# 8 Main Traditional Theories of Cost-of-production

8 Main Traditional Theories of Cost-of-production are described below:

#### 1. Total Fixed Cost (TFC):

In short period, some factors are fixed, while others are variable. Cost incurred on the hexed factors like machinery, building, etc. is called fixed cost. In other words, fixed cost is the cost of employing fixed factors in the short period. Fixed cost is a ‘fixed’ amount, which must be incurred by a firm, whether the output is large, small or even zero.

Thus, fixed cost is not related to the level of output. Even when the firm closes down for some time, but remains in business, this cost has to be borne by it. Salaries of managerial and administrative staff, rent, insurance charges, property taxes, interest on capital and maintenance cost, depreciation cost due to technical obsolescence are some examples of fixed cost, which do not change with the changes in output. It is also called as sunk cost, since; the expenditure has to be incurred irrespective of the level of production.

Fixed cost is also known as indirect cost or overhead cost or supplementary cost. Fixed cost curve is a horizontal straight line parallel to X-axis (Fig. 11.1). The curve shows that the total fixed cost remains same at different levels of output, even if the output is zero.

#### 2. Total Variable Cost (TVC):

Variable cost is incurred on the employment of variable factors like raw materials, direct labour, power, fuel, transportation, sales commission, depreciation charges associated with wear and tear of assets, etc. It varies directly with output.

Cost of a factor is obtained by the product of number of physical units of the factor and its price. The variable cost is incurred only, when some amount of output is produced and it rises with the increase in the level of production and vice versa.

In other words, variable cost is incurred so long as production continues, but the moment production stops, variable cost also ceases. If a firm shuts down its business for some time, it has not to incur any expenditure on variable cost.

However, the maximum quantity of the output that can be purchased depends upon the quantity of the fixed factors of production. Marshall calls the variable cost as prime cost. It is also called direct cost, since; it varies directly with the change in the level of output. Total variable cost is graphically shown in Fig. 11.2.

Total variable cost curve starts from the origin indicating that when output is zero, variable cost is nil. Further, the variable cost has a rising trend from left to right. Variable cost initially rises at decreasing rate, then, at increasing rate corresponding to the growth of total product (TP) at increas­ing rate and decreasing rate respectively. This is clear from the comparison of the shapes of TVC and TP curves.

#### 3. Total Cost (TC):

Total cost to a producer for the various levels of output is the sum of total fixed cost and total variable cost, i.e., TC = TFC + TVC. Total cost will change with the change in the ratio of output to input. Such changes may be the result of the changes in the efficiency of conversion process or changes in the prices of inputs.

Total cost is a positively sloped curve. Like total variable cost, it has broadly an inverse ‘S’ shape. It increases with an increase in the level of output, as total cost depends very much on total variable cost, whereas total fixed cost remains constant.

Total cost curve is obtained by adding up vertically total fixed cost curve and total variable cost curve (Fig. 11.2). The shape of the total cost curve is same as that of total variable cost curve, because, the same distance (equal to fixed cost) is added to variable cost at different levels of output to get total cost.

It is clear from the Fig. 11.2 that the vertical distance between TC and TVC is constant and it represents TFC. Similarly, the vertical distance between TC and TFC is TVC, which increases with increase in the level of output.

In case variable cost varies at constant returns, when output is expanded, variable cost as well as total cost curves would be upward sloping linear curves (with constant slope)

#### 4. Average Fixed Cost (AFC):

Per unit fixed cost of producing a commodity is called the average fixed cost. It is calculated by dividing the total fixed cost by the number of units of commodity produced. Therefore,

AFC=TFC/Q

Where, ‘Q’ is the total output.

Suppose, Kapil Khurana incurs an expenditure of Rs. 20,000/- on installing a stone cutter ma­chine. If he cuts 10,000 pieces of stones during the first month of installation, the average fixed cost will be Rs. 20,000/10,000 = Rs. 2. When the number of pieces he cuts increases to 20,000, the average fixed cost falls to Rs. 1. Thus, as the level of output increases, the average fixed cost falls. It is clear from the Fig. 11.3 given below.

Total fixed cost is a constant quantity. As the output increases, the total fixed cost spreads out over more and more units and therefore average fixed cost becomes lesser and lesser. When output becomes very large, average fixed cost approaches zero. Business Executives refer to it as ‘spreading the overheads’.

It will be seen that average fixed cost (AFC) falls continuously, as more units are being produced at the same fixed expenses. AFC corresponding to any point on the TFC curve is equal to the slope of the ray from origin to that point, i.e., perpendicular (total fixed cost) divided by base (total output) or tangent of the angle made by the ray with the X-axis. Graphically, the average fixed cost curve is a downward sloping curve, since the slope of the ray from origin to any point on TFC curve decreases, as one move to the right.

It will fall steeply in the beginning and will tend to touch X-axis, but will never become zero. Similarly, AFC curve can never touch Y-axis. It is so, because, TFC is a positive value at zero output and any positive value divided by zero will provide infinite value. Thus, AFC curve approaches both the axes asymptotically.

Further, the nature of AFC curve is rectangular hyper­bola indicating that every rectangle (TFC == AFC × Q) will be equal to every other rectangle in area. When the output increases by a certain percentage, the average fixed cost decreases by the same percentage such that their product representing total fixed cost remains constant throughout.

#### 5. Average Variable Cost (AVC):

Per unit variable cost of producing a commodity is called the average variable cost. It is com­puted by dividing total variable cost by the number of units produced.

Therefore,

AVC=TVC/Q

Where, ‘Q’ is the total output.

As output rises, average variable cost falls initially due to the occurrence of increasing returns (when total variable cost rises less than proportionately to output). It is minimum at the optimum capacity of output. At this level of output, all the factors used by the firm are being employed as efficiently as possible.

