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COST ANALYSIS
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Abhijeet Alte
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cloudy222
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Smile COST ANALYSIS - June 8th, 2009

COST ANALYSIS:

Cost is the expense incurred in producing a commodity. Cost analysis is very important for the business managers for many decision regarding profitability future expense and future revenue depend upon various types of cost. In estimating profit the managers is required to compare cost with revenue. The revenue depends upon the price of the product in the market. The business manager can not control the price prevailing in the market but he can control cost by restricting the output. The relationship between the cost and output is known as the cost function.

Thus cost function is derived from production functions. The production functions expenses the functional relationship between input and output. In simple term, the production function states that output depend upon various quantities of input. If price of inputs are known we can calculate cost of production. The cost of production of a commodity is the aggregate of price paid for the factors of production used in producing that commodity. So a firm has to engage the series of various factor of production say the land, labor and capital etc, These factors have to be rewarded by the firm for their contribution made in producing the commodity. This compensation usually in terms of factors price is generally known as cost. of production denotes the value of the factor of the production engaged for producing a given article. (Commodity)

From the above discussion two main points has been taken into consideration.
1) Cost function
2) Cost of production
A cost function expresses the relationship between cost and its determinants. Several factors influence cost. When their relationship to cost is expressed in a functional or mathematical form, it is called cost function. Symbolically

C = f (S, O, P, T … N)

Where C is cost P is price of inputs
S is size of plants T is technology
O is level of output N is no of other factors
Cost function can be formulated for the short run and long run depending upon the requirement of the firm. However, the short run and long run functions are interrelated.


DETERMINANTS OF COST FUNCTION
He following is the main determinants of a cost function:

SIZE OF PLANT:

The size of plant or the scale of production is inversely related to cost. As the size of plant increase costs decline and vice versa.



OUTPUT LEVEL:
Total output and total cost are positively related to each other. As the level of total output increase total cost also increase. As the level of output increase MC and AC decline initially and rise thereafter.

PRISE OF INPUTS
Input price are again positively related to cost. Increase in the input price brings a rise in the cost.

TECHNOLOGY:
Nature of technology also influences cost. Modern technology is cost efficient and cost saving.

MANAGERIAL AND ADMINISTRATIVE Efficiency:
Managers are the controllers and monitors of the firm. Through efficient supervision, control and administration they can improve the efficiency and productivity of factors inputs and thus minimize the cost.

COST CONCEPTS:

1) OPPORTUNITY COST:
The concept of opportunity cost occupies a very important place in modern economic analysis. The concept was first developed by an Austrian economist, WLESER. The other notable contributors are Daven Port, Knight and Robbins. The concept is based on the fundamental fact that factors of production are scares and versatile. Our wants are unlimited. The means to satisfy these wants are limited but they are capable of alternative uses. Therefore, the problem of choice arises. This is the essence of Robbins definition of economics.
The opportunity cost of anything is the alternative that has been forgone. This implies that one commodity can be produced only at the cost of foregoing the production of other commodity. In other words opportunity cost is the loss of earnings due to opportunities foregone due to scarcity of resources. If resources were unlimited there would no need to forego any income. Yielding opportunity and therefore there would be no opportunity cost.

Resources are not only scared but they have alternatives uses with different returns. Income maximizing resources owners put their scare resources to their most productive use and forgo the income expected from the second best use of the recourses.
Thus, the opportunity cost may be defined as the expected returns from the second best use of the resources forgone due to the scarcity of resources. The opportunity cost is also called alternative cost.
Fig. suppose that a person has, 1, 00,000 which he has only two alternative uses. He can either buy a computer or a typewriter. From computer he expect an annual income of, 20, 00 and from typewriter Rs 15,000. If he is profit maximizing investors, he would like invest his money in computers and forgo the expected income from the typewriter that is 15000 Rs. The opportunity cost arises because of the forgone opportunities. Thus the opportunity cost of using resources in computer, the best alternative is the expected return from the typewriter, the second best alternative. In assessing the alternative cost, both explicit and implicit cost are taken into account.

The other concept which is associated with the concept of opportunity cost is the concept of “economic rent” or” economic profit”. In our above example economic profit of the computers is the excess of its earning over the income expected from the typewriter. That is 20,000 – 15,000 = 5000.

IMPORTANCE OF THE OPPORTUNITY COST
The significance of opportunity cost is as follow:

IT HELPS IN DETERMINING RELATIVE PRISE OF GOODS.
The concept is useful in the determination of the relative price of different goods.f.e.If a given amount of factor can produce one table or three chairs, then the price of one table will tend to be three times equal to that price of one chair.

FIXATION OF REMUNERATION TO A FACTORS
The concept is also useful in fixing the price of a factor.F.g. Let’s assume that, the alternative employment of a college professor is work as an office in an insurance company at a salary of Rs 10,000 per month. In such a cases, he has to paid at least Rs 10,000 to continue to retain him in the college.

EFFICIENT ALLOCATION OF RESOURCES:
The concept is also useful in allocating the efficient resources. Suppose, opportunity cost is one table and three chair and the price of a chair is 100Rs While the price of a table is 400Rs.Under such situation, it is beneficial to produce one table rather than 3 chair because he produces 3 chair he will get only 300 Rs whereas a table fetches him Rs 400, that is Rs 100 more. Hence, it helps manager to decide what he should produce in the factory.

2) REAL COST
Real cost refers to those cost which are made to factory of production to compensate for the toil and effort in rendering their service.
According to Marshall “The exertions of all the different kind of labor that are directly or indirectly involved in making it, together with the abstinences or rather the waiting required, For saving the capital used in making it, all this sacrifices together will be called the rel cost of production of the commodity.
OR
The term real cost of production refers to the physical quantities at various factors used in producing a commodity.
OR
“The real cost of production of a commodity is expressed not in money but in effort of workers and sacrifices of capitalists undergone in the making of a commodity”

So we conclude that, real cost is computed in term of the pain and discomfort involved for labour when it is engage in production and also in the absent and sacrifice involved in capital accumulation. The concept of real cost does not carry any significance in the cost of production because it is subjective concept and lacks precision (accuracy).

3) MONEY COST
Money cost or the nominal cost of the total money expenses incurrent by a firm in producing the commodity.
OR
“Cost of production measure in terms of money is called the money cost.”
“Money cost” is the monetary expenditure on input of various kinds – raw materials, wages and salary of labour, expenditure on machinery and equipment, depreciation on machinery, building and such other capital goods, interest on capital, other expenses like advertisement. Insurance premium and taxes etc,. Required for the output. It is the money spent on purchasing the different unit of factors of production needed for the producing a commodity. Money cost is obviously the payment made for the factors in terms of money. Money cost is the outlay cost that is actual financial expenditure of the firm.

4) SUNK COST
Sunk cost is the costs that are not altered by a change in quantity and cannot be recovered. Sunk cost are a part of outlay cost.F.e.depriciation

5) INCREMENT COST
The increment costs are the addition to costs resulting from a change in product line, introduction of new product, replacement of obsolete plant and machinery etc. Conceptually increment cost are closely related to the concept of marginal cost but with a relatively wider discussion while MC refers to the cost of the marginal unit of output, incremental cost refers to the total additional cost associated with the marginal batch of output. The concept of the incremental cost is based on the fact that in the real world, it is not practicable for lack of lived of input to employ factors for each unit of output separately. Incremental cost arises owing to the change in product, replacement of worn out plant and machinery with a new one etc.

6) ACCOUNTING COST (EXPLICIT COST)
Accounting cost or explicit cost or paid out costs or contractual cash payment cost are those, which fall under actual, or business costs entered in the books of accounts. The payments for wages and salaries, material, license fee, insurance premium etc, are the example of explicit cost. These cost involve cash payment and are recorded in normal accounting practices.

