Analysis of Short Run Cost of Production

7/31/2019 Analysis of Short Run Cost of Production

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Analysis of Short Run Cost of Production:Definition of Short Run:Short run is a period of time over which at least one factor must remain fixed. For most of the firms, thefixed resource or factors which cannot be increased to meet the rising demand of the good is capital i.e.,plant and machinery.Short run, then, is a period of time over which output can be changed by adjusting the quantities ofresources such as labor, raw material, fuel but the size or scale of the firm remains fixed.Definition of Long Run:In the long run there is no fixed resource. All the factors of production are variable. The length of thelong run differs from industry to industry depending upon the nature of production.For example, a balloon making firm can change the size of firm more quickly than a car manufacturingfirm.Categories/Types of Costs in the Short Run:The total cost of a firm in the short run is divided into two categories (1) Fixed cost and (2) Variable cost.The two types of economic costs are now discussed in brief.

(1) Total Fixed Cost (TFC):Total fixed costoccur only in the short run. Total Fixed cost as the name implies is the cost of the

firm's fixed resources, Fixed cost remains the same in the short run regardless of how many units ofoutput are produced. We can say that fixed cost of a firm is that part of total cost which does not varywith changes in output per period of time. Fixed cost is to be incurred even if the output of the firm iszero.For example, the firm's resources which remain fixed in the short run are building, machinery and evenstaff employed on contract for work over a particular period.(2) Total Variable Cost (TVC):

Total variable costas the name signifies is the cost of variable resources of a firm that are used alongwith the firm's existing fixed resources. Total variable cost is linked with the level of output. When output

is zero, variable cost is zero. When output increases, variable cost also increases and it decreases withthe decrease in output. So any resource which can be varied to increase or decrease with the rate ofoutput is variable cost of the firm.For example, wages paid to the labor engaged in production, prices of raw material which a firm. incurson the production of output are variable costs. A firm can reduce its variable cost by lowering output butit cannot decrease its fixed cost. These expenses remain fixed in the short run. In the long run there areno fixed resources. All resources are variable. Therefore, a firm has no fixed cost in the long run. Alllong run costs are variable costs.(3) Total Cost (TC):

Total cost is the sum of fixed cost and variable cost incurred at each level of output. Total cost ofproduction of a firm equals its fixed cost plus its:


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Formula:

TC = TFC + TVCWhere:TC = Total cost.TFC = Total fixed cost.TVC = Total variable cost.Explanation:Short run costs of a firm is now explained with the help of a schedule and diagrams.

Schedule:(in Dollars)

Units of Output (in Hundred)TotalFixedCost

Total Variable Cost Total Cost

0 1000 0 1000

1 1000 60 1060

2 1000 100 1100

3 1000 150 11504 1000 200 1200

5 1000 400 1400

6 1000 700 1700

7 1000 1100 2100

The short run cost data of the firm shows that total fixed cost TFC (column 2) remains constant at$1000/- regardless of the level of output.The column 3 indicates variable cost which is associated with the level of output. Total variable cost iszero when production is zero. Total variable cost increases with the increase in output. The variable

does not increase by the same amount for each increase in output. Initially the variable cost increasesby a smaller amount up to 3rd unit of output and after which it increases by larger amounts.Column (4) indicates total cost which is the sum of TFC + TVC. The total cost increases for each levelof output. The rise in total cost is more sharp after the 4th level of output. The concepts of costs, i.e., (1)total fixed cost (2) total variable cost and (3) total cost can be illustrated graphically.(i) Total Fixed Cost Curve/Diagram:


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In this diagram (13.1) the total fixed cost of a firm is assumed to be $1000 at various levels of output. Itremains the same even if the firm's output is zero.(ii) Total Variable Cost Curve/Diagram:

In the figure (13.2), the total variable cost curve (TVC) increases with the higher level of output. It starts

from the origin. Then increases at a diminishing rate up to the 4th units of output. It then begins to riseat an increasing rate.Total Cost Curve Curve/Diagram:


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In the figure (13.3), total cost curve which is the sum of the total fixed cost and variable cost at variouslevels of output has nearly the same shape. The difference between the two is by only a fixed amount of$1,000. The total variable cost curve and the total cost curve begin to rise more rapidly as production isincreased. The reason for this is that after a certainoutput, the business has passed its most efficient use of its fixed costs machinery, building etc., and itsdiminishing return begins to set in.Analytical Importance of Fixed and Variable Costs:In the time of distinction between fixed cost and variable cost is a matter of degree, it all depends uponthe contracts of a firm and .the period of time under consideration.For example, if a firm makes contract with the labor for a certain period, then the firm has to bear thecost of the labor irrespective of the total produce. Under such conditions, the wages paid to the labor willbe classified as fixed cost and not variable cost, as discussed under the heading of variable cost.Secondly, when the period of time is short, the distinction between fixed cost and variable cost can bemade rigid but not in a longer period of time all fixed costs change into variable cost in the long run.

Average Cost:Definition and Explanation:The entrepreneurs are no doubt interested in the total costs but they are equally concerned in knowingthe cost per unit of the product. The unit cost figures can be derived from thetotal fixed cost, totalvariable cost and total cost by dividing each of them with corresponding output.Types/Classifications:(1) Average Fixed Cost (AFC):Average fixed costrefers to fixed cost per unit of output. Average fixed Cost is found out by dividing

the total fixed cost by the corresponding output.
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Formula:AFC = TFC

output (Q)For instance, if the total fixed cost of a shoes factory is $5,000 and it produces 500 pairs of shoes, thenthe average fixed cost is equal to $10 per unit. If it produces 1,000 pairs of shoes, the average fixedcost is $5 and if the total output is 5,000 pairs of shoes, then the average fixed cost is $1 pair of shoe.From the above example, it is clear, that the fixed cost, i.e., $5,000 remains the same whether theoutput is 1,000 or 5,000 units.Behavior of Average Fixed Cost (AFC):The average fixed cost begins to fall with the increase in the number of units produced, In our examplestated above, average fixed cost in the beginning was $10. As the output of the firm increased, it

gradually came down to $1. The AFC diminishes with every increase in the quantity of output producedbut it never becomes zero.Diagram/Curve:

The concept of average fixed cost can be explained with the help of the curve, in the diagram (13.4) theaverage fixed cost curve gradually falls from left to right showing the level of output. The larger the levelof output, the lower is the average fixed cost and smaller the level of output, the greater is the averagefixed cost. The AFC never becomes zero.(2) Average Variable Cost (AVC):Average variable costrefers to the variable expenses per unit of output Average variable cost is

obtained by dividing the total variable cost by the total output.


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For instance, the total variable cost for producing 100 meters of cloth is $800, the average variablecost will be $8 per meter.Formula:

AVC = TVC(Q)

Behavior of Average Variable Cost:When a firm increases its output, the average variable cost decreases in the beginning, reaches aminimum and then increases. Here, a question can be asked as to why AVC decreases in the beginningreaches a minimum and then increases. The answer to this question is very simple.When in the beginning, a firm is not producing to its full capacity, then the various factors of productionemployed for the manufacture of a particular commodity remain partially absorbed. As the output of thefirm is increased, they are used to its fullest extent. So the AVC begins to decrease. When the plantworks to its full capacity, the AVC is at its minimum. If the production is pushed further from the plant

capacity, then less efficient machinery and less, efficient labour may have to be employed. This resultsin the rise of AVC. It is in this way we say that as the output of a firm increases, the AVC decreases inthe beginning, reaches a minimum and then increases. The AVC can also be represented in the form ofa curve.Diagram/Curve:

The shape of the average variable cost curve (Fig. 13.5) is like a flat U-shaped curve. It shows thatwhen the output is increased, there is a steady fall in the average variable cost due to increasing returnsto variable factor. It is minimum when 500 meters of doth are produced. When production is increasedto 600 meters, of cloth or more, the average variable cost begins to increase due to diminishing returnsto the variable factor.

(3) Average Total Cost (ATC):Average total costrefers to cost (both fixed and variable) per unit of output. Average total cost isobtained by dividing the total cost by the total number of commodities produced by the firm or when thetotal sum of average variable cost and average fixed cost is added together, it becomes equal to

average total cost.


