RELATION BETWEEN AVERAGE FIXED COST, AVERAGE VARIABLE COST, AVERAGE TOTAL COST, MARGINAL COST

Average Total Cost (ATC) or Average Cost (AC). Average total cost (ATC) is obtained by dividing the total cost (TC) by the quantity of output (Q). Or alternatively, it can also be obtained by adding Average fixed Cost (AFC) and Average Variable Cost (AVC)

ATC =

ATC = AFC + AVC

Diagrammatically the vertical summation of average fixed cost and average variable cost curves gives us the average total cost curve. The ATC curve is also an U-shaped curve.

D. Marginal Cost (MC.) Marginal cost is the increase in total cost resulting from one unit increase in output. In short, it may be called incremental cost. Since a change in total is caused only by a change in total variable cost, marginal cost may also be defined as the increase in total variable cost resulting from on unit increase in output. Thus, marginal cost has nothing to do with the fixed costs.

MC =

or,

MC = TCn-TC_n-1

TC_n = Total cost of n units

TC_n-1= Total cost of n-1 units.

            Suppose the cost of 3 units of a commodity is Rs. 600 and now the total cost of 4 units becomes Rs.720 then the marginal cost will be Rs. 120(720-600).

            It is worth nothing that like other per unit cost curves, marginal cost curve also has an U-shape. The follows directly from the behavior of TVC and TC curves in the diagram, to begin with, they rise at a diminishing rate. Their rate of increase being the marginal cost, MC curve falls. When the rate of increase of TC and TVC stops falling, begin to increase at an increasing rate, MC reaches its minimum point at lower level of output than do the AVC and ATC moreover, it intersects them both at respective minimum points.

            The different short-run cost curves are illustrated in the following table and diagram.

Units of Output	TFC (RS.)	TVC (RS.)	TC (TFC + TVC) (RS.)	AFC (TVC/0) (RS.)	AVC (TVC/0) (RS.)	ATC (AFC + AVC) or (TC/0) (RS.)	MC (RS.)
1	2	3	4	5	6	7	8
0	200	0	200	-	-	-	-
1	200	180	380	200	180	380	180
2	200	300	500	100	150	250	120
3	200	400	600	66.7	133.3	200	100
4	200	520	720	50	130	180	120
5	200	650	850	40	130	170	130
6	200	820	1020	3.33	136.7	170	170
7	200	1060	1260	2.86	151.4	180	240
8	200	1400	1600	2.5	17.5	200	340

            The cost-output relationship can also be shown better by joint short output cost curve a run through the use of graph. It will be seen that the average fixed cost curve (AFC Curve) falls as output rises from lower levels to higher levels. The shape of the average fixed cost curve, therefore, is a rectangular hyperbola. The average variable cost curve (AVC curve), First falls and then rises so also that average total cost curve (ATC curve). However, the AVC curve starts rising earlier than the ATC curve. Further, the least cost level of output corresponds to the point LT on ATC curve and not to the point LV, which lies on the AVC curve.

            Another important point to be noted is that in Figure, the marginal cost curve (MC curve) intersects both the AVC curve and the ATC curve at their minimum points. This is very simple to explain. If marginal cost (MC) is less than the average cost (AC), it will pull AC down. If the MC is greater than AC, it will pull AC up. If the MC is equal to AC, it will neither pull Ac up nor down. Hence MC curve tends to intersect the AC curve at its lowest point. Similar is the position about the average variable cost curve. It will not make any difference whether MC is going up or down.

            The inter-relationship between AVC, ATC and AFC can be summed up as follows:

1.    If both AFC and AVC fall, ATC will fall.

2.    If AFC falls but AVC rises;

a.    ATC will fall where the drop in AFC is more than the rise in AVC.

b.    ATC will not fall where the drop in AFC is equal to the rise in AVC.

c.     ATC will rise where the drop in AFC is less than the rise in AVC.

AVERAGE FIXED COST, AVERAGE VARIABLE COST, AVERAGE TOTAL COST AND RELATIONSHIP BETWEEN THEM

Average Fixed Cost (AFC). Average fixed cost can be obtained by dividing total fixed cost (TFC) but the quantity of output (Q),

AFC=TFC. Q

Features of AFC

(i)         As output rises, the Average fixed cost (AFC) goes on decaling.