7) ECONOMIC COST (IMPLICIT COST)
In contrast with the above cost , three are certain other cost which do not take the form of cash outlay, nor do they appear in the accounting system such cost are known as implicit or imputed costs. Implicit cost may be defined as the earning expected from the second best alternative use of resources. Implicit cost is not taken into account while calculating the loss or gain of the business. But the form takes the important consideration in whether or not a factor would remain in present occupation.
The explicit and implicit costs together make the economic cost.

ECONOMIC COST = IMPLIOCIT COST + EXPLICIT COST

TYPES OF PRODUCTION COST AND THEIR MEASUREMNT
Total Fixed Cost ( TFC )
Total Variable Cost ( TVC )
Total Cost ( TC )
Average Fixed Cost ( AFC )
Average Variable Cost ( AVC )
Average Total Cost (ATC ) or Average Cost (AC )
Marginal Cost ( MC )

TOTAL FIXED COST
Fixed cost are those cost of items of expenditure, which are independent of the output that they do not change with the change in output unto certain level of production? Fixed cost thus are those cost, which are, remain fixed in the short run, at whatever, it may be the level of output. These cost are not affected by changes in the volume of production up to a certain level, these have to be incurred even if the output of the firm is nil or zero. Fixed costs are
v Payment of rent for the building
v Interest on borrowed capital
v Depreciation
v Administration expenses- salaries of managerial and office staff, watchman’s salary etc
v Insurance premiums
v Property and business taxes, license fees etc...

DIAGRAM











In the following diagram, FF is the fixes cost curve, which is parallel to X-axis. The cost remains fixed at OF whether the firm produces OA or OB or OC output. Fixed costs are not fixed permanently. In order to increase the production in the long run, the firm will haven to increase the size of plant, invest more capital, recruit more technical. Etc,. Thus FC become variable in the long run, fixed cost is also known as supplementary cost.

VARIABLE COST
Variable cost are those cost which change with output.hey are the function of output. TVC=F (Q)
Thus, variable costs are those cost which rise when output is increased and fall when output is decreased. When output is nil, they are reduced to zero.
Variable costs are also known as direct costs or prime costs which can be altering in the short run as output alter. These cost include following.
Cost of raw material
Wages of labour
Fuel and power charges
Excise duties, sales tax etc.









In this diagram, “OV” is the variable cost curve. The variable cost increase with increase in output. Thus for example when output is OA the variable cost is OE it increase to OF and OG as output increase to OB and OC respectively.

COMPERISON OF FC AND VC
1) FC is fixed while VC changes with the change in output.
2) During short period FC cannot be changed while VC can be changed.
3) FC curve is parallel to X- axis whereas VC curves slops up to the right.

TOTAL COST
TC refers the value of total resources requirement for the production of goods and services. It refers to the total outlays of money expenditure, on the resources used to produce a given level of output. It includes both fixed and variable costs. The total cost for a given output is given by the cost function.
TFC is the total expenditure by the firm for fixes inputs.
TVC is the firm’s total expenditure on variable inputs used to carry out production. Since higher output levels require greater utilization of variable inputs, they mean higher total variable cost.
TC is the sum of total fixed cost and total variable cost. Thus
TC = TFC + TVC where TC = Total cost
TFC = Total Fixed Cost
TVC = Total Variable Cost
It should be noted that, TFC is the some irrespective of the level of output. Therefore, a change in total cost is influenced by the change in variable cost only. The relationship between TFC, TVC and TC is shown in the following diagram.
DIAGRAM








In the diagram, the total cost curve TC has been obtained by adding TFC curve and TVC curve.

AVERAGE FIXED COST ( AFC )
The AFC is the fixes cost per unit of output. The more the units are produces, per unit cost on fixed factor falls. So we can say that per unit of cost on fixed factors is called AFC. It is obtained by dividing the total fixed cost by the number of unit of the commodity produced.
Symbolically

TFC
AFC = ----------- Where TFC = Total Fixed Cost
TQ TQ = Total Quantity

OR

AFC = AC- AVC
Where AC = Average cost
AVC = Average variable cost
The shape of the AFC is as follows.








It will be seen from this diagram that the AFC curve slops downwards through out its length. As output increases, the TFC get spread over to more and more units and therefore AFC became less and less. This continues falling of AFC as output expands are business people commonly called “Spreading the overhead”.
It should, however be noted that although the AFC curve sp downwards towards the X-axis, but it will never touch it because AFC can not be zero, how so ever large the level of output may be. Likewise, this curve will not touch the y axis also, because TFC is a positive value at zero output and any output and any positive value divided by zero will provide infinite value.
Thus the shape of the Arc curve therefore is a rectangular hyperbola.

AVERAGE VARIABLE COST
Average variable cost is the total variable cost devoted by the units of output.

Total Variable Cost
AVC = -------------------------
Total Quantity

Where the Q stands for the number of units of the product. Thus, the average variable cost is variable cost per unit of output.







It will see from this diagram that he average variable cost curve declines in the beginning up to the point – P and then start rising sharply after this point. This is so because in the beginning the output is below the normal capacity of the firm. AS the output increase and reach the normal capacity, the average cost per unit declines till the point.
P where it is the lowest. Since he output reaches the normal capacity at P, the variable cost per unit is the minimum or the lowest at this point. But when the output increase beyond the normal capacity of the firm, the variable cost per unit shows a sharp rise and goes on increasing with every increase in output.
These phenomena can also be explained with the help of the Law of variable proportion. The average variable cost is subject to the operation of this law. Thus for example. In the above diagram, up to the point P, it is the law of increasing returns which is in operation. The result is that average variable cost goes on diminishing up to this point. At the point P, the average variable cost gets stabilized on account of the operation of the law of diminishing returns.
The average variable cost curve generally U shaped.

6) AVERAGE TOTAL COST
Average total cost or what it simply called average cost is the total cost divided by total units of outputs. Thus,
Total Cost
Average Total Cost of Average Cost = -------------
Q
Where Q stands for the number of units of the product.
The average cost can also be computed simply by adding average fixed cost to the average variable cost. Thus

Average Total Cost = Average Fixed Cost + Average Variable Cost

It should be noted here that the behaviors of the average total cost curve depend upon the behaviors of the average fixed cost curve and average variable cost curve. In this connection, following observation may be made:
In the beginning when both AVC curve and AFC curve fall, the average total cost curve falls sharply.
When an average variable cost rises, but average fixed cost curve falls, the average total cost curve continues to fall because here the fall in the AFC curve is more than the rise in AVC curve.
DIAGRAM








But as out put increase here is a sharp rise in AVC which more than offsets the fall in AFC Therefore ATC curve raises after a point. In other words, ATC curve like the AVC curve first falls reaches its minimum and than rises. The ATC curve is therefore, almost of U shaped. This would be clear from the given on above diagram.

7) MARGINAL COST
Marginal cost is the addition to the total cost incurred by the producing an additional unit of output. It may also be defined as the cost of producing an additional unit. Thus, marginal cost is the addition to the total cost of producing n units instead of n – 1 unit.

MC = TCn – TC n – 1

Where MC = Marginal Cost
TC = Total Cost
N = Number of unit of output
Marginal cost can also be calculated by dividing the change in the total cost by the one unit change in output. Thus,

∆ TC
MC = ----------
∆1 Q
Where ∆ denotes change in output but output is assumed to change by 1 unit only and hence output change is denoted by ∆1.
It should also note here that marginal cost is the cost of producing an additional unit of output and not of average product. It indicates change in total cost as a result of producing an additional unit of output.
Further it has to be remembered that marginal cost is independent of the amount of fixed cost in the short run. Since fixed cost do not change with output and remain constant through out. There is no marginal fixed cost when output increased in the short run. It is only the variable cost that varies with the output in the short run. Change in marginal cost therefore, due to change in the variable cost. Marginal cost is not affected by the amount of the fixed cost. Thus marginal cost may also be defined as a change in total variable cost when one additional unit is produce. It can be calculated with reference to a change I the total variable as under:

MCn = TVCn –TVC n-1

Where 1) Mc is the marginal cost of producing n numbers of units.
2) TVCn is the total variable cost of producing n units.
3) TVC n-1 is the total variable cost of producing “n” minus one unit.