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Formula:

ATC = Total Cost (TC)Output (Q)

Behavior of Average Total Cost:

As the output of a firm increases, average total cost like the average variable cost decreases in thebeginning reaches a minimum and then it increases. The reasons for decline of ATC in the beginningare that it is the sum of AFC and AVC.Average fixed cost and average variable costs have both the tendency to fall as output is increased.Average total cost will continue falling so long average variable cost does not rise. Even if averagevariable cost continues rising, it is not necessary that the average total cost will rise. It can be due to thefact that the increase in average variable cost is less than the fall in average fixed cost. The increase inaverage variable cost is counterbalanced by a rapid fall of average fixed cost. If the rise in the averagevariable cost is greater than the fall in average fixed cost, then the average total cost will rise.The tendency to rise on the part of average total cost-in the beginning is slow, after a certain point itbegins to increase rapidly.Diagram/Curve:

The average total cost is represented here by a shaped curve in Fig. (13.6). The average total costcurve is also like a U-shaped curve. It shows that as production increases from 100 meters to 200meters of cloth, the cost falls rapidly, reaches a minimum but then with higher level of output, theaverage fixed cost begins to increase.

Short Run and Long Run Average Cost Curves:

Relationship and Difference:


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Short Run Average Cost Curve:In the short run, the shape of the average total cost curve (ATC) is U-shaped. The, short runaveragecost curve falls in the beginning, reaches a minimum and then begins to rise. The reasons for the

average cost to fall in the beginning of production are that the fixed factors of a firm remain the same.The change only takes place in the variable factors such as raw material, labor, etc.As the fixed cost gets distributed over the output as production is expanded, the average cost,therefore, begins to fall. When a firm fully utilizes its scale of operation (plant size), the average cost isthen at its minimum. The firm is then operating to its optimum capacity. If a firm in the short-runincreases its level of output with the same fixed plant; the economies of that scale of production changeinto diseconomies and the average cost then begins to rise sharply.Long Run Average Cost Curve:In the long run, all costs of a firm are variable. The factors of production can be used in varying

proportions to deal with an increased output. The firm having time-period long enough can build largerscale or type of plant to produce the anticipated output. The shape of the long run average costcurve is also U-shaped but is flatter that the short run curve as is illustrated in the following diagram:Diagram/Figure:

In the diagram 13.7 given above, there are five alternative scales of plant SAC1 SAC2, SAC3, SAC4and,SAC5. In the long run, the firm will operate the scale of plant which is most profitable to it.For example, if the anticipated rate of output is 200 units per unit of time, the firm will choose thesmallest plant It will build the scale of plant given by SAC1 and operate it at point A. This is because ofthe fact that at the output of 200 units, the cost per unit is lowest with the plant size 1 which is thesmallest of all the four plants. In case, the volume of sales expands to 400, units, the size of the plantwill be increased and the desired output will be attained by the scale of plant represented by SAC 2 at

point B, If the anticipated output rate is 600 units, the firm will build the size of plant given by SAC3

andoperate it at point C where the average cost is $26 and also the lowest The optimum output of the firmis obtained at point C on the medium size plant SAC3.
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If the anticipated output rate is 1000 per unit of time the firm would build the scale of plant given bySAC5 and operate it at point E. If we draw a tangent to each of the short run cost curves, we get thelong average cost (LAC) curve. The LAC is U-shaped but is flatter than tile short run cost curves.Mathematically expressed, the long-run average cost curve is the envelope of the SAC curves.In this figure 13.7, the long-run average cost curve of the firm is lowest at point C. CM is the minimumcost at which optimum output OM can be, obtained..

Marginal Cost (MC):Definition:

Marginal Costis an increase in total cost that results from a one unit increase in output. It is definedas:"The cost that results from a one unit change in the production rate".Example:For example, the total cost of producing one pen is $5 and the total cost of producing two pens is $9,then the marginal cost of expanding output by one unit is $4 only (9 - 5 = 4).The marginal cost of the second unit is the difference between the total cost of the second unit and totalcost of the first unit. The marginal cost of the 5th unit is $5. It is the difference between the total cost ofthe 6th unit and the total cost of the, 5th unit and so forth.Marginal Cost is governed only by variable cost which changes with changes in output. Marginal costwhich is really an incremental cost can be expressed in symbols.Formula:

Marginal Cost = Change in Total Cost = TCChange in Output q

The readers can easily understand from the table given below as to how the marginal cost is computed:

Schedule:

Units of Output Total Cost (Dollars) Marginal Cost (Dollars)

1 5 5

2 9 4

3 12 3

4 16 4

5 21 5

6 29 8

Graph/Diagram:


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MC curve, can also be plotted graphically. The marginal cost curve in fig. (13.8) decreases sharply withsmaller Q output and reaches a minimum. As production is expanded to a higher level, it begins to riseat a rapid rate.

