# Costs

## Fixed Costs and Variable Costs

The production of goods and services involves using a combination of fixed factors of production and variable factors.

Fixed factors are those that cannot be increased or decreased in the short run. They mainly comprise capital items such as machines, buildings and vehicles, but also the land upon which the buildings stand. It may take quite some time to build and equip a new factory, or to find a buyer for it if we want to close it down.

Variable factors are mainly labour and materials. They can be increased or decreased in the short run. If we want to raise or reduce output, we can work more or fewer hours, hire or fire more workers and buy more or less materials fairly quickly.

The short run is therefore defined as a period in which at least one factor is fixed and cannot be increased or reduced in quantity.

The long run is the period in which all factors can be increased or reduced in quantity. In other words all factors are variable in the long run.

The distinction between the short and long run periods varies between industries. For instance, it may only take a few weeks for a farmer to buy some new, more efficient tractors, but it can take years to build a new power station.

Fixed costs are the costs incurred of the fixed factors, such as rent, interest and depreciation in a given period of time.

Total Fixed Costs (TFC) do not vary with output in the short run. For instance, suppose a factory pays rent and interest (on a loan to buy a machine) totalling £1000 per month. It will have to pay this amount regardless of how much output is produced each month.

Average Fixed Cost (AFC) is the fixed cost per unit of output (Q). It is calculated using the formula: AFC = TFC / Q

For instance, if monthly fixed costs are £1000, and output is 200 units per month, AFC = £5.00.

It follows from this that AFC varies in inverse proportion to output; if output doubles, AFC halves, and so on. In the above example, an increase in output to 400 units per month means AFC is £2.50.

Variable costs are the costs of the variable factors, mainly labour (wages) and materials.

Total Variable Costs (TVC) will increase with increases in output; at higher output levels we will use more labour and materials. For instance we may use £400 of labour and materials at an output of 200 units per month, and £600 worth if output increases to 400 units.

Average Variable Cost (AVC) __is the variable cost per unit of output. It is found using the formula: __AVC = TVC / Q

In the above example, at an output of 200 units per month, AVC = £2.00 and at an output of 400 it is £1.50.

The relationship between output and AVC is complicated and is explained below under ‘diminishing returns’.

Total Cost (TC) is the total cost of producing a given output in a particular period of time. It can be calculated by the formula TC = TVC + TFC. For instance, using the data above, at an output of 400 units per month, TFC is £1000, and TVC is £600. therefore TC = £1600.

Alternatively, we can calculate total cost using the formula. TC = (AFC+AVC) X Q

At an output of 400 units per month, AFC is £2.50 and AVC is £1.50.

Therefore TC = (£2.50 + £1.50) x 400 = £4.00 x 400 = £1600

Average Total Cost (ATC) can be found by using the formula ATC = TC / Q or by the formula ATC = AFC + AVC

Using either formula at an output of 200 units per month, ATC is £7.00 per unit and at an output of 400 per month it is £4.00 per unit. (check this yourself using both methods)

Marginal Cost (MC) is the change in total costs when output is increased by one unit. It is calculated by the formula: MC = ΔTC / ΔQ

For instance, if output increased from 200 to 400, total cost rises from £1400 to £1600, so: MC = £200/200 = £1.00

## Diminishing Returns

One of the fundamental principles of economics is that of diminishing returns. In the short run we can only raise output by combining increasing quantities of variable factors (labour/materials) with a given quantity of fixed factors (capital/land).

Consider a simple example of a farm growing wheat, where land is the only fixed factor and labour is the only variable factor. If only one worker is employed, he will have to do all the tasks himself (weeding, ploughing, sowing etc) and will not be able to specialise in a task he is best suited to. It may not even be possible to cultivate all the land on the farm. The fixed factor is being under-utilised.

If a second worker is employed it is likely that the harvest of wheat will be more than double when only one worker is employed as they can work more efficiently by specialising in tasks they are good at.

We would say therefore that the return (extra output) to the variable factor is increasing. But beyond a certain number of workers, the extra output from employing an additional worker will start to fall. Total output will still be rising, but more slowly. This is what is meant by diminishing returns. There is some optimum balance between the number of workers and the plot of land available. Beyond this point the fixed factor is being over-utilised; the land is being worked too hard and additional workers can’t achieve much more output.