SHAPE OF THE MARGINAL COST CURVE
The marginal cost surve like the average cost curve falls in the beginning reaches its minimum and then starts rising .The fall in the marginal cost curve in the beginning is because of the operation of the law of increasing returns and its rise after a point is because of the operation of the law of diminishing returns. This would be clear from the following diagram.
DIAGRAM








The concept of marginal cost is of great importance in price theory. This concept along with the concept of marginal revenue helps the firm in deciding the size of its output. The firm will earn maximum profit at that point where the revenue earn from the marginal unit is equal to the cost incurred on that unit. In other words, equality of marginal cost and marginal revenue indices the points of profit maximization and consequently equilibrium of the firm.

RELATION BETWEEN AVERAGE COST AND MARGINAL COST
The relation between average cost and marginal cost will be clear from the following diagram which shows both these curves.







The following observation may be made from the above diagram.
1) When average cost is fill-in, marginal cost is lower than the average cost. Hence, the marginal cost curve is below his average cost curve.
2) When average cost is rising, marginal cost is higher than average cost and therefore the marginal cost curve is above the average cost curve.
3) When it comes to falling , marginal cost curve falls more rapidly than the average cost curve and when it comes into rising marginal cost curve rises more rapidly then the average cost curve.
4) When average cost is minimum, marginal cost and average cost are equal. At this point, the marginal cost curve cuts the average cost curve from the lowest point.

RELATION BETWEEN MARGINAL COST AND AVERAGE FIXED COST, AVERAGE VARIABLE COST AND AVERAGE VARIABLE COST.

The relation between marginal cost and average fixed cost, average variable cost and average total cost shall be clear from a study of the following diagram.






The following observation may be made from the following diagram.
!) Average cost curve is a downward sloping curve in the shape of a rectangular hyperbola.
2) Average variable cost curve at first falls and than rises.
3) Average total cost curve which is sum of average fixed and average variable cost curve is U shaped curve.
4) Marginal cost curve, after showing an initial fall rises continuously thereafter.
5) Average fixed cost curve, however, bears a definite relationship with average variable cost curve and average total cost curve. It cuts both these curves at their lowest points. Thus for example, marginal cost curve cuts the average variable cost curve at the A and average variable cost curve at the point B which are the lowest point.

COST OUTPUT RELATION
Cost output relationship can be studied under two heads.
Cost output relationship in the short run
Cost output relationship in the long run
A short run is period which does not permit any alterations in fixed equipment like machinery, building etc. and in the size of the plant. Here the quality of fixed factors like the size of the plant, technology etc, is fixed and can not be varied. In the short run, variation in output is possible only within the range permitted by the existing fixed equipment. Output can be increased or decreased only by the changing the amount of variable cost. If the firm wants to change output in the short run, it can do so only by changing the amount of variable factors. In short run, the firm in the short run can change its scale of operations, but it can not change its size.

COST OUTPUT RELATION IN THE SHORT RUN
The cost output relation in the short run may be studied in term of
1) Average fixed cost
2) Average variable cost and
3) Average total cost

1) Average fixed cost and output
As said earlier, fixed costs are those cost which remain fixed in the short run irrespective of the level of output. Accordingly, as the firm increases its output, average fixed cost fall. The reason is that total fixed cost remains the same and do not change with change in output. As output increases, the total fixed cost gets spread over to more and more units and therefore average fixed cost becomes less and less. The relation between output and fixed cost is universal one for all types of business.
The average fixed cost curve slopes downwards towards the X axis in the shape of rectangular hyperbola. This will be clear from the diagram.

2) Average variable cost and Output.
The average variable cost first falls and then rises as more and more units are produced. This is because of various internal economies which the first gets in the initial stages. As we add more and more units of variable factors in a fixed plant, the efficiency of the factors first increases and then declines, in the beginning, the output is below normal capacity, that is, there is no full utilization of its productive capacity. But as output increases, by adding more and more variable factors, average variable cost fails till the firm reaches its normal capacity. That is, till it achieve full utilization of its capacity. In other words, as more and more units variable cost are added to fixed factors, the average cost declines till the firm reaches its optimum capacity. And once the optimum capacity is obtained, any further increase in the output will increase average variable cost, that is, increased output can be obtained only at a higher average variable cost.







This is also in consonance with the law of variable proportions according to which as more and more units of a variable factors are added to the fixed factors, average variable cost falls in the beginning, reaches its minimum and then start rising. The average variable cost generally U shaped. This will be clear from the diagram.

3) Average Total Cost and output
Average Total cost is also commonly known as average cost. In the beginning it falls, then remains constant and eventually rises with every increase in output. Average total cost is also U shaped .these is because of their two components average fixed cost and average variable costcurve.At very low level of output, average total; cost is high because fixed cost is spread over a few units .As output increase, fixed cost increase over more units and in addition, variable factors can be used more efficiently relative to the fixed plant. A point then is reached where average total cost is at its minimum. This point gives the optimum level of output from the cost point of view.

Diagram






After this point, average total cost rises. The rise occurs because variable factor can not be used as efficiently as before. When the advantages of lower average fixed cost is outweighed by the increase of average variable cost rises. The average total cost curve, therefore, is U shaped. This will be clear from the given on the above diagram.

EXPLANATION OF COST-OUTPUT RALATIONSHIP IN SHORT RUN THROUGH COST CURVE
The following diagram will give an idea of cost output relationship in the short run through various cost curves.










The following observation may be made from a study of the above diagram.
1) As putouts increase, average fixed cost falls and therefore its curve downward sloping curve.
2) Average variable cost at first shows a rise after a point.
3) Average total cost also decline in the beginning, reaches iota minimum and then rises. Its curve is U shaped.
4) Marginal cost curve falls in the beginning and then start rising.
5) Average variable cost rises earlier than average total cost.
6) Marginal cost curve cuts average variable cost curve and total cost curve at their lowest points.
7) The least cost level of output air at point B on the average total cost curve and at point A on the average variable cost curve.

COST OUTPUT RELATIONSHIP IN THE LONG RUN
The long run is a period which is sufficiently long enough to enable the firm to make adjustment by changing all its factor inputs. In the long run, the distinction between fixed and variable costs looses all its importance.Al cost are variable in the long run. Thus, the firm in the long run can change theory plant size, install new machinery, adopt new technology, recruit additional technical and managerial staff,.etc, In the long run, there are no fixed cost, all cost are variable. The firm can change both scale of its operation and the size of its plant.
Now, since in the long run all factor of production can be used in varying proportion, it is possible for the firm to change its scale of operation and also the size of its plant in accordance with the requirement of output. Thus by varying the size of the plant and also the scale of its operation, the firm can produce a given output at a lower average cost in the long run than in short run. It should noted that in the short run it is not possible for the firm to change their scale of operation and the size of its plant because of the availability of the factor of production. But in the long run it is possible to do so. Now each time the scale of operation is changed, we have to draw a new short run average cost curve because the old cost curve becomes out of date with the change in the scale of operation. Thus, while in the short run, we have only one average cost curve, n the long run we have many average cost curve as there as changes in the scale of operation. This will clear from following diagram.

