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Cost theory

You need to be able to define and explain the following terms:

Fixed and variable costs

  • Fixed costs (FC) - costs that do not change as production is increased or decreased. They have to be paid in advance of production. They exist even if output is zero.
  • Variable costs (VC) - costs that vary with output.

Total, average and marginal cost

  • Total costs (TC) - the sum of fixed costs and variable costs at a particular level of output. So TC = TFC + TVC.
  • Marginal costs (MC) - the cost of one more unit of output. In other words the increase in total cost from producing one more unit of output.
  • Average costs (AC) - total costs divided by the level of output. There are three aspects of average cost: average total cost (ATC) which is total cost divided by the level of output, average fixed cost (AFC) which is total fixed cost divided by the level of output and average variable cost (AVC) which is total variable cost divided by the level of output.

These costs all relate to operations at a point in time, but they can all vary with time.

Fixed costs

These costs are those that remain unchanged as the output level of the firm changes. It does not matter what level of output the firm produces (even zero output makes no difference), any cost which is a fixed cost will remain the same. Common examples of fixed costs are as follows:

Examples of fixed costs

  • Rent
  • Interest on loans
  • Insurance
  • Depreciation

Fixed costs can be represented graphically and this would appear as follows:

Figure 1 Total fixed costs

Variable costs

Any cost which varies directly with the level of output would be classified as a variable cost. Varying directly means that the total variable cost will be dependent on the level of output. Common examples of variable costs are as follows:

Example of variable costs

  • Direct labour
  • Raw materials and components
  • Packaging costs
  • Heating and lighting

Variable costs can be represented on a graph and this would appear as follows:

Figure 2 Total variable cost

We could also classify costs as semi-variable costs. Have a think about what these might be and then follow the link below.

Semi-variable costs

Calculating costs

You also need to be able to calculate a firm's costs from given data, be able to draw cost curves and then interpret what they mean. We come to that skill later.

You will also need to identify and explain short-run and long-run cost curves. Look carefully at the following examples.

Figure 3 Short-run average cost curve

Figure 4 Long-run average cost curve

In the short-run, at least one factor input is fixed. In the long-run all inputs are variable. This means that short-run curves are models of what is happening. Long-run curves are planning data. A firm cannot operate with all inputs variable. Having decided what it wants from an examination of the long-run curves, the firm makes a decision to fix a factor, usually capital, and this gives rise to a new short-run situation.

Now, the calculations and the drawing!

You could be presented with data in the form of a table, like the one below

Output (units 0 1 2 3 4 5 6 7 8 9 10
Total cost ($k) 100 110 125 145 170 200 235 275 320 370 425


Plot this with output on the horizontal axis and total cost on the vertical axis and look at it.

There is also a static version of this graph available.

What do you know now?

  • The firm has fixed costs of $100,000, the cost of 'output zero'.
  • The total variable cost is increasing with increasing output

Now, some more sums. Work out the average cost (TC / output), the total variable cost (TC - FC), the variable cost (TVC / output), the average fixed cost (FC / Output) and the marginal cost (TC (Qx) - TC (Qx-1)).

Once you have had a go at calculating all these, follow the answer link below to compare how you got on.

Answer - cost calculations

Now plot this data on two separate graphs as follows, and see what it shows.

Graph 1 - Total cost, total variable costs and total fixed costs
Graph 2 - Marginal cost, average cost, average fixed cost and average variable cost

You should get the following:

Graph 1 Total cost, total variable costs and total fixed costs

There is also a static version of this graph available.

Graph 2 - Marginal cost, average cost, average fixed cost and average variable cost

There is also a static version of this graph available.

  • Average cost (AC) falls initially, then turns and starts to rise.
  • AFC + AVC = AC.
  • MC follows the same pattern, but at a more exaggerated rate.
  • Marginal cost and average cost cross at the minimum average cost.

See Figure 6 below for the standard representation of these curves.

Why do average and marginal cost cross at the minimum point of average cost?

Well think of this in terms of cricket scores. Your last innings is your 'marginal' innings, whereas your batting average is your 'average'. Say your average is 50 and in your next innings you get 20 runs. What happens to your average? It will fall. However, if in your next innings you get 80 runs. In this case your average will rise.

So, if the marginal is below the average, the average will fall and if the marginal is above the average, the average will rise.

There are many questions for you to work on in the questions section (click on the questions - module 2 link in the left hand navigation bar). It may also be worth having a look at the Diggin' diagrams sections (accessible from the course homepage) to check how well you understand your diagrams.

Interactive spreadsheet

To see how changes in cost affect the cost curves, why not have a look at our interactive spreadsheet. On this, you can make changes in the values of costs and instantly see the effect on the diagram of cost curves. Follow the link below to view the spreadsheet.

Total cost curves - interactive spreadsheets

Summary

Remember, a standard marginal and average cost curve diagram should look like this:

Figure 5 Marginal and average cost

Add in the average fixed and average variable cost curves and it should look like this:

Figure 6 Marginal cost, average cost, average fixed cost and average variable cost