# Costs and their Curves

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## Costs and their Curves

Before we look at the cost curves in detail, we need to start with a few definitions.

Although we will be looking at the costs of a firm in terms of wages, raw materials, etc., economists like to start with a more abstract term. What does an economist mean by the economic cost of production? This is the opportunity cost of production. As you have probably read in more textbooks than you care to remember, this is the value that could have been generated had the resources been employed in their next best use. Remember that this concept of opportunity cost is useful when dealing with production possibility frontiers.

It is also important that you understand the difference between fixed cost and variable costs. Fixed costs are those that do not vary as output increases. Examples include rent, office costs and, certainly in the short run, machinery.

Variable costs, surprise surprise, are costs that do vary as output increases. The best example is raw materials. If a firm wants to make more chocolate, for example, it will need more cocoa beans and sugar.

Labour is also a variable cost, but some textbooks refer to it as semi-variable. Many firms have a fairly permanent staff. If they need to increase output, the workers will be asked to do overtime. In a sense, this is still variable, because the number of man-hours worked will still rise, but the actual number of workers may not. Of course, if a firm is planning some serious expansion, the actual number of workers employed will eventually rise, but employers are nervous about employing someone permanently who may not be required in the long term. The cost of letting a permanent member of staff go can be much higher than sacking a part-time or contract worker.

#### Total, marginal and average costs

As with total, marginal and average product in the last Learn-It, we first need to define total, average and marginal cost.

Total cost (TC). This is the total cost to the firm of producing a given number of units. This can be sub-divided. Total cost = total fixed costs + total variable costs (or TC = TFC + TVC). A cost is either fixed or variable. There is no third group. If a cost is not fixed, then, by definition, it must vary with output.

Average cost (AC). This is the cost, on average, per unit of output produced. If a firm made 100 bars of chocolate at a total cost of £10, then the cost, on average, per bar of chocolate produced, is 10p. So, algebraically:

It also follows that average cost = average fixed cost + average variable cost (AC = AFC + AVC). This is derived by simply dividing both sides of the total cost equation by Q. Average cost is often called average total cost so as to distinguish it from AFC and AVC.

Marginal cost (MC). This is the additional cost incurred by a firm as a result of producing one more unit of output. It is the extra cost at the margin (i.e. by producing the marginal unit of output).

#### Why the marginal curve cuts the average curves where they are momentarily flat

Imagine you are with a group of friends, waiting at the bus stop in anticipation of a great Friday night out. You all decide to check that you have enough money for the frivolities that lie ahead.

There are nine of you and, coincidentally, you all have exactly £20 each. This means that the average amount of money that each of you holds is also £20.

Your tenth friend is late, but finally arrives. He only has £10 on him. This means that between you the total amount of money is £190, and the new average is £190 divided by 10, which is £19. The arrival of your tenth friend has reduced the average because the amount he added to the total, the marginal, was less than the prevailing average.

If your tenth friend had had £30 on him, the new total would have been £210, and the new average would have been £210 divided by 10, which is £21. The arrival of your tenth friend would have increased the average because the amount he added to the total, the marginal, was more than the prevailing average.

If your tenth friend had also exactly £20 on him, then the average would have remained unchanged; £200 divided by 10 is still £20.

This is exactly what is going on with the average and marginal cost curves. When the marginal curve is above the average curve, then the average is rising. When the marginal curve is below the average curve, then the average is falling. When the marginal is the same as the average (which is where they cross) then the average remains the same.

The issue is not whether the marginal is rising or falling, but whether it is above or below the average curve. In the diagram, you can see that the marginal cost curve falls to start with and then begins to rise, but the average cost curve only starts to rise when the marginal cost curve rises above the average curve in question.

#### How the cost curves are derived

It is important to understand why the cost curves look like they do. The concept of Diminishing marginal Returns is the one from which we derive the cost curves. Look at the two diagrams below.

The top diagram shows a sketch of the marginal cost curve and the average cost curve. The average variable cost curve has been left out to make the diagram easier to follow, but the following statement applies to the latter as well. After all, the shape of the average cost curve is derived directly from the shape of the average variable cost curve. The only variable part of total cost is the variable cost.

The bottom diagram shows a sketch of the marginal product curve and the average product curve (go back to The law of diminishing marginal returns Learn-It if you need a reminder of where they come from).

Can you see any link between the two sets of curves? Can you see that one is the reflection of the other? This is not a coincidence.

Let us assume that each additional worker is paid the same wage, say £20 a day. Also, we shall continue to assume that the only two factors of production in use are capital, which is fixed (as we are still in the short run), and labour, which can vary.

At point A on the bottom diagram, we have a situation where each worker adds more to total output than the last. But each worker is paid the same wage, so each marginal unit that this new worker produces will cost less, on average, than the units produced by the last worker (given that we are assuming that the only variable cost is labour). Hence, the marginal cost curve must be falling (see point B on the top diagram).

At point B on the bottom diagram, we have a situation where each worker adds the same amount to total output than the last. Each worker is paid the same wage, so each marginal unit that this new worker produces will cost the same, on average, than the units produced by the last worker. Hence, the marginal cost curve must be constant, or flat (see point B on the top diagram).

At point C on the bottom diagram, we have a situation where each worker adds fewer units to total output than the last (diminishing marginal returns have set in). But each worker is still paid the same wage, so each marginal unit that this new worker produces will cost more, on average, than the units produced by the last worker. Hence, the marginal cost curve must be rising (see point C on the top diagram).

So the marginal cost and average cost curves come from the product curves, which are, in turn, derived from the law of diminishing marginal returns. The average variable cost curve comes from the product curves in exactly the same way.