DIAGRAM








In this diagram, we have drawn three average cost curve SRAC1, SRAC2 and SRAC3 corresponding to three scale of operation.
To begin with, let us assume that the firm is producing according to the scale of operation represented by SRAC1.In this case; the firm will produce OB output which is obtained at the lowest average cost BQ.
Now, assume that the firm wants to increase their output from OB to OC, but has no time to change the scale of operation because ii is producing in the short period. The firm than will be able to produce OC output at a higher average cost, namely CT.
But if the firm were producing in the long run and had enough time to change the scale of its operation and size, then by adopting a new scale at SRAC2, it can produce the same output at a lower average cost by CR.
Likewise, if the firm wants to reduce its output from OB to OA, than with the existing scale of operation, it can get OA output at a higher average cost of AS. But in the long run by adopting a new size of the plant, namely SRAC3, it can get the same output at a lower average cost of AP.
Thus by changing the size of its plant ad the scale of its operation, the firm can produce a given output at a lower average cost in the long run than in the short run.
We can, thus, draw a long run average cost curve which will indicates the long run cost of producing each level of output. Thus, the long run average cost curve is the envelope of the short run average cost curve. This will clear from the following diagram.










In this diagram, LARC is the long run average cost curve which is tangent to all the three short run cost curve. Thus for instant, it to SRAC at B and SRAC3 at c. It will also be seen that SRAC2 ha s lowest minimum point at Q.The optimum level of outputs obtained at point B.

CHARACTERISTIC OF LONG RUN AVERAGE COST CURVE
We can now summaries the main characteristic of the long run average cost curve as follow.
The long run average cost curve is derived from short run average cost curve .Each point on long run average cost curve is a tangent of short run average cost curve to the long run average cost curve.
The long run average cost curve is sometimes also referred to as envelope curve because it envelope all the short run cost curves,
For any output level, long run average cost curve is lower than short run because in the long run all adjustment can be made to minimize the cost. In the words, no plant on short run average cost curve ever is below the long run average cost curve.
Each short run average cost curve shows the cost of different levels of output, given the size of the plant, while long run average cost curve shows the cost after the including all the plant sizes.
The long run average cost curve like the short run average cost curves is also U shaped, but the difference, however is that long run average cost is flatter than the short run average cost curve. This is because of the following reasons.
In the long period, there is only variable cost. There is very little cost which remains fixed in the long run. Thus, longer the period under the consideration, fewer costs are fixed and more costs are variable. In the short run, if output of the firm is reduce, fixed cost can not be reduce with the result that fixed cost will be spread over a smaller output raising the average fixed cost can be reduced to some extent and therefore the average fixed cost will rise less sharply when output is increased in the long run as compared with short run. That is why U shaped of the long run average cost curve is less sharp or more pronounced or dish-shaped.

The long run average cost curve is less pronounced shows dish shaped implies that in the long run when the firm adopts a large scale of output its long run average cost in the beginning trends to decrease , at a certain point it remains constant and then it rises. This behavior of the long run average cost is attributed to the laws of returns and since returns are based on the internal economies and diseconomies of scale, the long run average cot curve traces these economies of scale. Thus, economies of scale explain the falling segment of the long run average cost curve.

Long run average cost curve is flatter because in the long run such economies are possible as cannot be had in the short run, likewise, some of the diseconomies which are faced in the short run may not have to be faced in the long run.


A still another reason may be given in terms of greater divisibility of the factors of production in the long run .In the short run, some of the factors say like machines, management,etc are indivisible and can not be used in different proportion to bring about changes in output. But in the long run, these indivisible factors do not remain completely indivisible in the long run and that explain why long run average cost curve is more flatters.

6) The minimum cost point of long run average cost curve shows the optimum production level and the optimum size of the plant.

7) The long run average cost curve is called the planning curve, because it represents the cost data which are relevant to thee firm when it is planning its policy in regard to its scale of operations, output and price over a long period of time.

REVENUE CURVES

We have discussed the above the various concepts of cost curves and their inter relationship. We also know that a firm plays the role both of a producer or a seller as a producer, the objective of a firm is to produce at the least cost. And how much the firm should produce depend among other things on the market availability for its product and the expected sales revenue in relation to the cost incurred. The equilibrium, output will be that output which gives the firm maximum profits.
The earning which a firm gets from the scale of its products are knows as revenue.



THREE CONCEPT OF REVENUE

1) TOTAL REVENUE
The total revenue may be defined as the total earning of the firm from the sale of its product. It can be obtained by multiplying the price per unit of the product sold. Thus,

TOTAL REVENUE = PRICE PER UNIT × TOTAL NUMBER OF UNIT OF THE PRODUCT SOLD

For example, the price of the product is Rs 5 per unit and the sales are 100 units, than
TOTAL REVENUE = Rs 5 * 100 = 500

2) AVERAGE REVENUE
Average revenue is the revenue per unit of the product sold. It is determined by dividing the total revenue by the number of units of the product sold. Thus,

TOTAL REVENUE
AVERAGE REVENUE = -----------------------------------------------
TOTAL NUMBER OF UNIT SOLD
If the total revenue of the firm says is 1000 and total sales are 10 units, then.

1000
AVERAGE REVENUE = -----------
100

= 10 Rs.
It should noted here that as the different units of the product are sold at the same price, average revenue and price are equal. Thus, average revenue is just the same thing as price per unit. Both are calculated by dividing the total revenue by the number of unit of the product sold. Both are equal in all circumstances and under all type of market situation. The average revenue curve is also known as the consumer’s demand curve.

MARGINAL REVENUE
Marginal revenue is the addition to the total revenue by selling an additional unit of the firm product.Algebralcally; we may say that marginal revenue is the addition to the total revenue earned by selling n +1 unit instead of n units. Thus, for example, suppose a firm earn a total revenue of Rs 1000 by selling 10 units. Now, if it sells one more unit, that is, that is 11 unit and earn Rs 1070, the marginal revenue will be Rs.70.In short, marginal revenue is the difference between total revenue when n units are a sold and the new total revenue when n + 1 units are sold.

AVERAGE REVENUE CURVE AND MARGINAL REVENUE CURVE IN PERFECT COMPETITION
In perfect competition, the average revenue curve is a straight line parallel to X axis. This is because under condition of perfect competition, no individual firm can by its own action affect the market price of the product. It has to accept the prevailing price in the market as given, it can not influence the price by its own action. At the same time, the firm can sell any number of units at the prevailing price, it has to lower the price in order to sell the additional unit of the product, because under perfect competition \\, the output of an individual firms form a very small part of the total output. Thus, the average revenue curve of a firm in perfect competition is perfectly elastic, it is a horizontal straight line parallel to X axis.
Now, since the firm sells additional unit of output at the prevailing price, marginal revenue is equal to average revenue. This will clears from the following example.

UNITS PRICE PER UNIT TOTAL REVENUE
10 2 20
11 2 22

AVERAGE REVENUE = 2Rs
MARGINAL REVENUE = 2 Rs
The marginal revenue curve therefore, coincides with the average revenue curve under perfect competition. This will be seen from the diagram given below.







AVERGE REVENUE CURVE AND MARGINAL REVENUE CURVE UNDER MONOPOLY AND MONOPOLISTIC Competitions

In monopoly and monopolistic competition however, the shape of average revenue and marginal revenues different. These are downward sloping towards the right. The main reason for this is that under condition of both, the monopoly and monopolistic, the firm has to lower the price in order to sell additional units. Accordingly, the average revenue curve is downward sloping curve and so the marginal revenue curve also falls. However, the fall in the marginal revenue curve is more rapid than the average revenue curve. In other words, under monopoly and monopolistic competition, the marginal revenue curve lies below the average revenue curve and normally slopes downwards.[/SIZE][/SIZE][/SIZE]
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Re: COST ANALYSIS
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Re: COST ANALYSIS - April 4th, 2016

Quote:
Originally Posted by cloudy222 View Post
COST ANALYSIS:

Cost is the expense incurred in producing a commodity. Cost analysis is very important for the business managers for many decision regarding profitability future expense and future revenue depend upon various types of cost. In estimating profit the managers is required to compare cost with revenue. The revenue depends upon the price of the product in the market. The business manager can not control the price prevailing in the market but he can control cost by restricting the output. The relationship between the cost and output is known as the cost function.

