THEORY OF COST
Cost Theory
Introduction:
The firm’s costs determine its supply. Supply along with demand determines price. To understand the process of price determination and the forces behind supply, we must understand the nature of costs. We study some important concepts of costs, and traditional and modern theories of cost.
Cost concepts:
Costs are very important in business decision-making. Cost of production provides the floor to pricing. It helps managers to take correct decisions, such as what price to quote, whether to place a particular order for inputs or not whether to abandon or add a product to the existing product line and so on.
Ordinarily, costs refer to the money expenses incurred by a firm in the production process. But in economics, cost is used in a broader sense. Here, costs include imputed value of the entrepreneur’s own resources and services, as well as the salary of the owner-manager.
There are various concepts of cost that a firm considers relevant under various circumstances. To make a better business decision, it is essential to know the fundamental differences and uses of the main concepts of cost.
Accounting and Economic Costs:
Money costs are the total money expenses incurred by a firm in producing a commodity. They include wages and salaries of labour; cost of raw materials; expenditures on machines and equipment; depreciation and obsolescence charges on machines; buildings and other capital goods; rent on buildings; interest on capital borrowed; expenses on power, light, fuel, advertisement and transportation; insurance charges, and all types of taxes.
There are the accounting costs which an entrepreneur takes into consideration in making payments to the various factors of production. These money costs are also known as explicit costs that an accountant records in the firm’s books. But there are other types of economic costs called implicit costs. Implicit costs are the imputed value of the entrepreneur’s own resources and services.
The salary of the owner-manager who is content with having normal profits but does not receive any salary, estimated rent of the building if it belongs to the entrepreneur, and interest on capital invested by the entrepreneur himself at the market rate of interest. Thus economic costs include accounting costs plus implicit costs, that is, both explicit and implicit costs.
Production Costs:
The total costs of production of a firm are divided into total variable costs and total fixed costs. The total variable costs are those expenses of production which change with the change in the firm’s output. Larger output requires larger inputs of labour, raw materials, power; fuel, etc. which increase the expenses of production. When output is reduced, variable costs also diminish. They cease when production stops altogether. Marshall called these variable costs as prime costs of production.
The total fixed costs, called supplementary costs by Marshall, are those expenses of production which do not change with the change in output. They are rent and interest payments, depreciation charges, wages and salaries of the permanent staff, etc. Fixed costs have to be incurred by the firm, even if it stops production temporarily. Since these costs are over and above the usual expenses of production, they are described as overhead costs in business parlance.
Actual Costs and Opportunity Costs:
Actual costs refer to the costs which a firm incurs for acquiring inputs or producing a good and service such as the cost of raw materials, wages, rent, interest, etc. The total money expenses recorded in the books of accounts are the actual costs.
Opportunity cost is the cost of sacrifice of the best alternative foregone in the production of a good or service. Since resources are scarce, they cannot be used to produce all things simultaneously. Therefore, if they are used to produce one thing, they have to be withdrawn from other uses. Thus the cost of the one is the alternative forgone. It is the opportunity missed or alternative forgone in having one thing rather than the other or in putting a factor-service to one use instead of the other.
The cost of using land for wheat growing is the value of alternative crop that could have been grown on it. The real cost of labour is what it could get in some alternative employment. The cost of capital to the capitalist is the amount of interest he could earn elsewhere. The normal earnings of management are what an entrepreneur could earn as a manager in some other joint stock company. In this way, opportunity cost is the cost of the opportunity missed or alternative forgone.
Importance of Opportunity Cost:
The concept of opportunity cost is very important in the following areas of managerial decision making:
(i) Decision-Making and Efficient Resource Allocation:
The concept of opportunity cost is very important for rational decision-making by the producer. Suppose, a producer has to decide whether he should produce black and white T.V. or colour T.V. from his given resources. He can come to rational decision only by measuring opportunity cost of production of both types of T.V. and by comparing these products with existing market prices.
As a result, efficient allocation of resources will also be possible. A resource will always be used in that business where it will have the highest opportunity cost. For example, if a graduate is receiving Rs. 3,000 as a shop assistant but can earn Rs. 5,000 as a clerk, then he will join the job of a clerk leaving the shop because his opportunity cost is high.
