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# Worked Example of Costs and their Curves

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## Worked Example of Costs and their Curves

As with the last Learn-It, it is worth looking at these relationships in more detail. Look at this table below. Q is output per week for a firm making computer laser printers. The cost figures are all in pounds and rounded to the nearest pound.

Q | TFC | TVC | AFC | AVC | TC | AC | MC |
---|---|---|---|---|---|---|---|

0 | 500 | 0 | - | - | 500 | - | - |

1 | 500 | 100 | 500 | 100 | 600 | 600 | 100 |

2 | 500 | 180 | 250 | 90 | 680 | 340 | 80 |

3 | 500 | 250 | 167 | 83 | 750 | 250 | 70 |

4 | 500 | 310 | 125 | 78 | 810 | 202 | 60 |

5 | 500 | 380 | 100 | 76 | 880 | 176 | 70 |

6 | 500 | 470 | 83 | 78 | 970 | 162 | 90 |

7 | 500 | 580 | 71 | 83 | 1080 | 154 | 110 |

8 | 500 | 730 | 63 | 91 | 1230 | 154 | 150 |

9 | 500 | 930 | 56 | 103 | 1430 | 159 | 200 |

The first column shows the progressive units of output produced.

The second column shows **total fixed costs**. Notice that this figure stays the same (500) for every level of output. Remember that fixed costs **do not** vary with output.

The third column shows **total variable costs**. The figure is always rising but does so at slightly different rates. The rate of increase slows down a little in the middle and then picks up again towards the end (see the diagram below).

The fourth column shows **average fixed costs**. This was calculated by dividing total fixed costs by output (Q).

The fifth column shows **average variable costs**. This was calculated by dividing total variable costs by output (Q).

The sixth column shows **total cost**. This is calculated by adding TFC and TVC together.

The seventh column shows **average cost** (often called **average total cost**). This is the average of the total cost, so we divide total cost by output (Q). You could also work it out by adding AFC and AVC. In the example above this doesn't always work because the numbers have been rounded to the nearest pound.

The final column shows **marginal cost**. As with marginal product, this can be calculated by finding the difference between the total cost of producing the given number of units and the total cost of producing one less unit of output. For instance, to find the marginal cost of the fifth unit of output, you take the total cost of producing five units and subtract the total cost of producing four units. Algebraically: MC_{5} = TC_{5} − TC_{4} = 880 − 810 = 70.

Now try and work out the answers to the table below. Click on the relevant sections in the table to reveal the answers. Remember that all the numbers should be rounded up or down to the nearest pound, so you might need a calculator.

Here are the relevant curves. They have been plotted using the figures from the **first** table; not the one you have just filled in.

Both diagrams have four lines on them; the three average curves and the marginal cost curve.

On the top one, the lines have been plotted from the figures in the initial cost table for the firm making computer laser printers. They look a bit odd, but there are some key points to pick up.

First, the average fixed cost curve is continually falling, albeit at a slower rate towards the end. This makes sense, because a fixed number (in this case 500) is being divided by an ever-increasing number (i.e. output).

Secondly, the two average curves start fairly high, fall, and then rise again. This is due to the fact that initially the totals are being divided by very small numbers, giving large averages. The reason why the curves turn, will be explained shortly under 'How the cost curves are derived'

Finally, and most importantly, the marginal cost curve cuts the average cost **and** average variable cost curves at their minimum points, where they are temporarily flat. The reason for this is **exactly the same** as the reason why the marginal product curve cut the average product curve at the maximum. It is worth going through this again to save you looking back at the last Learn-It, the explanation can be found just after the next diagram.

The bottom diagram (of the two above) shows **sketches** of the four curves. Although you can see that they are not totally accurate, they do have the same characteristic as the actual curves, and they are **much** easier to deal with for analysis purposes, as you will see in the topic on '**Market structure**'. Notice that the MC still cuts the AC and AVC at their minimum and the AFC is continually downward sloping.

This diagram shows the three 'total' curves. There are a couple of points to note here.

First, the TFC curve is flat. This is to be expected because fixed costs remain constant.

Secondly, the TC and TVC curves are parallel. This is because the difference between the two is the fixed cost, which is constant. This means that every point on the TVC curve simply shifts up by 500.

Finally, the TC and TFC curve both start on the y-axis at 500, to represent the fixed cost. The TVC curve does not exist until Q = 1. Remember, there are no variable costs until something is actually produced!