Thus cost function is derived from production functions. The production functions expenses the functional relationship between input and output. In simple term, the production function states that output depend upon various quantities of input. If price of inputs are known we can calculate cost of production. The cost of production of a commodity is the aggregate of price paid for the factors of production used in producing that commodity. So a firm has to engage the series of various factor of production say the land, labor and capital etc, These factors have to be rewarded by the firm for their contribution made in producing the commodity. This compensation usually in terms of factors price is generally known as cost. of production denotes the value of the factor of the production engaged for producing a given article. (Commodity)

From the above discussion two main points has been taken into consideration.
1) Cost function
2) Cost of production
A cost function expresses the relationship between cost and its determinants. Several factors influence cost. When their relationship to cost is expressed in a functional or mathematical form, it is called cost function. Symbolically

C = f (S, O, P, T … N)

Where C is cost P is price of inputs
S is size of plants T is technology
O is level of output N is no of other factors
Cost function can be formulated for the short run and long run depending upon the requirement of the firm. However, the short run and long run functions are interrelated.


DETERMINANTS OF COST FUNCTION
He following is the main determinants of a cost function:

SIZE OF PLANT:

The size of plant or the scale of production is inversely related to cost. As the size of plant increase costs decline and vice versa.



OUTPUT LEVEL:
Total output and total cost are positively related to each other. As the level of total output increase total cost also increase. As the level of output increase MC and AC decline initially and rise thereafter.

PRISE OF INPUTS
Input price are again positively related to cost. Increase in the input price brings a rise in the cost.

TECHNOLOGY:
Nature of technology also influences cost. Modern technology is cost efficient and cost saving.

MANAGERIAL AND ADMINISTRATIVE Efficiency:
Managers are the controllers and monitors of the firm. Through efficient supervision, control and administration they can improve the efficiency and productivity of factors inputs and thus minimize the cost.

COST CONCEPTS:

1) OPPORTUNITY COST:
The concept of opportunity cost occupies a very important place in modern economic analysis. The concept was first developed by an Austrian economist, WLESER. The other notable contributors are Daven Port, Knight and Robbins. The concept is based on the fundamental fact that factors of production are scares and versatile. Our wants are unlimited. The means to satisfy these wants are limited but they are capable of alternative uses. Therefore, the problem of choice arises. This is the essence of Robbins definition of economics.
The opportunity cost of anything is the alternative that has been forgone. This implies that one commodity can be produced only at the cost of foregoing the production of other commodity. In other words opportunity cost is the loss of earnings due to opportunities foregone due to scarcity of resources. If resources were unlimited there would no need to forego any income. Yielding opportunity and therefore there would be no opportunity cost.

Resources are not only scared but they have alternatives uses with different returns. Income maximizing resources owners put their scare resources to their most productive use and forgo the income expected from the second best use of the recourses.
Thus, the opportunity cost may be defined as the expected returns from the second best use of the resources forgone due to the scarcity of resources. The opportunity cost is also called alternative cost.
Fig. suppose that a person has, 1, 00,000 which he has only two alternative uses. He can either buy a computer or a typewriter. From computer he expect an annual income of, 20, 00 and from typewriter Rs 15,000. If he is profit maximizing investors, he would like invest his money in computers and forgo the expected income from the typewriter that is 15000 Rs. The opportunity cost arises because of the forgone opportunities. Thus the opportunity cost of using resources in computer, the best alternative is the expected return from the typewriter, the second best alternative. In assessing the alternative cost, both explicit and implicit cost are taken into account.

The other concept which is associated with the concept of opportunity cost is the concept of “economic rent” or” economic profit”. In our above example economic profit of the computers is the excess of its earning over the income expected from the typewriter. That is 20,000 – 15,000 = 5000.

IMPORTANCE OF THE OPPORTUNITY COST
The significance of opportunity cost is as follow:

IT HELPS IN DETERMINING RELATIVE PRISE OF GOODS.
The concept is useful in the determination of the relative price of different goods.f.e.If a given amount of factor can produce one table or three chairs, then the price of one table will tend to be three times equal to that price of one chair.

FIXATION OF REMUNERATION TO A FACTORS
The concept is also useful in fixing the price of a factor.F.g. Let’s assume that, the alternative employment of a college professor is work as an office in an insurance company at a salary of Rs 10,000 per month. In such a cases, he has to paid at least Rs 10,000 to continue to retain him in the college.

EFFICIENT ALLOCATION OF RESOURCES:
The concept is also useful in allocating the efficient resources. Suppose, opportunity cost is one table and three chair and the price of a chair is 100Rs While the price of a table is 400Rs.Under such situation, it is beneficial to produce one table rather than 3 chair because he produces 3 chair he will get only 300 Rs whereas a table fetches him Rs 400, that is Rs 100 more. Hence, it helps manager to decide what he should produce in the factory.

2) REAL COST
Real cost refers to those cost which are made to factory of production to compensate for the toil and effort in rendering their service.
According to Marshall “The exertions of all the different kind of labor that are directly or indirectly involved in making it, together with the abstinences or rather the waiting required, For saving the capital used in making it, all this sacrifices together will be called the rel cost of production of the commodity.
OR
The term real cost of production refers to the physical quantities at various factors used in producing a commodity.
OR
“The real cost of production of a commodity is expressed not in money but in effort of workers and sacrifices of capitalists undergone in the making of a commodity”

So we conclude that, real cost is computed in term of the pain and discomfort involved for labour when it is engage in production and also in the absent and sacrifice involved in capital accumulation. The concept of real cost does not carry any significance in the cost of production because it is subjective concept and lacks precision (accuracy).

3) MONEY COST
Money cost or the nominal cost of the total money expenses incurrent by a firm in producing the commodity.
OR
“Cost of production measure in terms of money is called the money cost.”
“Money cost” is the monetary expenditure on input of various kinds – raw materials, wages and salary of labour, expenditure on machinery and equipment, depreciation on machinery, building and such other capital goods, interest on capital, other expenses like advertisement. Insurance premium and taxes etc,. Required for the output. It is the money spent on purchasing the different unit of factors of production needed for the producing a commodity. Money cost is obviously the payment made for the factors in terms of money. Money cost is the outlay cost that is actual financial expenditure of the firm.

4) SUNK COST
Sunk cost is the costs that are not altered by a change in quantity and cannot be recovered. Sunk cost are a part of outlay cost.F.e.depriciation

5) INCREMENT COST
The increment costs are the addition to costs resulting from a change in product line, introduction of new product, replacement of obsolete plant and machinery etc. Conceptually increment cost are closely related to the concept of marginal cost but with a relatively wider discussion while MC refers to the cost of the marginal unit of output, incremental cost refers to the total additional cost associated with the marginal batch of output. The concept of the incremental cost is based on the fact that in the real world, it is not practicable for lack of lived of input to employ factors for each unit of output separately. Incremental cost arises owing to the change in product, replacement of worn out plant and machinery with a new one etc.

6) ACCOUNTING COST (EXPLICIT COST)
Accounting cost or explicit cost or paid out costs or contractual cash payment cost are those, which fall under actual, or business costs entered in the books of accounts. The payments for wages and salaries, material, license fee, insurance premium etc, are the example of explicit cost. These cost involve cash payment and are recorded in normal accounting practices.