(ii) Determination of Relative Prices of Goods:
If the same group of resources can produce either a colour T.V. or four black and white T. V.s, the price of a colour T.V. will be kept equal to at least a four-fold price of a black and white T.V. Hence, the concept of opportunity cost is useful in the determination of relative prices of various goods.
(iii) Determination of Normal Remuneration of a Factor:
Opportunity cost determines the price for the best alternative use of a factor of production. Suppose a manager can earn Rs. 20,000 per month as a lecturer in a management school, the firm will have to pay him at least Rs. 20,000 for continuing his service as a manager.
Hence, it is obvious that the concept of opportunity cost has special importance in management.
Direct Costs and Indirect Costs:
Direct costs are the costs that have direct relationship with a unit of operation, i.e., they can be easily and directly identified or attributed to a particular product, operation or plant. For example, the salary of a branch manager, when the branch is a costing unit, is a direct cost. Direct costs directly enter into the cost of production but retain their separate identity.
On the other hand, indirect costs are those costs whose source cannot be easily and definitely traced to a plant, a product, a process or a department, such as electricity, stationery and other office expenses, depreciation on building, decoration expenses, etc. All the direct costs are variable because they are linked to a particular product or department. Therefore, they vary with changes in them. On the contrary, indirect costs may or may not be variable.
Private and Social Costs:
Private costs are the costs incurred by a firm in producing a commodity or service. These^ include both explicit and implicit costs. However, the production activities of a firm may lead to economic benefit or harm for others. For example, production of commodities like steel, rubber and chemicals, pollutes the environment which leads to social costs.
On the other hand, production of such services as education, sanitation services, park facilities, etc. leads to social benefits. Take for instance, education which not only provides higher incomes and other satisfactions to the recipients but also more enlightened citizens to the society. If we add together the private costs of production and economic damage upon others such as environmental pollution, etc., we arrive at social costs.
Incremental Costs and Sunk Costs:
Incremental costs denote the total additional costs associated with the marginal batch of output. These costs are the additions to costs resulting from a change in the nature and level of business activity, e.g., change in product line or output level, adding or replacing a machine, changes in distribution channels, etc. In the long-run, firms expand their production, employ more men, materials, machinery and equipment. All these expenses are incremental costs.
Sunk costs are the costs that are not affected or altered by a change in the level or nature of business activity. It cannot be altered, increased or decreased by varying the level of activity or the rate of output. All past or actual costs are regarded as sunk costs. Thus, sunk costs are irrelevant for decision making as they do not vary with the changes expected for future by the management, whereas incremental costs are relevant to the management for business making.
Explicit Costs and Implicit Costs:
Explicit costs are those payments that must be made to the factors hired from outside the control of the firm. They are the monetary payments made by the entrepreneur for purchasing or hiring the services of various productive factors which do not belong to him. Such payments as rent, wages, interest, salaries, payment for raw materials, fuel, power, insurance premium, etc. are examples of explicit costs.
Implicit costs refer to the payments made to the self-owned resources used in production. They are the earnings of owner’s resources employed in their best alternative uses. For example, a businessman utilises his services in his own business leaving his job as a manager in a company.
Thus, he foregoes his salary as a manager. This loss of salary becomes an implicit cost of his own business. Implicit costs are also known as imputed costs. They are important for calculation of profit and loss account. They play a crucial role in the analysis of business decisions.
Incremental Costs and Marginal Costs
There is close relation between marginal cost and incremental cost. But they have difference also. In reality, incremental cost is used in a broad sense in relation to marginal cost. Marginal cost is the cost of producing an additional unit of output, while incremental cost is defined as the change in cost resulting from a change in business activities.
In other words, incremental cost is the total additional cost related to marginal quantity of output. The concept of incremental cost is very important in the business world because, in practice, it is not possible to use every unit of input separately.
The Cost Function:
The cost function expresses a functional relationship between total cost and factors that determine it. Usually, the factors that determine the total cost of production (C) of a firm are the output (0, the level of technology (T), the prices of factors (Pf) and the fixed factors (F). Symbolically, the cost function becomes
C=f (Q, T, Pf, F)
Such a comprehensive cost function requires multi-dimensional diagrams which are difficult to draw. In order to simplify the cost analysis, certain assumptions are made. It is assumed that a firm produces a single homogeneous good (q) with the help of certain factors of production. Some of these factors are employed in fixed quantities whatever the level of output of the firm in the short run. So they are assumed to be given.
