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BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

Subject BUSINESS ECONOMICS

Paper No and Title 1, Microeconomic Analysis

Module No and Title 13, Short Run Theory of Costs

Module Tag BSE_P1_M

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

1. Learning Outcomes

2. Introduction

3. Cost as opportunity cost

4. Different measures of short run costs

4 Total Cost (TC)

4.1 Total Fixed Cost (TFC)

4.1 Total Variable Cost (TVC)

4 Average total Cost (ATC)

4.2 Average Fixed Cost (AFC)

4.2 Average Variable Cost (AVC)

4 Marginal Cost (MC)

5. Relationship between ATC, AVC and MC

5 Relationship between AVC and MC

5 Relationship between ATC and MC

6. Why we need cost

6 Why we need AVC and ATC in short run?

6 Why we need MC?

7. Cost estimation

7. Problems in measuring costs

7 Simple Regression Technique

8. Mathematical example

9. Summary

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

the resources would earn in an alternate use. E., if a firm uses its own land, it does not have to pay any rent on it; the rent this land could have earned had it been rented out is its imputed or implicit cost to the firm.

Economists and accountants treat costs differently. Economists are concerned about economic profits which equal total revenue minus total cost (where total cost includes explicit costs plus implicit costs). On the other hand, accountants worry about accounting profits which equal total Revenue minus explicit costs.

4. Different measures of short run costs

There are many measures of costs of production in the short run that are helpful in taking production and pricing decisions. These measures are:

4 Total Cost (TC)

Total cost is the cost incurred on producing a particular good or service. Total cost is the sum total of fixed and variable costs.

𝑻𝒐𝒕𝒂𝒍 𝑪𝒐𝒔𝒕 (𝑻𝑪) = 𝑻𝒐𝒕𝒂𝒍 𝒇𝒊𝒙𝒆𝒅 𝒄𝒐𝒔𝒕(𝑻𝑭𝑪) + 𝑻𝒐𝒕𝒂𝒍 𝒗𝒂𝒓𝒊𝒂𝒃𝒍𝒆 𝒄𝒐𝒔𝒕(𝑻𝑽𝑪)

4.1 Total Fixed cost (TFC)

It is the cost incurred on fixed factors of production. Recall, fixed factors are those factors of production that cannot be altered or changed in a short span of time in order to increase or decrease production.

4.1 Total variable cost (TVC)

This is the cost incurred on variable inputs. Variable inputs are defined as factors of production that can be altered or changed in a short span of time to increase or decrease the level of production.

4 Average Total Cost (ATC)

Average total cost is the per unit cost of a commodity. Average total cost is the sum total of the average fixed costs and average variable costs.

𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑻𝒐𝒕𝒂𝒍 𝑪𝒐𝒔𝒕 (𝑨𝑻𝑪) = 𝑻𝒐𝒕𝒂𝒍 𝑪𝒐𝒔𝒕(𝑻𝑪)

𝑸𝒖𝒂𝒏𝒕𝒊𝒕𝒚

=

𝑻𝑭𝑪

𝑸𝒖𝒂𝒏𝒕𝒊𝒕𝒚

+

𝑻𝑽𝑪

𝑸𝒖𝒂𝒏𝒕𝒊𝒕𝒚

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

𝑨𝑻𝑪 = 𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝒇𝒊𝒙𝒆𝒅 𝒄𝒐𝒔𝒕(𝑨𝑭𝑪) + 𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝒗𝒂𝒓𝒊𝒂𝒃𝒍𝒆 𝒄𝒐𝒔𝒕(𝑨𝑽𝑪)

Average total cost can be calculated by dividing the total cost by total quantity produced or by adding average fixed cost and average variable cost.

4.2 Average Fixed cost (AFC)

It is the fixed cost per unit of output.

𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑭𝒊𝒙𝒆𝒅 𝑪𝒐𝒔𝒕 (𝑨𝑭𝑪) = 𝑻𝒐𝒕𝒂𝒍 𝑭𝒊𝒙𝒆𝒅 𝑪𝒐𝒔𝒕 (𝑻𝑭𝑪)

𝑸𝒖𝒂𝒏𝒕𝒊𝒕𝒚

Average fixed cost is calculated by dividing total fixed cost by the quantity produced.

4.2 Average variable cost (AVC)

It is the variable cost per unit of output.

𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑽𝒂𝒓𝒊𝒂𝒃𝒍 𝑪𝒐𝒔𝒕 (𝑨𝑽𝑪) = 𝑻𝒐𝒕𝒂𝒍 𝑽𝒂𝒓𝒊𝒃𝒍𝒆 𝑪𝒐𝒔𝒕(𝑻𝑽𝑪)

𝑸𝒖𝒂𝒏𝒕𝒊𝒕𝒚

Average variable cost is calculated by dividing total variable cost by the quantity produced.

4 Marginal Cost (MC)

Marginal cost is defined as the change in the total cost when one more unit of the product is produced.

𝑴𝒂𝒓𝒈𝒊𝒏𝒂𝒍 𝒄𝒐𝒔𝒕 (𝑴𝑪) =

∆𝑻𝑪

∆𝑸𝒖𝒂𝒏𝒕𝒊𝒕𝒚

= ∆𝑻𝑭𝑪

∆𝑸

+ ∆𝑻𝑽𝑪

∆𝑸

= ∆𝑻𝑽𝑪

∆𝑸

The above formula for MC shows that it can be calculated by dividing the change in the total cost (∆𝑻𝑪) by one unit change in the quantity produced (∆𝑸). Alternatively marginal cost can be calculated by taking the ratio of the change in the TVC (∆𝑻𝑽𝑪) to unit change in quantity (∆𝑸) as, by definition, change in TFC is zero (in the short run fixed inputs and hence fixed costs remain unchanged). Mathematically MC can be calculated by taking the first order derivative of the TC or TVC with respect to quantity.

To better understand all the measures of short run costs let's do a numerical exercise. Following is the data of a firm that produces milk.

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

Figure1: TC, TFC, TVC

Figure 1 represents the shapes of the Total Cost (TC), Total Variable Cost (TVC) and Total Fixed Cost(TFC) curves. TFC is horizontal to the x-axis, as TFC does not change with changes in the level of output. TVC and TC have similar S-shapes. To show the shapes of the TC and TVC the above figure is divided into two sections. The first section represents increasing returns to the variable factor, meaning that if the variable inputs are increased, output increases at a faster rate in this zone. The second section represents diminishing returns to the variable factor, which means if variable inputs are increased further, the output increases at a slower rate in this zone. Up to 5000 liter of milk production, diminishing returns do not set in and there is increasing returns to the variable factor, hence the shape of TC and TVC is concave up to this point. Beyond 5000 liters of milk production, the shape of TC and TVC is convex and the curves are upward rising as diminishing returns to the variable factor starts to dominate.

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

Figure2: Average Fixed Cost

As output increases average fixed costs decline throughout. This has been shown in Figure 2. The reason behind the inverse relation between AFC and output is that, fixed costs always remains constant in the short run and does not change with the level of production; so if output increases the ratio of TFC to output will decline.

Figure3: Average Variable Cost

Figure 3 represents the shape of the average variable cost curve. The AVC is U shaped and the reason for this is the law of diminishing marginal returns. As long as increasing returns to the variable factor prevails this curve is downward sloping and when the diminishing returns starts to

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

Figure 5: Marginal Cost Curve

Figure 5 shows the behavior of marginal cost when output is increased. First it declines and then increases with an increase in output. The marginal cost curve is also U shaped and once again, the explanation for its shape runs in terms of the law of diminishing marginal returns.

5. Relationship between ATC, AVC and MC

Figure 6 shows the relation between Average Variable Cost (AVC), Average Total Cost (ATC) and Marginal Cost (MC).

