costs and their curves

BTEC HND IN BIT Business Environment

Costs and their CurvesBefore 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:

1Mrs. Ramziya Begam BBM, MBA in Finance (India)


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.



Worked Example of Costs and their CurvesAs 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 MC0 500 0 - - 500 - -1 500 100 500 100 6002 500 180 250 90 6803 500 250 167 83 7504 500 310 125 78 8105 500 380 100 76 8806 500 470 83 78 9707 500 580 71 83 10808 500 730 63 91 12309 500 930 56 103 1430

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



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!

Revenues and their Curves

First, we need to define revenue. The revenue of a firm constitutes the receipts of money from the sale of goods and services over a given time period. Some textbooks also refer to the revenue of a firm as its turnover.

Many students confuse revenue with profit (see the next Learn-It). It is easy to mistakenly talk about revenue as the amount of money that the firm 'makes'. The amount of money that a firm 'makes' is the profit; it is the amount of money left after costs are taken away from revenue.

Total, marginal and average revenues

Now we need to look at specifics: total, average and marginal revenue.

Total revenue (TR). This is the total receipts of money received by a firm from the sale of its good or service in a given time period. It can be calculated by multiplying the quantity sold by the price at which the goods were sold, or TR = P × Q.

Average revenue (AR). This is the amount of money received, on average, for each good sold. If you think about it, this is effectively the price.

We know that TR = P × Q, so we can substitute this into the equation above:

Marginal revenue (MR). Marginal cost is the cost of producing one more unit of output. Marginal revenue is the revenue received from selling one more unit of output. It is the extra revenue at the margin (i.e. by selling the marginal unit of output).



As with the Learn-It on costs, it is worth looking at these relationships in more detail. Look at the table below. Q, which was output in the cost table, now represents sales for our laser printer firm. All revenue figures are in pounds.

Sales (Q) Average revenue (AR) Total revenue (TR) Marginal revenue (MR)1 3002 2803 2604 2405 2206 2007 1808 1609 14010 120

The first column shows the progressive units of output sold.

The second column shows average revenue. Notice that this figure falls as the quantity sold (or demanded) rises. Remember also that AR = price. So in essence as the price falls, demand rises. As you will see when we draw the diagrams in the next sub-section, the AR curve is the demand curve!

The third column shows total revenue. As we said earlier, TR = P × Q. So the figures in this column were calculated by multiplying the number in the first column (Q) by the corresponding number in the second column (P). So, TR = Q × AR.

The final column shows marginal revenue. Using the same method as we did for marginal cost and marginal product, the marginal revenue for, say, the seventh good sold is the difference between the total revenue received from selling 7 units and the total revenue received from selling 6 units. Algebraically, MR7 = TR7 − TR6 = 1260 − 1200 = 60.

Now try and work out the answers to the table below. Click on the relevant sections in the table to reveal the answers.



The total, marginal and average revenue curves

In the last section, an important fact was revealed. The AR curve is, in fact, the firm's demand curve. Demand curves tell you how much of a good is demanded at any given price. But they can also tell you the price for a given level of demand. So if the AR curve is the price curve, then it must also be the demand curve.

In the topic called 'Market structure', you will see that firms in most market structures have 'normal' downward sloping demand curves. In the unique market structure of perfect competition, firms have a horizontal, or perfectly elastic demand curve. There are two sets of diagrams below. The first set looks at the case where the firm in question has a downward sloping demand (AR) curve. The second set looks at the more unusual case where the demand (AR) curve is perfectly elastic.

When the AR curve is a 'normal' downward sloping demand curve

ProfitDifferent definitions

We said earlier that profit was the money a firm has left over after its costs are taken away from its revenues. So total profit = total revenue - total cost (TR − TC).

It is also worth noting that profit per unit can be calculated by subtracting average cost from average revenue (AR − AC). This leaves average profit, which is profit per unit. Of course, once you have average profit, you can work out total profit; simply multiply by the number of units sold (or output, Q).

The Law of Diminishing Marginal ReturnsAlthough this topic is called 'Costs and revenues', it is important that we look at the law of diminishing marginal returns first because it is from this law that the cost curves are derived. To start with, we need to define a few terms.

Total, average and marginal product

Before commencing the bulk of the topic, it is important to make a few assumptions. The following analysis applies to the short run only. The short run is defined as the period of time where at least one factor of production is fixed. Only in the long run can we assume that the amount of capital (e.g. machines) can vary.



For simplicity, we will only be dealing with capital and labour, and ignoring the other two factors of production; land and the entrepreneur. So, in the short run, we will assume that capital is fixed, but the firm can vary the amount of labour used.

Now we need to define the terms that we will be using.

Total product This is the quantity of output produced by a given number of workers over a given period of time. Remember the amount of capital (or machines) is fixed.

Average productThis is the quantity of output per unit of input. In this model, the input is labour. In other words, we are dealing with the output per worker, on average.

Marginal productThe addition to total output produced by one extra unit of input (again, labour). It is the extra output produced at the margin (i.e. by adding a marginal unit of labour).

At this point it is worth looking at the relationship between the total, average and the marginal in more detail. It will come up again when we look at costs and then revenues, so it is important that you understand it fully.

Look at the table below. Let us assume that the firm in question is making computer laser printers and they have four machines in the factory (capital = 4).

Capital Labour (L) Marginal product (MP) Total product (TP) Average product (AP)4 0 - 0 -4 1 5 5 5.04 2 8 13 6.54 3 10 23 7.74 4 11 34 8.54 5 10 44 8.84 6 7 51 8.54 7 4 55 7.94 8 1 56 7.04 9 -2 54 6.0

Remember that capital is fixed in the short run. I have assumed that capital is fixed at 4 units (or machines, in this case).

The second column shows the progressive addition of units of labour.



Notice that the point at which diminishing marginal returns sets in is to the left of the point where diminishing average returns begins. Also, the total product keeps rising even though the marginal, and the average, product is falling. This is not hard to understand. Just because the marginal product is falling, it is still positive. Hence, these extra workers may well be adding less than previous workers, but they are still contributing to the grand total. Total product keeps rising, albeit at a diminishing rate. It is only when the marginal product is negative, with the addition of the ninth worker that total product starts to fall.

Finally, notice that the marginal product curve cuts the average product curve at its highest point, where it is momentarily flat. It is important that you understand why this happens because this concept is applied to the cost and revenue curves. I think it deserves its own little section:


costs and their curves

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