Beyond the optimum capacity, the average variable cost will rise steeply because of the operation of diminishing returns (when total variable cost rises more than proportionately to output). This is illustrated in Fig. 11.4. Graphically, the average variable cost curve is U- shaped due to the operation of the law of returns.

This curve is drawn by considering the average variable cost (AVC) at each level of output derived from the slope of a ray drawn from the origin to the point on the total variable cost (TVC) corresponding to the particular level of output.

The slope of the ray through the origin declines continuously until the ray becomes tangent to the total variable cost. To the right of this point, the slopes of rays through origin start increasing.

Thus, the AVC falls initially as the productivity of the variable factor (s) increases; reaches a minimum, when the plant is operated (with the optimal combination of fixed and variable factors), and rises beyond that point.

If the total variable cost curve is a linear curve, the average variable cost will be constant and is equal to marginal cost (derivative of total cost with respect to output or change in total cost divided by change in output). Suppose,

TC = A + b Q (‘a’ is total fixed cost, ‘b’ is constant and ‘Q’ is output)

TVC = b Q

AVC = b = MC

#### 6. Average Total Cost (ATC):

Average total cost is the sum of the average fixed cost and average variable cost. Alternatively, ATC is computed by dividing total cost by the number of units of output.

Therefore,

ATC or AC = AFC + AVC

=TFC /Q + TVC/Q

=TFC + TVC/Q = TC/Q

Average cost is also known as unit cost, as it is cost per unit of output produced. It is graphically shown in Fig. 11.5. It is derived from total cost curve in the same way as the average variable cost curve is derived from total variable cost curve. If the total cost curve is linear, the average total cost curve continues to decline, as output increases.

Given,

TC =a + b Q

ATC =a/Q+b

The behaviour of the average total cost depends upon the behaviour of the average fixed cost and average variable cost. Initially, average total cost is high, as both the average fixed cost and average variable cost are high at low levels of output.

As the level of output increases in the initial stages, ATC falls sharply, as both AFC and AVC curves fall. When AVC curve begins to rise, AFC curve still continues to fall. The ATC curve continues to fall, because, the fall in AFC curve outweighs the rise in AVC curve.

Therefore, the minimum point of ATC curve is reached for a larger output than the minimum point on AVC curve. When fall in AFC becomes equal to rise in AVC, ATC reaches its minimum point, which is the optimum point of output.

If output increases further, rise in AVC more than offsets the fall in AFC. ATC rises after that point as a result. Thus, ATC curve like the AVC curve first falls reaches its minimum value and then rises. That is why; it is U-shaped curve, similar to that of AVC.

At each level of output, AC curve lies above AVC curve at a distance equal to the corresponding height of curve AFC. As the output increases, both AVC and ATC tend to come closer and closer, as the gap between them (given by AFC) becomes smaller and smaller. When AFC curve approaches X- axis, the AVC curve approaches the ATC curve.

#### 7. Marginal Cost (MC):

The concept of marginal cost occupies an important place in Economics. It is the addition to total cost required to produce one additional unit of a commodity. It is measured by the change in total cost resulting from a unit increase in output. For example, if the total cost of producing 5 units of a commodity is Rs. 100 and that of 6 units is Rs. 110, then the marginal cost of producing 6th unit of. Commodity is Rs. 110 – Rs. 100 = Rs. 10. The formula for marginal cost is

MCn =TCn –TCn-1,

It means that marginal, cost of ‘n’ units of output (MCn) can be obtained by subtracting the total cost of production of ‘n-l’ units (TCn-1) from the total cost of production of ‘n’ units (TCn). Alternatively, marginal cost can be expressed as

MC=∆TC5/∆Q = d(TC)/dQ

Here, ∆TC stands for change in total cost and ∆Q stands for change in total output.

It is worth noting that marginal cost is independent of the fixed cost, as fixed cost does not change with output (in the short period). Marginal cost is affected only by the variable cost, over which the firm has the most direct control. Marginal cost can be saved by reducing total output.

Thus, the firm has most direct control over marginal cost. A firm’s decision as to what output level to produce is largely influenced by this cost. Marginal cost can be obtained by comparing either the change in total cost or the change in total variable cost, when output is increased by one unit. This point can be explained with the help of simple algebra as follows:

Therefore, marginal cost reflects only the change in total variable cost. The summation of mar­ginal costs of different sellers gives the supply of a commodity, which together with demand influence price and hence production decision.

The behaviour of marginal cost is also influenced by the law of returns. Initially, marginal cost falls (when total or variable cost rises slowly), then it remains constant and finally it rises (when total or variable cost rises fast). Thus, MC curve is U-shaped. MC curve is graphically illustrated in Fig. 11.6.

MC at each level of output is derived from the slope of the TC or TVC curve. The slope of a curve at any point is the slope of the tangent at that point, which decreases initially and then rises. With an inverse-S shape of the TC or TVC curve, the MC curve will be U-shaped.

The slope of the tangent to the total cost curve declines gradually, until it becomes minimum at some point, then starts rising. This explains the shape of MC curve.

#### 8. U-Shaped Unit Cost Curves:

There are various mathematical forms, which lead to U-shaped unit cost curves. The cubic polynomial form is the simplest total cost function, which incorporates the law of variable propor­tions.

The total cost curve is roughly inverted U-shaped curve. The number of bends in the graph is two, i.e., one less than the highest exponent of ‘Q’. The ATC, the AVC and the MC are all U-shaped curves. The marginal cost curve intersects AVC curve and AC curve at their respective minimum points in that order. AFC curve given by a/Q is continuously downward sloping curve.