PRODUCTION FUNCTION

4.1 What is Production?

It’s an activity that transforms input into output.

4.1.1 Factors Affecting Productivity

  • Technology
  • Inputs
    • Labor
    • Capital
    • Machinery
    • Land
    • Raw material
    • Power
  • Time period

4.2 Production Function

A production function can be an equation, table or graph presenting the maximum amount of a commodity that a firm can produce from a given set of inputs during a period of time

The production function can be mathematically written as

Q = f(X1, X2, …, Xk)

where

Q = output

X1, …, Xk = inputs

For our current analysis, let’s reduce the inputs to two, capital (K) and labor (L):

Q = f(L, K)

4.2.1 Uses of Production Function

  • How to obtain Maximum output
  • Helps the producers to determine whether employing variable inputs /costs are profitable
  • Highly useful in longrun decisions
  • Least cost combination of inputs and to produce an output

Two Types of Factor Inputs

  • FIXED INPUTS :

Fixed inputs are those factors the quantity of which remains constant irrespective of the level of output produced by a firm. For example, land, buildings, machines, tools, equipments, superior types of labour, top management etc.

  • VARIABLE INPUTS :

Variable inputs are those factors the quantity of which varies with variations in the levels of output produced by a firm.For example, raw materials, power fuel, water, transport, labour and communication etc.

Definitions

Total Product or Output (TP):

  • It refers to the total volume of goods produced during a specified period of time.
  • Total product (TP)can be raised only by increasing the quantity of variable factors employed in production.

Average Product (AP):

            The AP of an input is the TP divided by the amount of input used to produce this amount of output. Thus AP is the output-input ratio for each level of variable input usage.

APL = Q/L

Where:

Q = Total Product

L = Number of workers

Marginal Product (MP):

The MP of an input is the addition to TP resulting from the addition of one unit of input, when the amounts of other inputs are constant.

MPL = W Q/WL

Where:

W means ‘the change in’

Example

4.3 Law of Diminishing Returns (Diminishing Marginal Product)

Holding all factors constant except one, the law of diminishing returns says that:

  • As additional units of a variable input are combined with a fixed input, at some point, the additional output (i.e., marginal product) starts to diminish.

e.g. trying to increase labor input without also increasing capital will bring diminishing returns

Types Of Production Function

  • The fixed proportion production function.
  • The variable proportion production

Fixed Proportion Production Function

  • There is only one way in which the factors may be combined to produce a given level of output efficiently.
  • It requires a fixed combination of inputs to produce a given level of output.
  • There is no possibility of substitution between the factors of production.

Variable Proportions Production Function

  • to it, a given level of output can be produced by several alternative combinations of factors of production, say capital and labour.
  • It is assumed that the factors can be combined in infinite number of ways.
  • The common level of output obtained from alternative combinations of capital and labour is given by an isoquant Q in Fig.

4.4 Analysis of Production Function: Short Run

  • In the short run at least one factor be fixed in supply but all other factors are capable of being changed.
  • Reflects ways in which firms respond to changes
    in output (demand).
  • Can increase or decrease output using more or less of some factors.
  • Increase in total capacity only possible in the long run.

4.6 Analysis  the Production Function: Long Run

  • The long run is defined as the period of time taken to vary all factors of production
    • By doing this, the firm is able to increase its total capacity – not just short term capacity
    • Associated with a change in the scale of production
    • The period of time varies according to the firm and the industry.

4.7 Isoquants

  • Isoquant is a curve that shows the various combinations of two inputs that will produce a given level of output.
  • Slope of an isoquant indicates the rate at which factors K and L can be substituted for each other while a constant level of production is maintained.
  • The slope is called Marginal Rate of Technical Substitution (MRTS)

4.7.1 Properties of Isoquants

  • There is a different isoquant for every output rate the firm could possibly produce with isoquants farther from the origin indicating higher rates of output
  • Along a given isoquant, the quantity of labor employed is inversely related to the quantity of capital employed è isoquants have negative slopes
  • Isoquants do not intersect. Since each isoquant refers to a specific rate of output, an intersection would indicate that the same combination of resources could, with equal efficiency, produce two different amounts of output
  • Isoquants are usually convex to the origin.

4.8 The Marginal Rate of Technical Substitution (MRTS)

The rate, at which one input can be substituted for another input, if output remains constant, is called the marginal rate of technical substitution (MRTS).  

It is the absolute value of the slope of the isoquant.