The remaining factors are variable whose supply is assumed to be known and available at fixed market prices. Further, the technology which is used for the production of the good is assumed to be known and fixed. Lastly, it is assumed that the firm adjusts the employment of variable factors in such a manner that a given output Q of the good q is obtained at the minimum total cost, C.
Thus the total cost function is expressed as:
C=f (Q)
Which means that the total cost (C) is a function if) of output (Q), assuming all other factors as constant. The cost function is shown diagrammatically by a total cost (TC) curve. The TC curve is drawn by taking output on the horizontal axis and total cost on the vertical axis, as shown in Figure 1.
It is a continuous curve whose shape shows that with increasing output total cost also increases. The total cost function and the TC curve relate total cost to output under given conditions. But if any of the given conditions such as the technique of production change, the cost function is changed.
For instance, if there is an improved technique of production, the cost of production for any given output will be less than before which will shift the new cost curve TС1below the old curve TC, as shown in Figure 1. On the other hand, if the prices of factors rise, the cost of production will increase which will shift the cost curve upwards from TC to TС2 as shown in Figure 1.
Cost-Output Relation:
The Cost-output relation is discussed in the traditional and modem theories of costs under the short-run and long-run cost analysis which are explained as under.
The Traditional Theory of Costs:
The traditional theory of costs analyses the behaviour of cost curves in the short run and the long run and arrives at the conclusion that both the short run and the long run curves are U-shaped but the long-run cost curves are flatter than the short-run cost curves.
(A) Firm’s Short-Run Cost Curves:
The short run is a period in which the firm cannot change its plant, equipment and the scale of organisation. To meet the increased demand, it can raise output by hiring more labour and raw materials or asking the existing labour force to work overtime.
Short-Run Total Costs:
The scale of organisation being fixed, the short-run total costs are divided into total fixed costs and total variable costs:
TC = TFC + TVC
Total Costs or TC:
Total costs are the total expenses incurred by a firm in producing a given quantity of a commodity. They include payments for rent, interest, wages, taxes and expenses on raw materials, electricity, water, advertising, etc.
Total Fixed Costs or TFC:
Are those costs of production that do not change with output. They are independent of the level of output. In fact, they have to be incurred even when the firm stops production temporarily. They include payments for renting land and buildings, interest or borrowed money, insurance charges, property tax, depreciation, maintenance expenditures, wages and salaries of the permanent staff, etc. They are also called overhead costs.
Total Variable Costs or TVC:
Are those costs of production that change directly with output. They a rise when output increases, and fall when output declines. They include expenses on raw materials, power, water, taxes, hiring of labour, advertising etc., They are also known as direct costs.
The relation between total costs, variable costs and fixed costs is presented in Table 1, where column (1) indicates different levels of output from 0 to 10 units. Column (2) indicates that total fixed costs remain at Rs. 300 at all levels of output. Column (3) shows total variable costs which are zero when output is nothing and they continue to increase with the rise in output.
In the beginning they rise quickly, and then they slow down as the firm enjoys economies of large scale production with further increases in output and later on due to diseconomies of production, the variable costs start rising rapidly. Column (4) relates to total costs which are the sum of columns (2), and (3) i.e., TC – TFC + TVC. Total costs vary with total variable costs when the firm starts production.
The curves relating to these three total costs are shown diagrammatically in Figure 2. The TC curve is a continuous curve which shows that with increasing output total costs also increase. This curve cuts the vertical axis at a point above the origin and rises continuously from left to right. This is because even when no output is produced, the firm has to incur fixed costs.
The TFC curve is shown as parallel to the output axis because total fixed costs are the same (Rs. 300) whatever the level of output. The TVC curve has an inverted-S shape and starts from the origin О because when output is zero, the TVCs are also zero. They increase as output increases.
So long as the firm is using less variable factors in proportion to the fixed factors, the total variable costs rise at a diminishing rate. But after a point, with the use of more variable factors in proportion to the fixed factors, they rise steeply because of the application of the law of variable proportions. Since the TFC curve is a horizontal straight line, the TC curve follows the TVC curve at an equal vertical distance.
Short-Run Average Costs:
In the short run analysis of the firm, average costs are more important than total costs. The units of output that a firm produces do not cost the same amount to the firm. But they must be sold at the same price. Therefore, the firm must know the per unit cost or the average cost. The short-run average costs of a firm are the average fixed costs, the average variable costs, and the average total costs.