7) ECONOMIC COST (IMPLICIT COST)
In contrast with the above cost , three are certain other cost which do not take the form of cash outlay, nor do they appear in the accounting system such cost are known as implicit or imputed costs. Implicit cost may be defined as the earning expected from the second best alternative use of resources. Implicit cost is not taken into account while calculating the loss or gain of the business. But the form takes the important consideration in whether or not a factor would remain in present occupation.
The explicit and implicit costs together make the economic cost.

ECONOMIC COST = IMPLIOCIT COST + EXPLICIT COST

TYPES OF PRODUCTION COST AND THEIR MEASUREMNT
Total Fixed Cost ( TFC )
Total Variable Cost ( TVC )
Total Cost ( TC )
Average Fixed Cost ( AFC )
Average Variable Cost ( AVC )
Average Total Cost (ATC ) or Average Cost (AC )
Marginal Cost ( MC )

TOTAL FIXED COST
Fixed cost are those cost of items of expenditure, which are independent of the output that they do not change with the change in output unto certain level of production? Fixed cost thus are those cost, which are, remain fixed in the short run, at whatever, it may be the level of output. These cost are not affected by changes in the volume of production up to a certain level, these have to be incurred even if the output of the firm is nil or zero. Fixed costs are
v Payment of rent for the building
v Interest on borrowed capital
v Depreciation
v Administration expenses- salaries of managerial and office staff, watchman’s salary etc
v Insurance premiums
v Property and business taxes, license fees etc...

DIAGRAM











In the following diagram, FF is the fixes cost curve, which is parallel to X-axis. The cost remains fixed at OF whether the firm produces OA or OB or OC output. Fixed costs are not fixed permanently. In order to increase the production in the long run, the firm will haven to increase the size of plant, invest more capital, recruit more technical. Etc,. Thus FC become variable in the long run, fixed cost is also known as supplementary cost.

VARIABLE COST
Variable cost are those cost which change with output.hey are the function of output. TVC=F (Q)
Thus, variable costs are those cost which rise when output is increased and fall when output is decreased. When output is nil, they are reduced to zero.
Variable costs are also known as direct costs or prime costs which can be altering in the short run as output alter. These cost include following.
Cost of raw material
Wages of labour
Fuel and power charges
Excise duties, sales tax etc.









In this diagram, “OV” is the variable cost curve. The variable cost increase with increase in output. Thus for example when output is OA the variable cost is OE it increase to OF and OG as output increase to OB and OC respectively.

COMPERISON OF FC AND VC
1) FC is fixed while VC changes with the change in output.
2) During short period FC cannot be changed while VC can be changed.
3) FC curve is parallel to X- axis whereas VC curves slops up to the right.

TOTAL COST
TC refers the value of total resources requirement for the production of goods and services. It refers to the total outlays of money expenditure, on the resources used to produce a given level of output. It includes both fixed and variable costs. The total cost for a given output is given by the cost function.
TFC is the total expenditure by the firm for fixes inputs.
TVC is the firm’s total expenditure on variable inputs used to carry out production. Since higher output levels require greater utilization of variable inputs, they mean higher total variable cost.
TC is the sum of total fixed cost and total variable cost. Thus
TC = TFC + TVC where TC = Total cost
TFC = Total Fixed Cost
TVC = Total Variable Cost
It should be noted that, TFC is the some irrespective of the level of output. Therefore, a change in total cost is influenced by the change in variable cost only. The relationship between TFC, TVC and TC is shown in the following diagram.
DIAGRAM








In the diagram, the total cost curve TC has been obtained by adding TFC curve and TVC curve.

AVERAGE FIXED COST ( AFC )
The AFC is the fixes cost per unit of output. The more the units are produces, per unit cost on fixed factor falls. So we can say that per unit of cost on fixed factors is called AFC. It is obtained by dividing the total fixed cost by the number of unit of the commodity produced.
Symbolically

TFC
AFC = ----------- Where TFC = Total Fixed Cost
TQ TQ = Total Quantity

OR

AFC = AC- AVC
Where AC = Average cost
AVC = Average variable cost
The shape of the AFC is as follows.








It will be seen from this diagram that the AFC curve slops downwards through out its length. As output increases, the TFC get spread over to more and more units and therefore AFC became less and less. This continues falling of AFC as output expands are business people commonly called “Spreading the overhead”.
It should, however be noted that although the AFC curve sp downwards towards the X-axis, but it will never touch it because AFC can not be zero, how so ever large the level of output may be. Likewise, this curve will not touch the y axis also, because TFC is a positive value at zero output and any output and any positive value divided by zero will provide infinite value.
Thus the shape of the Arc curve therefore is a rectangular hyperbola.

AVERAGE VARIABLE COST
Average variable cost is the total variable cost devoted by the units of output.

Total Variable Cost
AVC = -------------------------
Total Quantity

Where the Q stands for the number of units of the product. Thus, the average variable cost is variable cost per unit of output.







It will see from this diagram that he average variable cost curve declines in the beginning up to the point – P and then start rising sharply after this point. This is so because in the beginning the output is below the normal capacity of the firm. AS the output increase and reach the normal capacity, the average cost per unit declines till the point.
P where it is the lowest. Since he output reaches the normal capacity at P, the variable cost per unit is the minimum or the lowest at this point. But when the output increase beyond the normal capacity of the firm, the variable cost per unit shows a sharp rise and goes on increasing with every increase in output.
These phenomena can also be explained with the help of the Law of variable proportion. The average variable cost is subject to the operation of this law. Thus for example. In the above diagram, up to the point P, it is the law of increasing returns which is in operation. The result is that average variable cost goes on diminishing up to this point. At the point P, the average variable cost gets stabilized on account of the operation of the law of diminishing returns.
The average variable cost curve generally U shaped.

6) AVERAGE TOTAL COST
Average total cost or what it simply called average cost is the total cost divided by total units of outputs. Thus,
Total Cost
Average Total Cost of Average Cost = -------------
Q
Where Q stands for the number of units of the product.
The average cost can also be computed simply by adding average fixed cost to the average variable cost. Thus

Average Total Cost = Average Fixed Cost + Average Variable Cost

It should be noted here that the behaviors of the average total cost curve depend upon the behaviors of the average fixed cost curve and average variable cost curve. In this connection, following observation may be made:
In the beginning when both AVC curve and AFC curve fall, the average total cost curve falls sharply.
When an average variable cost rises, but average fixed cost curve falls, the average total cost curve continues to fall because here the fall in the AFC curve is more than the rise in AVC curve.
DIAGRAM








But as out put increase here is a sharp rise in AVC which more than offsets the fall in AFC Therefore ATC curve raises after a point. In other words, ATC curve like the AVC curve first falls reaches its minimum and than rises. The ATC curve is therefore, almost of U shaped. This would be clear from the given on above diagram.

7) MARGINAL COST
Marginal cost is the addition to the total cost incurred by the producing an additional unit of output. It may also be defined as the cost of producing an additional unit. Thus, marginal cost is the addition to the total cost of producing n units instead of n – 1 unit.

MC = TCn – TC n – 1

Where MC = Marginal Cost
TC = Total Cost
N = Number of unit of output
Marginal cost can also be calculated by dividing the change in the total cost by the one unit change in output. Thus,

∆ TC
MC = ----------
∆1 Q
Where ∆ denotes change in output but output is assumed to change by 1 unit only and hence output change is denoted by ∆1.
It should also note here that marginal cost is the cost of producing an additional unit of output and not of average product. It indicates change in total cost as a result of producing an additional unit of output.
Further it has to be remembered that marginal cost is independent of the amount of fixed cost in the short run. Since fixed cost do not change with output and remain constant through out. There is no marginal fixed cost when output increased in the short run. It is only the variable cost that varies with the output in the short run. Change in marginal cost therefore, due to change in the variable cost. Marginal cost is not affected by the amount of the fixed cost. Thus marginal cost may also be defined as a change in total variable cost when one additional unit is produce. It can be calculated with reference to a change I the total variable as under:

MCn = TVCn –TVC n-1

Where 1) Mc is the marginal cost of producing n numbers of units.
2) TVCn is the total variable cost of producing n units.
3) TVC n-1 is the total variable cost of producing “n” minus one unit.