4.9 Economic region of production

  • There are certain combinations of inputs that the firm should not use in the long run no matter how cheap they are (unless the firm is being paid to use them)
  • These input combinations are represented by the portion of an isoquant curve that has a positive slope
  • A positive sloped isoquant means that merely to maintain the same level of production, the firm must use more of both inputs if it increases its use of one of the inputs
  • The marginal product of one input is negative, and using more of that input would actually cause output to fall unless more of the other input were also employed.
  • Ridge Lines – are lines connecting the points where the marginal product of an input is equal to zero in the isoquant map and forming the boundary for the economic region of production
  • Economic Region of Production – is the range in an isoquant diagram where both inputs have a positive marginal product. It lies inside the ridge lines

4.10 Isocost Lines

  • Isocost lines show different combinations of inputs which give the same cost
  • At the point where the isocost line meets the vertical axis, the quantity of capital that can be purchased equals the total cost divided by the monthly cost of a unit of capital→ TC / r
  • Where the isocost line meets the horizontal axis, the quantity of labor that can be purchased equals the total cost divided by the monthly cost of a unit of labor → TC / w
  • The slope of the isocost line is given by
    • Slope of isocost line = -(TC/r)/(TC/w) = -w/r

4.10.1 Choice of Input Combinations

  • The profit maximizing firm wants to produce its chosen output at the minimum cost è it tries to find the isocost closest to the origin that still touches the chosen isoquant.
  • Isocost Line –  is a line that shows the various combinations of two inputs that can be bought for a given dollar cost
  • The equation for an isocost line is:      C =L. PL +K. PK

Maximizing Output for a given cost

Minimizing Cost subject to given Output

4.10.2 Least Cost Factor Combination or Producer’s Equilibrium or Optimal Combination of Inputs

The firm can achieve maximum profits by choosing that combination of factors which will cost it the least. The choice is based on the prices of factors of production at a particular time. The firm can maximize its profits either by maximizing the level of output for a given cost or by minimizing the cost of producing a given output. In both cases the factors will have to be employed in optimal combination at which the cost of production will be minimum. The least cost factor combination can be determined by imposing the isoquant map on isocost line. The point of tangency between the isocost and an isoquant is an important but not a necessary condition for producer’s equilibrium. The essential condition is that the slope of the isocost line must equal the slope of the isoquant. Thus at a point of equilibrium marginal physical productivities of the two factors must be equal the ratio of their prices. The marginal physical product per rupee of one factor must be equal to tht of the other factor. And isoquant must be convex to the origin. The marginal rate of technical substitution of labour for capital must be diminishing at the point of equilibrium.

4.10.3 Expansion Path

  • If we imagine a set of isoquants representing each possible rate of output, and given the relative cost of resources, we can then draw isocost lines to determine the optimal combination of resources for producing each rate of output
  • Expansion Path leads to Total Cost Curve
  • An expansion path is a long-run concept (because all inputs can change)
  • Each point on the expansion path represents a cost-minimizing combination of inputs
  • Given input prices, each point represents a total cost of producing a given level of output when the entrepreneur can choose any input combination he or she want
  • If the relative prices of resources change, the least-cost resource combination will also change →the firm’s expansion path will change
  • For example, if the price of labor increases, capital becomes relatively less expensive → the efficient production of any given rate of output will therefore call for less labor and more capital

4.11 Elasticity of Factor Substitution

The concept of elasticity of factor substitution was developed by J.R. Hicks in his book ‘The Theory of Wages’ in 1932 to estimate the relative responsiveness of the capital labour ratio to given proportional changes in the marginal rate of technical substitution of capital for labour.It measures the relative extent to which one factor will be replaced by the other, whenever there is change in their relative prices. For example, if capital becomes cheaper, the producer will substitute capital for labour.

On the other hand, if wages (price of labour) fall, the producer will use relatively more labour than capital. The manner and the rate at which the two factors will be substituted for each other will depend upon the marginal rate of technical substitution between the factors and change in their relative prices.

Elasticity of factor substitution is defined as the proportionate change in the factor- proportions to the proportionate change in the marginal rate of technical substitution, so that the output remains the same (one moves along an isoquant. It measures the strength of substitution effect. Therefore,

Intuitively, elasticity of factor substitution can also be thought of as a measure of the degree of ease with which one factor is substituted for the other. It can also be conceived as a measure of similarity of factors of production from a technological point of view.

