually diminish.

Key point to note:

👉 Returns are the payments or income earned by the owners of the factors of production, like land, labour, and capital.

👉 Increasing Returns: At first, when production increases, each additional unit costs less to make because resources are used more efficiently → AVC goes down with increased production → business starts experiencing increasing returns, earning more because they are spending less per unit.

👉 Diminishing Returns: After a certain point (like 6 units) making even more units becomes harder and more expensive → AVC starts to go up because the business needs more resources, like additional workers or equipment, to produce more units → business spends more on each unit and starts experiencing decreasing returns, reducing the income or returns because they are now spending more per unit.

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Example: Diminishing Marginal Product of Labour in the Office of an Energy Supplier

Let’s imagine a new energy supplier that has committed to an office space for a 5-year lease. The company is having great success and has doubled their number of staff in the first 3 years.

🏢 Since the amount of space – and therefore desk space – is fixed, once there is enough staff for each desk, each worker hired adds an element of friction. More time is spent coordinating between employees and less time is spent billing customers and taking calls.

So there is an overworking of the fixed factors (e.g captial, land, entrepreneurship) leading to declining productivity of extra labour

Critically, there are increasing and diminishing returns to variable costs. This leads to a U-shaped average variable cost curve:

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Knowledge checkpoint: Explain, using a diagram, the shapes of average fixed and average variable cost curves.

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Knowledge checkpoint: Explain the law of diminishing marginal returns.

Total cost

What is total cost?

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Total cost is the product of adding fixed cost and variable cost together.

Total cost is a critical metric for understanding the profitability of a firm in the short- and long-run.

Output	Fixed cost	Variable cost	Total cost
0	50	0	50
1	50	40	90
2	50	70	120
3	50	90	140
4	50	100	150
5	50	120	170
6	50	150	200
7	50	190	240
8	50	240	290
9	50	300	350
10	50	370	420

What is average total cost?

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Average Total Cost (ATC) is the total cost per unit of output, calculated by adding average fixed cost (AFC) and average variable cost (AVC).

\text{ATC} = \frac{\text{Fixed Cost + Variable Cost}}{\text{Quantity of Output}}

Output	Total cost	Average total cost
0	50	–
1	90	90
2	120	60
3	140	46.7
4	150	37.5
5	170	34
6	200	33.3
7	240	34.3
8	290	36.3
9	350	38.9
10	420	42

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Note that the Average total Cost (ATC) is also called the Short-run Average Cost (SRAC) and the Average Cost (AC)

ATC = SRAC = AC

In theory, the shape of the ATC curve should be U-shaped

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When the ATC is Downward Sloping:

Spreading Effect: We are seeing the spreading effect take place as fixed cost is spread over more units of output. This causes the average total cost (ATC) to decrease initially.
Point of Maximum Efficiency: The lowest point on the ATC curve represents the point of maximum efficiency, where costs are at their lowest per unit (at output 6 units)

The curve falls initially due to several factors:

Increasing Returns: Output increases more than costs initially due to efficient use of resources.
Specialisation Benefits: Workers and processes become more specialised, increasing productivity and reducing costs.
Fixed Cost Distribution: Fixed costs are spread over a larger number of units, reducing the fixed cost per unit.
Output vs. Cost Growth: Output rises faster than costs, leading to a lower ATC.

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When the ATC is Upward Sloping:

Diminishing Returns: As production increases further, the ATC starts to rise due to diminishing returns. More units of input are required to produce each additional unit of output.
Curve Rise Factors: The curve begins to rise due to:

Diminishing Returns/Law of Diminishing Marginal Returns: Additional inputs contribute less to output, increasing costs.
Erosion of Specialisation Benefits: The advantages of specialisation decrease, and the fixed factor becomes overworked.
Cost vs. Output Growth: Costs begin to rise faster than output, increasing the ATC.

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Knowledge checkpoint: Explain, using a diagram, the shape of a short run average cost curve.

Marginal Cost

What is marginal cost?

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The marginal cost is the additional cost of producing one more unit of output

Output	Total cost	Marginal cost
0	50	–
1	90	40
2	120	30
3	140	20
4	150	10
5	170	20
6	200	30
7	240	40
8	290	50
9	350	60
10	420	70

For example, to produce 4 output units instead of 3 output units, total costs rose from 140 to 150 which is an increase of 10 which is the additional/marginal cost to produce 4 output units

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The graphical representation of marginal cost is the marginal cost curve which Diminishing marginal returns arise from increasing quantity of an input while other inputs remain fixed

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A way to think about it:

If the marginal (next) person to enter a room is taller than the average height, average height increases, however if they are smaller than the average height, average height decreases.

Therefore

if MC>AC, MC will push AC up‼️
if MC<AC, MC will pull AC down‼️

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Knowledge checkpoint: Describe the factors which cause average costs to fall in the short run.

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Knowledge checkpoint: Describe, using a diagram, the relationship between marginal cost and average total cost.

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