Average Fixed Costs or AFC equal total fixed costs at each level of output divided by the number of units produced:
AFC = TFC /Q
The average fixed costs diminish continuously as output increases. This is natural because when constant total fixed costs are divided by a continuously increasing unit of output, the result is continuously diminishing average fixed costs. Thus the AFC curve is a downward sloping curve which approaches the quantity axis without touching it, as shown in Figure 3. It is a rectangular hyperbola.
Short-Run Average Variable Costs (or SAVC) equal total variable costs at each level of output divided by the number of units produced:
SAVC = TVC/Q
The average variable costs first decline with the rise in output as larger quantities of variable factors is applied to fixed plant and equipment. But eventually they begin to rise due to the law of diminishing returns. Thus the SAVC curve is U-shaped, as shown in Figure 3.
Short-Run Average Total Costs (or SATC or SAC) are the average costs of producing any given output.
They are arrived at by dividing the total costs at each level of output by the number of units produced:
SAC or SATC = TC/Q TFC/Q + TVC/Q = AFC+ AVC
Average total costs reflect the influence of both the average fixed costs and average variable costs. At first average total costs are high at low levels of output because both average fixed costs and average variable costs are large. But as output increases, the average total costs fall sharply because of the steady decline of both average fixed costs and average variable costs till they reach the minimum point.
This results from the internal economies, from better utilisation of existing plant, labour, etc. The minimum point В in the figure represents optimal capacity. As production is increased after this point, the average total costs rise quickly because the fall in average fixed costs is negligible in relation to the rising average variable costs.
The rising portion of the SAC curve results from producing above capacity and the appearance of internal diseconomies of management, labour, etc. Thus the SAC curve is U- shaped, as shown in Figure 3.
Why is SAC curve U-shaped?
The U-shape of the SAC curve can also be explained in terms of the law of variable proportions. This law tells that when the quantity of one variable factor is changed while keeping the quantities of other factors fixed, the total output increases but after some time it starts declining.
Machines, equipment and scale of production are the fixed factors of a firm that do not change in the short run. ’On the other hand, factors like labour and raw materials are variable. When increasing quantities of variable factors are applied on the fixed factors, the law of variable proportions operates.
When, say the quantities of a variable factor like labour are increased in equal quantities, production rises till fixed factors like machines, equipment, etc. are used to their maximum capacity. In this stage, the average costs of the firm continue to fall as output increases because it operates under increasing returns.
Due to the operation of the law of increasing returns when the variable factors are increased further, the firm is able to work the machines to their optimum capacity. It produces the optimum output and its average costs of production will be the minimum which is revealed by the minimum point of the SAC curve, point В in Figure 3.
It the firm tries to raise output after this point by increasing the quantities of the variable factors, the fixed factors like machines would be worked beyond their capacity. This would lead to diminishing returns. The average costs will start rising rapidly. Hence, due to the working of the law of variable proportions the short-run AC curve is U-shaped.
Short Run Marginal Cost:
A fundamental concept for the determination of the exact level of output of a firm is the marginal cost.
Marginal cost is the addition to total cost by producing an additional unit of output:
SMC = ∆ТС/∆Q
Algebraically, it is the total cost of n + 1 units minus the total cost of n units of output MCn = TCn+1 – TCn. Since total fixed costs do not change with output, therefore, marginal fixed cost is zero. So marginal cost can be calculated either from total variable costs or total costs. The result would be the same in both the cases. As total variable costs or total costs first fall and then rise, marginal cost also behaves in the same way. The SMC curve is also U-shaped, as shown in Figure 3.
Conclusion:
Thus the short-run cost curves of a firm are the SAVC curve, the AFC curve, the SAC curve and the SMC curve. Out of these four curves, the AFC curve is insignificant for the determination of the firm s exact output and is, therefore, generally neglected.
(B) Firm’s Long-Run Cost Curves:
In the long run, there are no fixed factors of production and hence no fixed costs. The firm can change its size or scale of plant and employ more or less inputs. Thus in the long run all factors are variable and hence all costs are variable.
The long run average total cost or LAC curve of the firm shows the minimum average cost of producing various levels of output from all-possible short-run average cost curves (SAC). Thus the LAC curve is derived from the SAC curves. The LAC curve can be viewed as a series of alternative short-run situations into any one of which the firm can move.
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