            The AFC curve is therefore an onward sloping curve. (ii) As output approaches Zero, average fixed cost approaches infinity, but AFC curve never touches the Y-axis. On the other hand, as output reaches very high levels, average fixed cost approaches zero, but it never reduces itself to zero, it always remains positive. Hence the AFC curve never touches the X-axis also. Thus it follows that AFC curve never touches either of the axis. Actually this curve takes the shape of rectangular hyperbola, which shows that the area under the curve (i.e., total fixed cost) always remains the same. AFC is illustrated in the following table and diagram.

Units of	TFC (Rs)	AFC (Rs)
1	200	-
2	200	200
3	200	100
4	200	667
5	200	50
6	200	333

B. Average Variable Cost and Output:

            Average variable costs mean the total variable costs divided by the number of units produced. The Average variable costs will come down and then rise as more and more units are produced with a given plant. This is because as we add more units of variable factors in a fixed plant, the efficiency of the inputs first increases then it decreases.

            The variable factors tend to produce a little more efficient near a firm's optimum output than a very low levels of output. But once the optimum capacity is reached, any further in output will doubtlessly increase average variable cost quite sharply. Greater output may be obtained but at much greater average variable costs. As for example, if more and more workers are engaged, it may in the end, lead to overcrowding and bad organization.

Even more workers may be required to be paid higher wages for over-time work.

            Average Variable (AVC)–Average variable cost can be obtained by dividing total fixed cost (TFC) by the quantity of output (Q),

            AFC =

This is illustrated in the following example and diagram:

Example

Unit of Production	TVC (Rs.)	AVC (Rs.)
0	0	-
1	180	180
2	300	150
3	400	13.33
4	520	130
5	650	130
6	820	136.7
7	1060	151.4
8	1400	175.0

            As output, the AVC curves first falls, reaches a minimum and then begins to rise. Thus, AVC curve has a U-shape. Its U-shape can be explained with the help of laws of retunes. Suppose for the optimum utilization of its plant a firm requires 60 laborers. If in the beginning there are only 30 laborers in a firm, out put will rise more than proportionate with the increase in the number of laborers. Because the increase in numbers would enable laborers to utilize the plant more efficiently through division of labor and specialization. Hence average variable cost will fall with the rise in the number of workers and output.

            The points of optimum productive-Capacity for the firm will be at 60 laborers. If we would increase the number of laborers beyond this capacity (i.e., after 60 laborers), the average variable cost will rise. Thus in short, up to the point of optimum capacity of the plant operates the law of increasing returns which reduces the average variable cost with the rise in output, and after the point of optimum capacity operates the law of diminishing returns which increases the average variable cost. Thus, the average variable cost curve becomes U-shaped curve. In our example AVC fall up to 4 units of output thereafter it starts of rise.

C. Average total cost and output. Average cost, consists of average fixed costs and average variable costs. As we see, average fixed costs begin to fall with an increase output while average variable costs come down and rise. Till the average variable cost come down, the average total cost also comes down, but a point comes when the average variable costs is more then the drop in average fixed cost then average total cost will show a rise. In this way, a stage will come when the average variable cost may have started rising, though the average total is less than the drop in average fixed cost.

            Average Total Cost (ATC) or Average Cost (AC). Average total cost (ATC) is obtained by dividing the total cost (TC) by the quantity of output (Q). Or alternatively, it can also be obtained by adding Average fixed Cost (AFC) and Average Variable Cost (AVC)

ATC =

ATC = AFC + AVC

Diagrammatically the vertical summation of average fixed cost and average variable cost curves gives us the average total cost curve. The ATC curve is also an U-shaped curve.

SHORT RUN COST - FIXED COST - VARIABLE COAT - TOTAL COST WITH TABLE AND DIAGRAMMATICALLY REPRESENTATION

Short Run Costs

The short period, short is defined as the period of time over which some factor inputs, called fixed factors, connote be varied. In other words, the scale of plant is given and constant. Land, factory building, heavy capital equipments services of management of high category are some of the factors that cannot be varied in a short span of time. That is why they are called fixed factors.

On the other, are some factor-inputs that con being varied as and when required, they are called variable factors. For instance, power, fuel, labour, raw materials, etc. are the examples of variable factor-inputs.