We can show these relationships in Table 1 below:

 Number of Workers Total Product (tonnes) Marginal Product (tonnes per worker) Average Product (tonnes per worker) 1 4 4 4 2 10 6 5 3 18 8 6 4 23 5 5.75 5 27 4 5.4 6 30 2 5 7 30 0 4.3 8 28 -2 3.5

Total Product (TP) is the total output when any given number of units of variable factors is employed.

Marginal Product (MP) is the change in output when one more unit of variable factors is employed (in this case one more worker). It can be calculated using the formula: MP = ΔTP/Δ no of workers (NB Marginal Product can be negative)

Average Product (AP) is the average output per unit of variable factors employed (in this case output per worker). It can be calculated using the formula: MP = TP/no of workers

The data in Table 1 is shown in Fig 1 below: The following points can be seen from the diagram and should be noted:

AP and MP initially rise and thereafter fall as more workers are employed.

MP is equal to AP when AP is at a maximum.

TP falls when MP is negative.

## Short Run Cost Curves

Let’s assume:

that the farmer pays annual rent of £200, and this is his only fixed cost.

All workers are paid £100 per year (and labour is the only variable cost)

Combining this cost data with the data from Table 1, we can derive the figures for AFC, AVC, ATC and MC, which are shown in Table 2 below:

 Number of Workers TP (tonnes) MP (tonnes/worker) AP (tonnes/worker) TFC (£) TVC (£) TC (£) AFC (£ per unit) AVC (£) ATC (£) MC (£) 1 4 4 4 100 100 200 25 25 50 25 2 10 6 5 100 200 300 10 20 30 16.7 3 18 8 6 100 300 400 5.5 16.7 22.2 12.5 4 23 5 5.75 100 400 500 4.3 17.4 21.7 20 5 27 4 5.4 100 500 600 3.7 18.5 22.2 25 6 30 2 5 100 600 700 3.3 20 23.3 50 7 30 0 4.3 100 700 800 3.3 23.3 26.6 * 8 28 -2 3.5 100 800 900 3.6 28.6 32.2 *

* When more than 6 workers are employed there is no further increase in output (MP becomes negative), so the farmer will not be willing to employ more than 6 workers. His costs would increase while output is falling, so it would reduce his profit.

We can plot the data from Table 1 to derive the cost curves for AFC, AVC, ATC and MC. These are shown in Fig 2 below: The following points can be seen from the diagram and should be noted:

1. AFC falls continuously as output increases
2. MC initially falls then rises. This is because MP initially rises then falls. Diminishing marginal returns causes the marginal cost of additional units to rise.
3. When MC is below AVC, AVC is falling. When MC is above AVC, AVC is rising. When MC is equal to AVC (where they cross), AVC is at its minimum.
4. AVC and ATC are both U shaped curves.
5. ATC falls faster than AVC and rises more slowly. This is because AFC is continuously falling as output increases. But the rate at which AFC falls slows down, so the difference between AVC and ATC gets smaller as output increases.
6. MC also equals ATC when ATC is at its minimum.

We can also plot the data for TFC, TVC and TC on a graph. This is shown in Fig 3 below, The following points can be seen from the diagram and should be noted:

1. TFC is a horizontal straight line. This is because TFC does not vary with output.
2. TVC initially rises at a decreasing rate (the curve is flattening off). This is because MC is falling. But when M starts to rise, TVC increases at an accelerating rate, so the curve gets steeper.
3. TVC is zero when output is zero, but TC=TFC when output is zero.
4. TVC and TC are parallel to each other. This is because the difference between them (TFC) is always the same.

## Long Run Costs

Short run costs per unit eventually start to rise because of diminishing returns. A factory that is operating close to its maximum output can squeeze a little more output by working its machines an employees more intensively (eg more overtime hours), but tired workers will be less productive and machines more likely to break down.

Remember that in the short run, a firm cannot increase (or reduce) its quantity of fixed factors. But in the long run it can acquire more (or less) land, buildings and machines. So if a firm wants to increase output AND reduce its costs per unit, it can do so by increasing the scale of production.

Explain in a paragraph why costs per unit initially fall and then rise as output increases.
Your answer should include: Average Product / Marginal Product / Diminishing Returns / Marginal Cost / Average Variable Cost / Average Total Cost