5 Relationship between AVC and MC

 If marginal cost is less than the average variable cost then average variable cost is falling.  If marginal cost is equal to the average variable cost then average variable cost is at its minimum point. i. marginal cost cuts the average variable cost curve at its minimum point.  If marginal cost is greater than average variable cost then average variable cost is rising.

5 Relationship between ATC and MC

 If marginal cost is less than the average total cost then average total cost is falling.  If marginal cost is equal to the average total cost then average total cost is at its minimum point. i. marginal cost cuts the average total cost curve at its minimum point.  If marginal cost is greater than the average total cost then average total cost is rising.

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

Figure 6: Relationship between ATC, AVC and MC

Note that the above relation between total, marginal and average magnitudes is analogous to the relation observed between total product (TP), marginal product (MP) and average product (AP) in an earlier module. Also note that the AVC and MC curves can essentially be viewed as the ‘mirror images’ of the AP and MP curves respectively. The AP curve first rises, reaches a maximum and then falls, corresponding to which, the AVC curve first falls, reaches a minimum and then rises. Similarly, the MP curve first rises, reaches a maximum and then falls and the MC curve is simply its mirror image, as it first falls, attains a minimum and then rises.

6. Why we need costs

6 Why we need AVC and ATC in short run?

In the short run, there are both fixed and variable inputs. Fixed inputs are always paid irrespective of the level of output. If average revenue (total revenue divided by output) is greater than average variable cost at a level of output it means that the fixed cost is covered at that output. So firms should continue operation and not shut down at such output levels.

6 Why we need MC?

Marginal cost is very important because the pricing decision of firms is based on marginal cost and not on average cost. In fact the optimal output of a firm is attained when marginal cost is equal to the marginal revenue.

You will learn the concepts of average and marginal revenue in subsequent modules and then the usefulness and relevance of the concepts discussed in this section will become clearer.

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

Theoretically, the wage rate (w) and interest rate(r) should reflect the opportunity cost of labour and capital. However, in reality the reported costs, based on actual payments tend to be different from the opportunity cost. This factor has to be taken into account and appropriate adjustments made while applying these concepts in real business situations.

7 Simple Regression Technique

Simple regression technique can be used to estimate short run cost functions using firm level data on costs of production and on output (e., as in Table 1). Out of AVC, TVC and MC, if we are able to estimate one of the cost functions, then we can get the other two cost functions quite easily. To estimate short run costs first we assume that the average variable cost curve is U shaped. Therefore, mathematically we define the AVC as a quadratic function as follows:

𝐴𝑉𝐶 = 𝑎 + 𝑏𝑄 + 𝑐𝑄 2

In this case we will have a U-shaped AVC function if b < 0 and c > 0.

Given the AVC function we can find the TVC as follows:

𝐴𝑉𝐶 = 𝑇𝑉𝐶

𝑄

𝑇𝑉𝐶 = 𝐴𝑉𝐶 × 𝑄

𝑇𝑉𝐶 = (𝑎 + 𝑏𝑄 + 𝑐𝑄 2 )𝑄 = 𝑎𝑄 + 𝑏𝑄 2 + 𝑐𝑄 3

This is a cubic function indicating that TVC will be a S-Shaped curve

The marginal cost curve can be derived from TVC by taking first differential of the TVC function with respect to Q (output). So the MC function can be obtained as follows:

𝑀𝐶 = 𝜕𝑇𝑉𝐶

𝜕𝑄

= 𝑎 + 2𝑏𝑄 + 3𝑐𝑄 2

So you can see that once we estimate the three unknowns a, b and c we can easily estimate AVC, ATC and MC. We can make use of the t test and F tests to test the significance of these parameters. The TC function is easy to estimate once we have the TVC function; we can simply add TFC to the TVC function to get TC function. Similarly to obtain the ATC function we can add AFC to the AVC function.

