Drawing cost curves

Economists like to split costs into two main types:

A fixed cost is a cost that is fixed with respect to changes in output.

A variable cost is one that varies with respect to output.

When the writer Alan Bennett offered to make a cup of coffee for Miss Shepherd (a lady who lived in a van in his garden) she said, “I don’t want to put you out, just half a cup”.

This is funny because the bulk of the costs of making coffee are fixed (i.e. boiling the kettle, spooning in the coffee granules, adding sugar, adding milk, stirring). Whether you’re making a half a cup, or a full cup, doesn’t matter much. The variable costs are pretty low, and so her offer to reduce them is comical.

This chart shows an example of how fixed costs remain constant with respect to output, while variable costs increase.

We’re now going to look at a series of short (and relatively fun) videos which explain the shape of cost curves:

This phenomenon is known as the law of diminishing marginal returns (DMR), and states that as more and more units of a variable resource (in this case labour) are combined with a fixed number of another resources (capital), then using additional units of the variable resource will eventually increase output at a decreasing rate. At such a point (the point of diminishing returns) it takes successively larger amounts of the variable factor to expand output by one unit. Or, to put it more simply, as you expand output marginal productivity (the extra output that you get for extra input) will eventually decline.

If the marginal cost (MC) is lower than the average cost (AC), then AC must fall. If a student’s grade is below their average, then it brings the average down. Diminishing returns mean that eventually marginal costs will begin to rise, so eventually average costs will.

In this video, I apply the concepts discussed to the probation service:

If we treat fixed costs as being sunk (at least in the short term), it means that we should ignore them. If a cost is sunk, it has no opportunity cost, and is therefore irrelevant to decision-making. If you can’t affect something, and it will occur in any scenario, it can’t help you choose between scenarios. Therefore it is variable costs that should be the focus of attention, or, more accurately, the relationship between revenue and variable costs. The shutdown condition states that a business unit should be open provided it can cover its variable costs. According to the shutdown condition, fixed costs are not relevant to the decision about whether to be open for business or not. Ultimately, you need to cover total costs. And if you can’t, you should sell up the business or liquidate the assets. But in the short run, when you are deciding about whether to open or not, the only hurdle you need to meet is variable costs. If you expect to generate enough revenue to cover those, you’re in business.

My favourite example of the importance of an intuitive understanding of your cost curves is Mr Morita:

So far we’ve established that:

  • As output increases average fixed costs will fall (you are dividing a fixed numerator by a steadily increasing denominator).
  • The variable input (in our case labour) will exhibit increasing returns to scale over a certain range of output, putting downward pressure on average costs.
  • But at some point diminishing returns will kick in, putting upward pressure on average costs.

What this means is that an average cost curve will always be a “U” shape. It may be shallow, it may be steep. It may bottom out at a low level of output, or a high level. But diminishing returns will mean that it will always be a “U” shape.