SHAPE OF THE MARGINAL COST CURVE
The marginal cost surve like the average cost curve falls in the beginning reaches its minimum and then starts rising .The fall in the marginal cost curve in the beginning is because of the operation of the law of increasing returns and its rise after a point is because of the operation of the law of diminishing returns. This would be clear from the following diagram.
DIAGRAM








The concept of marginal cost is of great importance in price theory. This concept along with the concept of marginal revenue helps the firm in deciding the size of its output. The firm will earn maximum profit at that point where the revenue earn from the marginal unit is equal to the cost incurred on that unit. In other words, equality of marginal cost and marginal revenue indices the points of profit maximization and consequently equilibrium of the firm.

RELATION BETWEEN AVERAGE COST AND MARGINAL COST
The relation between average cost and marginal cost will be clear from the following diagram which shows both these curves.







The following observation may be made from the above diagram.
1) When average cost is fill-in, marginal cost is lower than the average cost. Hence, the marginal cost curve is below his average cost curve.
2) When average cost is rising, marginal cost is higher than average cost and therefore the marginal cost curve is above the average cost curve.
3) When it comes to falling , marginal cost curve falls more rapidly than the average cost curve and when it comes into rising marginal cost curve rises more rapidly then the average cost curve.
4) When average cost is minimum, marginal cost and average cost are equal. At this point, the marginal cost curve cuts the average cost curve from the lowest point.

RELATION BETWEEN MARGINAL COST AND AVERAGE FIXED COST, AVERAGE VARIABLE COST AND AVERAGE VARIABLE COST.

The relation between marginal cost and average fixed cost, average variable cost and average total cost shall be clear from a study of the following diagram.






The following observation may be made from the following diagram.
!) Average cost curve is a downward sloping curve in the shape of a rectangular hyperbola.
2) Average variable cost curve at first falls and than rises.
3) Average total cost curve which is sum of average fixed and average variable cost curve is U shaped curve.
4) Marginal cost curve, after showing an initial fall rises continuously thereafter.
5) Average fixed cost curve, however, bears a definite relationship with average variable cost curve and average total cost curve. It cuts both these curves at their lowest points. Thus for example, marginal cost curve cuts the average variable cost curve at the A and average variable cost curve at the point B which are the lowest point.

COST OUTPUT RELATION
Cost output relationship can be studied under two heads.
Cost output relationship in the short run
Cost output relationship in the long run
A short run is period which does not permit any alterations in fixed equipment like machinery, building etc. and in the size of the plant. Here the quality of fixed factors like the size of the plant, technology etc, is fixed and can not be varied. In the short run, variation in output is possible only within the range permitted by the existing fixed equipment. Output can be increased or decreased only by the changing the amount of variable cost. If the firm wants to change output in the short run, it can do so only by changing the amount of variable factors. In short run, the firm in the short run can change its scale of operations, but it can not change its size.

COST OUTPUT RELATION IN THE SHORT RUN
The cost output relation in the short run may be studied in term of
1) Average fixed cost
2) Average variable cost and
3) Average total cost

1) Average fixed cost and output
As said earlier, fixed costs are those cost which remain fixed in the short run irrespective of the level of output. Accordingly, as the firm increases its output, average fixed cost fall. The reason is that total fixed cost remains the same and do not change with change in output. As output increases, the total fixed cost gets spread over to more and more units and therefore average fixed cost becomes less and less. The relation between output and fixed cost is universal one for all types of business.
The average fixed cost curve slopes downwards towards the X axis in the shape of rectangular hyperbola. This will be clear from the diagram.

2) Average variable cost and Output.
The average variable cost first falls and then rises as more and more units are produced. This is because of various internal economies which the first gets in the initial stages. As we add more and more units of variable factors in a fixed plant, the efficiency of the factors first increases and then declines, in the beginning, the output is below normal capacity, that is, there is no full utilization of its productive capacity. But as output increases, by adding more and more variable factors, average variable cost fails till the firm reaches its normal capacity. That is, till it achieve full utilization of its capacity. In other words, as more and more units variable cost are added to fixed factors, the average cost declines till the firm reaches its optimum capacity. And once the optimum capacity is obtained, any further increase in the output will increase average variable cost, that is, increased output can be obtained only at a higher average variable cost.







This is also in consonance with the law of variable proportions according to which as more and more units of a variable factors are added to the fixed factors, average variable cost falls in the beginning, reaches its minimum and then start rising. The average variable cost generally U shaped. This will be clear from the diagram.

3) Average Total Cost and output
Average Total cost is also commonly known as average cost. In the beginning it falls, then remains constant and eventually rises with every increase in output. Average total cost is also U shaped .these is because of their two components average fixed cost and average variable costcurve.At very low level of output, average total; cost is high because fixed cost is spread over a few units .As output increase, fixed cost increase over more units and in addition, variable factors can be used more efficiently relative to the fixed plant. A point then is reached where average total cost is at its minimum. This point gives the optimum level of output from the cost point of view.

Diagram






After this point, average total cost rises. The rise occurs because variable factor can not be used as efficiently as before. When the advantages of lower average fixed cost is outweighed by the increase of average variable cost rises. The average total cost curve, therefore, is U shaped. This will be clear from the given on the above diagram.

EXPLANATION OF COST-OUTPUT RALATIONSHIP IN SHORT RUN THROUGH COST CURVE
The following diagram will give an idea of cost output relationship in the short run through various cost curves.










The following observation may be made from a study of the above diagram.
1) As putouts increase, average fixed cost falls and therefore its curve downward sloping curve.
2) Average variable cost at first shows a rise after a point.
3) Average total cost also decline in the beginning, reaches iota minimum and then rises. Its curve is U shaped.
4) Marginal cost curve falls in the beginning and then start rising.
5) Average variable cost rises earlier than average total cost.
6) Marginal cost curve cuts average variable cost curve and total cost curve at their lowest points.
7) The least cost level of output air at point B on the average total cost curve and at point A on the average variable cost curve.

COST OUTPUT RELATIONSHIP IN THE LONG RUN
The long run is a period which is sufficiently long enough to enable the firm to make adjustment by changing all its factor inputs. In the long run, the distinction between fixed and variable costs looses all its importance.Al cost are variable in the long run. Thus, the firm in the long run can change theory plant size, install new machinery, adopt new technology, recruit additional technical and managerial staff,.etc, In the long run, there are no fixed cost, all cost are variable. The firm can change both scale of its operation and the size of its plant.
Now, since in the long run all factor of production can be used in varying proportion, it is possible for the firm to change its scale of operation and also the size of its plant in accordance with the requirement of output. Thus by varying the size of the plant and also the scale of its operation, the firm can produce a given output at a lower average cost in the long run than in short run. It should noted that in the short run it is not possible for the firm to change their scale of operation and the size of its plant because of the availability of the factor of production. But in the long run it is possible to do so. Now each time the scale of operation is changed, we have to draw a new short run average cost curve because the old cost curve becomes out of date with the change in the scale of operation. Thus, while in the short run, we have only one average cost curve, n the long run we have many average cost curve as there as changes in the scale of operation. This will clear from following diagram.