We can also obtain an estimate of the output level at which TVC is minimum or the point where the MC curve cuts the AVC curve. We know that the MC is equal to AVC at the point where the AVC curve reaches its minimum. Therefore,

𝑀𝐶 = 𝐴𝑉𝐶 𝑎 + 2𝑏𝑄 + 3𝑐𝑄 2 = 𝑎 + 𝑏𝑄 + 𝑐𝑄 2 𝑏𝑄 + 2𝑐𝑄 2 = 0

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

𝑄∗ = − 𝑏

2𝑐

Q* is the quantity at which the average variable cost will achieve its minimum.

8. Mathematical Example

Consider the following Cobb-Douglas production function that we had introduced in the earlier modules:

𝑸 = 𝟏𝟎𝟎𝑲𝟏/𝟐𝑳𝟏/𝟐

Assume that Capital (K) is a fixed input and Labour (L) is a variable input; also assume capital is fixed at 4 units irrespective of the level of output and the prices of capital (r) and Labour (w) are given as Rs. 4 and Rs. 1 respectively.

𝑻𝒐𝒕𝒂𝒍 𝑪𝒐𝒔𝒕 = 𝑻𝒐𝒕𝒂𝒍 𝑭𝒊𝒙𝒆𝒅 𝑪𝒐𝒔𝒕 + 𝑻𝒐𝒕𝒂𝒍 𝑽𝒂𝒓𝒊𝒂𝒃𝒍𝒆 𝑪𝒐𝒔𝒕 = 𝑷 ̅̅̅𝑳̅ 𝑳 + 𝑷 ̅̅̅𝑲̅ 𝑲̅

TC= L+4(4) (i)

𝑸 = (𝟏𝟎𝟎)𝟒𝟏/𝟐𝑳𝟏/𝟐= 2𝟎𝟎𝑳𝟏/𝟐

𝑳

𝟏 𝟐 =

𝑸

𝟐𝟎𝟎 𝑳 =

𝑸𝟐 𝟒𝟎𝟎𝟎𝟎 (ii)

Substituting (ii) in (i) we get the short run total cost function as follows :

𝑻𝑪 =

𝑸𝟐

𝟒𝟎𝟎𝟎𝟎

+ 𝟏𝟔

Thus short run marginal cost function is given by :

𝑴𝑪 = 𝝏𝑻𝑪

𝝏𝑸

=

𝑸

𝟐𝟎𝟎𝟎𝟎

= 𝟎. 𝟎𝟎𝟎𝟎𝟓𝑸

Short run average cost function is given by :

𝑨𝑪 = 𝑻𝑪

𝑸

=

𝑸

𝟒𝟎𝟎𝟎𝟎

+ 𝟏𝟔

𝑸

We can prove that MC will cut the AC at its minimum point; in other words, at the minimum point of the average cost curve, marginal cost is equal to average cost. To find the output level at

BUSINESS

PAPER NO.: 1, MICROECONOMIC ANALYSIS

9. Summary

 Costs are a very important element in production and supply decisions. With a given level of output entrepreneurs tries to minimize their cost, so that they can maximize their profits.  Broadly costs are of two types explicit and implicit. Accountants do not measure implicit costs whereas economists consider both explicit and implicit costs in decision making. This may cause a problem in estimation of true economic costs.  The various measures of short run cost are TC, TVC, TFC, ATC, AVC, AFC and MC.  The shape of TC and TVC is S shape. The reason behind this is the law of diminishing marginal returns.  AFC is a downward sloping curve.  The AC, AVC and MC curves are U shaped. The reason AVC is U shaped is the law of diminishing marginal returns.  MC curve cuts the AVC and AC curves at their minimum points.  Regression technique can be used to estimate the cost of production.  There are two basic problems attached to measurement of costs based on actual data. First, recorded costs may not be adjusted for inflation; and second, economic costs differ from accounting costs.

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