Long Run Marginal Cost Curve:The long run marginal cost curve like the long run average cost curve is U-shaped. As productionexpands, the marginal cost falls sharply in the beginning, reaches a minimum and then rises sharply.Relationship Between Log Run Average Cost and Marginal Cost:The relationship between the long run average total cost and log run marginal cost can be understoodbetter with the help of following diagram:

It is clear from the diagram (13.9), that the long run marginal cost curve and the long run average totalcost curve show the same behavior as the short run marginal cost curve express with the short run


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average total cost curve. So long as the average cost curve is falling with the increase in output, themarginal cost curve lies below the average cost curve.When average total cost curve begins to rise, marginal cost curve also rises, passes through theminimum point of the average cost and then rises. The only difference between the short run and longrun marginal cost and average cost is that in the short run, the fall and rise of curves LRMC is sharp.

Whereas In the long run, the cost curves falls and rises steadily.

Relation of Average Variable Cost and Average Total Cost

to Marginal Cost:Before we explain, the relationof average variable cost (AVC) and average total cost (ATC) tomarginal cost (MC),it seems necessary that the various types of costs and their relationship should beshown in the form of a table. This is illustrated in the table below:Schedule:Units ofOutput

Total FixedCost

(TFC)

Total VariableCost (TVC)

Average TotalCost (ATC)

AverageFixed Cost

(AFC)

AverageVariable Cost

(AVC)

Marginal Cost(MC)

($) ($) ($) ($) ($) ($)

1 30 15 45 30 15 15

2 30 16.9 23.4 15 8.4 1.9

3 30 18.4 16.1 10.1 6.1 1.5

4 30 19.4 12.3 7.5 4.8 15 30 20 10 6 4.0 0.6

6 30 22 8.7 5 3.7 2

7 30 25 7.8 4.3 3.6 3

8 30 30 7.5 3.7 3.7 5

9 30 36 7.3 3.3 4 6

10 30 43 7.3 3 4.3 7

11 30 60 8.2 2.7 5.5 17

12 30 90 10 2.5 7.5 30

13 30 125 11.9 2.3 9.6 35

14 30 165 13.9 2.1 11.8 40

15 30 210 16 2 14.8 45

16 30 270 18.7 1.9 16.7 60From the table, the reader can understand the relation of various types of costs to each other. We take,first of all, the relation of average total cost to marginal cost. As production increases, the average totalcost and the marginal cost both begin to decrease.The average total cost goes on decreasing up to the 9th unit and then after 10, it begins to rise. Themarginal cost goes on falling up to 5th unit and then it begins to increase. So long as the average totalcost does not rise, the marginal cost remains below it. When average total cost begins to increase, toemarginal cost rises more than the average total cost.

Summing Up:


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(1) When average cost is falling, the marginal cost is always lower than the average cost.

(2) When average cost is rising, marginal cost lies above AC and rises faster than AC.(3) The marginal cost curve must cut the average cost curve at the minimum point of AC.

Average Variable Cost and Marginal Cost:The relation of average variable cost and marginal cost is also very clear from the diagram given below.The AVC goes on falling up to the 7th unit, and then it steadily moves upwards. On the other hand themarginal cost falls up to the 5th unit and then rises more rapidly than average variable cost.Diagram/Figure:

In the diagram (13.10) AFC, AVC, ATC and MC curves are shown. Here, units of production aremeasured along OX and cost along OY. ATC and AVC both fall in the beginning, reach a minimum pointand then begin to rise. So is the case with the marginal costcurve. It first falls and then after rising, sharply crosses through the lowest point of average variable costand average total cost and rises.

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Analysis of Short Run Cost of Production