DIAGRAM








In this diagram, we have drawn three average cost curve SRAC1, SRAC2 and SRAC3 corresponding to three scale of operation.
To begin with, let us assume that the firm is producing according to the scale of operation represented by SRAC1.In this case; the firm will produce OB output which is obtained at the lowest average cost BQ.
Now, assume that the firm wants to increase their output from OB to OC, but has no time to change the scale of operation because ii is producing in the short period. The firm than will be able to produce OC output at a higher average cost, namely CT.
But if the firm were producing in the long run and had enough time to change the scale of its operation and size, then by adopting a new scale at SRAC2, it can produce the same output at a lower average cost by CR.
Likewise, if the firm wants to reduce its output from OB to OA, than with the existing scale of operation, it can get OA output at a higher average cost of AS. But in the long run by adopting a new size of the plant, namely SRAC3, it can get the same output at a lower average cost of AP.
Thus by changing the size of its plant ad the scale of its operation, the firm can produce a given output at a lower average cost in the long run than in the short run.
We can, thus, draw a long run average cost curve which will indicates the long run cost of producing each level of output. Thus, the long run average cost curve is the envelope of the short run average cost curve. This will clear from the following diagram.










In this diagram, LARC is the long run average cost curve which is tangent to all the three short run cost curve. Thus for instant, it to SRAC at B and SRAC3 at c. It will also be seen that SRAC2 ha s lowest minimum point at Q.The optimum level of outputs obtained at point B.

CHARACTERISTIC OF LONG RUN AVERAGE COST CURVE
We can now summaries the main characteristic of the long run average cost curve as follow.
The long run average cost curve is derived from short run average cost curve .Each point on long run average cost curve is a tangent of short run average cost curve to the long run average cost curve.
The long run average cost curve is sometimes also referred to as envelope curve because it envelope all the short run cost curves,
For any output level, long run average cost curve is lower than short run because in the long run all adjustment can be made to minimize the cost. In the words, no plant on short run average cost curve ever is below the long run average cost curve.
Each short run average cost curve shows the cost of different levels of output, given the size of the plant, while long run average cost curve shows the cost after the including all the plant sizes.
The long run average cost curve like the short run average cost curves is also U shaped, but the difference, however is that long run average cost is flatter than the short run average cost curve. This is because of the following reasons.
In the long period, there is only variable cost. There is very little cost which remains fixed in the long run. Thus, longer the period under the consideration, fewer costs are fixed and more costs are variable. In the short run, if output of the firm is reduce, fixed cost can not be reduce with the result that fixed cost will be spread over a smaller output raising the average fixed cost can be reduced to some extent and therefore the average fixed cost will rise less sharply when output is increased in the long run as compared with short run. That is why U shaped of the long run average cost curve is less sharp or more pronounced or dish-shaped.

The long run average cost curve is less pronounced shows dish shaped implies that in the long run when the firm adopts a large scale of output its long run average cost in the beginning trends to decrease , at a certain point it remains constant and then it rises. This behavior of the long run average cost is attributed to the laws of returns and since returns are based on the internal economies and diseconomies of scale, the long run average cot curve traces these economies of scale. Thus, economies of scale explain the falling segment of the long run average cost curve.

Long run average cost curve is flatter because in the long run such economies are possible as cannot be had in the short run, likewise, some of the diseconomies which are faced in the short run may not have to be faced in the long run.


A still another reason may be given in terms of greater divisibility of the factors of production in the long run .In the short run, some of the factors say like machines, management,etc are indivisible and can not be used in different proportion to bring about changes in output. But in the long run, these indivisible factors do not remain completely indivisible in the long run and that explain why long run average cost curve is more flatters.

6) The minimum cost point of long run average cost curve shows the optimum production level and the optimum size of the plant.

7) The long run average cost curve is called the planning curve, because it represents the cost data which are relevant to thee firm when it is planning its policy in regard to its scale of operations, output and price over a long period of time.

REVENUE CURVES

We have discussed the above the various concepts of cost curves and their inter relationship. We also know that a firm plays the role both of a producer or a seller as a producer, the objective of a firm is to produce at the least cost. And how much the firm should produce depend among other things on the market availability for its product and the expected sales revenue in relation to the cost incurred. The equilibrium, output will be that output which gives the firm maximum profits.
The earning which a firm gets from the scale of its products are knows as revenue.



THREE CONCEPT OF REVENUE

1) TOTAL REVENUE
The total revenue may be defined as the total earning of the firm from the sale of its product. It can be obtained by multiplying the price per unit of the product sold. Thus,

TOTAL REVENUE = PRICE PER UNIT × TOTAL NUMBER OF UNIT OF THE PRODUCT SOLD

For example, the price of the product is Rs 5 per unit and the sales are 100 units, than
TOTAL REVENUE = Rs 5 * 100 = 500

2) AVERAGE REVENUE
Average revenue is the revenue per unit of the product sold. It is determined by dividing the total revenue by the number of units of the product sold. Thus,

TOTAL REVENUE
AVERAGE REVENUE = -----------------------------------------------
TOTAL NUMBER OF UNIT SOLD
If the total revenue of the firm says is 1000 and total sales are 10 units, then.

1000
AVERAGE REVENUE = -----------
100

= 10 Rs.
It should noted here that as the different units of the product are sold at the same price, average revenue and price are equal. Thus, average revenue is just the same thing as price per unit. Both are calculated by dividing the total revenue by the number of unit of the product sold. Both are equal in all circumstances and under all type of market situation. The average revenue curve is also known as the consumer’s demand curve.

MARGINAL REVENUE
Marginal revenue is the addition to the total revenue by selling an additional unit of the firm product.Algebralcally; we may say that marginal revenue is the addition to the total revenue earned by selling n +1 unit instead of n units. Thus, for example, suppose a firm earn a total revenue of Rs 1000 by selling 10 units. Now, if it sells one more unit, that is, that is 11 unit and earn Rs 1070, the marginal revenue will be Rs.70.In short, marginal revenue is the difference between total revenue when n units are a sold and the new total revenue when n + 1 units are sold.

AVERAGE REVENUE CURVE AND MARGINAL REVENUE CURVE IN PERFECT COMPETITION
In perfect competition, the average revenue curve is a straight line parallel to X axis. This is because under condition of perfect competition, no individual firm can by its own action affect the market price of the product. It has to accept the prevailing price in the market as given, it can not influence the price by its own action. At the same time, the firm can sell any number of units at the prevailing price, it has to lower the price in order to sell the additional unit of the product, because under perfect competition \\, the output of an individual firms form a very small part of the total output. Thus, the average revenue curve of a firm in perfect competition is perfectly elastic, it is a horizontal straight line parallel to X axis.
Now, since the firm sells additional unit of output at the prevailing price, marginal revenue is equal to average revenue. This will clears from the following example.

UNITS PRICE PER UNIT TOTAL REVENUE
10 2 20
11 2 22

AVERAGE REVENUE = 2Rs
MARGINAL REVENUE = 2 Rs
The marginal revenue curve therefore, coincides with the average revenue curve under perfect competition. This will be seen from the diagram given below.







AVERGE REVENUE CURVE AND MARGINAL REVENUE CURVE UNDER MONOPOLY AND MONOPOLISTIC Competitions

In monopoly and monopolistic competition however, the shape of average revenue and marginal revenues different. These are downward sloping towards the right. The main reason for this is that under condition of both, the monopoly and monopolistic, the firm has to lower the price in order to sell additional units. Accordingly, the average revenue curve is downward sloping curve and so the marginal revenue curve also falls. However, the fall in the marginal revenue curve is more rapid than the average revenue curve. In other words, under monopoly and monopolistic competition, the marginal revenue curve lies below the average revenue curve and normally slopes downwards.[/SIZE][/SIZE][/SIZE]
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Please check attachment for Cost Analysis Step by Step by David H. Greenberg, so please download and check it.
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