Since in the short-run a firm employs two types of factors-fixed factors and variable factors, costs are also of two types-fixed costs and variable costs.

i.     Fixed Costs. Fixed costs (also known as supplementary costs or overhead costs) are the expenses incurred on the fixed factors of production. Or, the fixed costs are the costs that do not vary with the output. Rent; interest; insurance premium; salaries of permanent employees, etc are the example of fixed cost.

ii.    Variable costs. Variable costs (or prime costs) are the expenses incurred on the variable factors of production or the costs that vary directly with the output. Expenses on raw materials, power and fuel; wages of daily laborers, etc. are the examples of variable cost.

Total Costs Curves in the Short Run

            There are three concepts concerning total cost in the short period: Total fixed cost: total variable cost and total cost.

i.     Total Fixed Cost (TFC). Total fixed Costs are those costs that not vary with the output. They will be the same if output is zero or units or 1 million units. Thus, they are totally unaffected by the changes in rate of outputs. Examples of fixed costs are: (i) Initial establishment expenses, (ii) Rent of the factory, (iii) Expenses on the maintenance of machinery, (iv) Wages and salaries of the permanent staff, (v) Interests on bonds, (vi) Insurance premium.

TFC = quantities of the fixed productive service X factor price.

Total fixed cost of a firm is illustrated in the following table and TFC

Units of output                   TFC (Rs)

0                                             200 1                                             200 2                                             200 3                                             200 4                                             200 5                                             200

            Curve is a horizontal curve parallel to the X-axis that tells us that total fixed cost remains the same at all levels of output.

ii.    Total Variable Cost (TVC). The costs that directly with the output, rising as more is produced and falling as less is produced, are called total variable costs. They are also referred as prime costs or Direct costs or Avoidable costs, Example of variable costs are: (i) wages of temporary laborers; (ii) raw material; (iii) fuel;  (iv) Electric power, etc.

TVC = quantities of the variable productive service X factor price.

Total Variable cost is illustrated in the following table and diagram:

Units of Output                   TVC (Rs)

0                                              0 1                                             180 2                                             300 3                                             400 4                                             520 5                                             650 6                                             820 7                                           1060 8                                           1400

            Our above table and diagram speak that total cost varies directly with the volume of output. TVC curve form the origin, up to a certain range it remains concave from below and then it become convex. It shows that in the beginning total variable cost rises at a diminishing rate and thereafter it rises at an increasing rate.

iii.  Total Costs. Total cost means the total cost of producing any given amount of output. When we ass total fixed and total variable costs at different rates of output, we get the corresponding total costs.

Thus,

TC = TFC + TVC

            Since, fixed cost are constant and variable costs necessarily rise as output rises, total costs also rise with the output or, to put the point more formally, TC is a function of total product and varies directly with it. TC = f (9)

            TC (Total cost) curve can be obtained by adding TFC and TVC curves vertically at each point.

            Again, since the total fixed costs by definition remain constant, the changes in total costs are entirely due to the changes in total variable costs. In other words, the rate of increase of total cost is the same as of total variable cost, as one of the two components of total cost, remains constant. TC and TVC curves therefore have the similar shapes; the only difference is that TVC starts from origin (0) while TC curve starts above the origin.

            The relationship between these three – TFC, TVC and TC is illustrated in the following table and diagram:

Units of Output	TFC (Rs.)	TVC (Rs.)	TC (Rs.)
0	200	0	200
1	200	180	380
2	200	300	500
3	200	400	600
4	200	520	720
5	200	650	850
6	200	820	1020
7	200	1060	1260
8	200	1400	1600

            The difference between the TFC and TC curves represents the TVC. Since TVC rises with the increase in output, this difference between TFC and TC also goes on increasing. This is shown in the following diagram.

            Similarly the vertical difference between TC and TVC curve represents the Total fixed Cost (TFC). Since total curves also remains the same. That is way TC and TVC curves remain parallel to each.

Unit Cost Curves in the Short-Run. The cost output relationship can be studied in the following discussion. The main short-run cost curves are;

a.            Average Fixed Cost and Output. The more output, the less the fixed cost per unit i.e. the average fixed cost go down with the increase in output. The reason is simple to understand-that total fixed costs remain the same and do not, vary with a change in output. This relationship between output and fixed cost is universal for all types of business concerns.

Average Cost (AC) curve; and Marginal Cost (MC) curve, for price and output determination, per unit cost curves are more useful than the total costs just discussed.

In this way, average fixed cost increases with the decrease in output or vice versa. In other words, average fixed cost and output have inverse relationship.

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