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Theory of Cost

Short Run Average Costs

While the total cost of production helps firms understand the overall expenses incurred, the average costs help identify the expenditures involved in manufacturing a single unit. In this article, we will look at the short run average costs and marginal costs of production.

Short Run Average Costs

1. Average Fixed Cost (AFC)

The average fixed cost is the total fixed cost divided by the number of units produced. Hence, if TFC is the total fixed cost and Q is the number of units produced, then

$$AFC = \frac {TFC}{Q}$$

Therefore,  AFC is the fixed cost per unit of output.

Example: The TFC of a firm is Rs. 2,000. If the output is 100 units, the average fixed cost is,

$$AFC = \frac {TFC}{Q} = \frac {2000}{100} = Rs. 20$$

If the output is increased to 200 units, then

$$AFC =\frac {TFC}{Q} = \frac {2000}{200}= Rs. 10$$

Since TFC is constant, any increase in output decreases the AFC. Note that, while the AFC can become really small, it is never zero.

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2. Average Variable Cost (AVC)

The second aspect of short-run average costs is an average variable cost. Average variable cost is the total variable cost divided by the number of units produced. Hence, if TVC is the total fixed cost and Q is the number of units produced, then

$$AVC =\frac {TVC}{Q}$$

Therefore, AVC is the variable cost per unit of output.

Usually, the AVC falls as the output increases from zero to normal capacity output. Beyond the normal capacity, the AVC rises steeply due to the operation of diminishing returns.

3. Average Total Cost (ATC)

The average total cost is the sum of the average variable cost and the average fixed costs. That is,

ATC = AFC + AVC

In other words, it is the total cost divided by the number of units produced.

The diagram below shows the AFC, AVC, ATC, and Marginal Costs (MC) curves:

short run average costs

It is important to note that the behaviour of the ATC curve depends upon that of the AVC and AFC curves. Observe that:

  • In the beginning, both AVC and AFC curves fall. Hence, the ATC curve falls as well.
  • Next, the AVC curve starts rising, but the AFC curve is still falling. Hence, the ATC curve continues to fall. This is because, during this phase, the fall in the AFC curve is greater than the rise in the AVC curve.
  • As the output rises further, the AVC curve rises sharply. This offsets the fall in the AFC curve. Hence, the ATC curve falls initially and then rises.

Marginal Cost (MC)

Another concept to learn in short-run average costs is Marginal Cost. Marginal cost is the addition made to the cost of production by producing an additional unit of the output. In simpler words, it is the total cost of producing t units instead of t-1 units. Let’s look at an example to understand this better:

A firm produces 5 units at a total cost of Rs. 200. For some reasons, it is required to produce 6 units instead of 5 and the total cost is Rs. 250. Therefore, the marginal cost is Rs. 250 – Rs. 200 = Rs. 50.

A note about marginal costs: It is independent of fixed costs. This is because fixed costs do not change with the output. On the other hand, in the short run, the variable costs change with the output. Hence, marginal costs are due to changes in variable costs. Therefore,

$$MC = \frac {ΔTC}{ΔQ}$$ … where ΔTC is the change in the total cost and ΔQ is the change in the output. This equation can also be written as:

MCn = TCn – TCn-1

In the Fig. 1 above, you can see that the MC curve falls as the output increases in the beginning and starts rising after a certain level of the output. This is because of the influence of the law of variable proportions. Since the marginal product rises first, reaches a maximum and then declines, the marginal costs decline first, reaches its minimum and then rises.

The following table outlines the behaviour of all these costs:

Units of output Total fixed cost Total variable cost Total Cost Average fixed cost Average variable cost Average total cost Marginal cost
0 150 0 150
6 150 50 200 25.0 8.33 33.33 50/6 = 8.33
16 150 100 250 9.38 6.25 15.63 50/10 = 5.0
29 150 150 300 5.17 5.17 10.34 50/13 = 3.85
44 150 200 350 3.41 4.55 7.95 50/15 = 3.33
55 150 250 400 2.73 4.55 7.27 50/11 = 4.55
60 150 300 450 2.50 5.0 7.50 50/5 = 10.0

From the table, we can make the following observations:

  • Since the fixed cost does not change with the output, the average fixed cost decreases as the output increases.
  • The average variable cost does not always increase in proportion to an increase in the output.
  • Marginal costs also come down until 44 units are produced after which they start rising.

Relationship between Average Cost and Marginal Cost

  1. If the average cost falls due to an increase in the output, the marginal cost is less than the average cost.
  2. If the average cost rises due to an increase in the output, the marginal cost is more than the average cost.
  3. Marginal cost is equal to the average cost when the marginal cost is minimum. You can see in Fig. 1 that the MC curve cuts the ATC curve at its minimum or optimum point.

Solved Question on Short Run Average Costs

Q1. Which of the following statements is true of the relationship between the average cost functions in short run average costs?

  1. ATC = AFC – AVC.
  2. AVC = AFC + ATC.
  3. AFC = ATC + AVC.
  4. AFC = ATC – AVC.

Answer: By the definition of the Average Total Cost (ATC), we know that

ATC = AFC + AVC

Therefore, from the options given above, option d is the current answer. That is,

AFC = ATC – AVC

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OLAYINKA BABAITA

I love this

patience
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patience

i like this indeed

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Akash

pls provied brief theory on theory of cost for ugc net

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