In equilibrium position, the marginal rate of technical substitution in the formula of ‘a’ will be replaced by the ratio of factor prices. Thus, in equilibrium

Thus, when exogenous input price ratio (PK/PL) change, we expect a simultaneous change in optimal input ratio (L/K) in the reverse direction. The reason is simple. We always substitute relatively cheaper factor for the dearer one. That is, the direction of change is clear, but the extent of input substitution will be measured by the above formula of elasticity of substitution.

Elasticity of factor substitution can take any value from zero to infinity, always being positive. If marginal rate of technical substitution declines slowly, elasticity of substitution between the two factors will be high. If, on the other hand, it declines rapidly, elasticity of substitution will be low. Elasticity of factor substitution is zero for Leontief function, one for Cobb Douglas function and constant for linear and CES function.

The shape of the isoquant is related to its elasticity of substitution. The magnitude of the elasticity of substitution can be assessed by looking at the curvature of isoquants. The greater the convexity of isoquants, the smaller would be the elasticity of substitution.

In the extreme case, when the two factors of production are perfect substitutes, production can be carried through both the factors or through any one of them. Here, both the factors are identical for all purposes. Hence, increase in one factor will be accompanied by a constant decrease in the other factor.

Thus, the marginal rate of technical substitution will be constant and uniform. Further, ∆MRTSK, I = 0 or L/K = 0. The isoquants between them will be straight lines. Therefore, a fall in the price of one factor will induce the producer to replace the costly factor completely by the cheaper one. In such a case, the elasticity of substitution between the two factors is infinite.

On the other extreme, suppose the two factors are perfect complements in the sense that both have to be combined in fixed proportions to produce a given output, i.e., ∆ (K/L) = 0. The marginal rate of technical substitution between such factors will be infinite or zero, as output will not increase by substitution of one factor by the other.

Hence, one and only one combination of inputs can produce specified output. Here, change in the relative price of a factor cannot lead to any substitution and therefore, elasticity of factor substitution is zero and the isoquants will be right angled in such case. Here, MPK = 0 along vertical stretch and MPL = 0 along horizontal stretch of the isoquant.

The elasticity of substitution between factors is simply the ratio of proportionate change in the slopes of two rays from the origin to two points on an isoquant to the proportionate change in the slopes of isoquants at these points (Fig. 7.16).

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Therefore, elasticity of substitution

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Substitution curve can be plotted (Fig. 7.17) by taking K/L ratio on the X-axis and MRTS on Y-axis. Where the substitution curve AB is steep (above point ‘A’), the elasticity of factor substitution is low. Capital and labour are not good substitutes here.

On the other hand, the elasticity of factor substitution is high in the flat portion of substitution curve (below point ‘B’). In this case, capital and labour are good substitutes. The substitution curve becomes vertical at point ‘C’. Here, a given percentage changes in MRTS fails to bring in change in the capital labour ratio.

Hence, the elasticity of factor substitution becomes zero. On the other extreme, at point ‘D’, the substitution curve becomes horizontal. Here, even no change in MRTS brings an infinitely large change in the capital-labour ratio. Hence, the elasticity of factor substitution is equal to infinity.

Somewhere between points ‘A’ and ‘B’, a given percentage change in MRTS brings an equal change in capital-labour ratio making the elasticity of factor substitution equal to unity. Thus, it is clear that the elasticity of factor substitution increases from zero to infinity, as one move downwards along a substitution curve (Fig. 7.17).

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4.12 Laws of Returns to Scale

  • Let us now consider the effect of proportional increase in all inputs on the level of output produced.
  • To explain how much the output will increase we will use the concept of returns to scale
  • If all inputs into the production process are doubled, three things can happen:
  • output can more than double
    • increasing returns to scale (IRTS)
  • output can exactly double
    • constant returns to scale (CRTS)
  • output can less than double
    • decreasing returns to scale (DRTS)

4.12.1 Increasing Returns To Scale (IRTS)

If output increases by more than an increase in inputs, then the situation is  of increasing returns to scale

4.12.2 Constant Returns To Scale (CRTS)

If output increases by exactly the same proportion as inputs, then the situation is of constant returns to scale.

4.12.3 Decreasing Returns To Scale (DRTS)

If output increases by less than the increase in inputs, then the situation is of decreasing returns to scale.

4.13 Economies and diseconomies of scale

Economies of Scale

In their most basic form, economies of scale refer to the idea that as more products are produced the marginal cost, or cost per unit, decreases because of increased efficiencies. Overhead costs can be shared over more products. Often the desire for economies of scale drives an organization to become larger or to merge with a like-minded company, which can bring additional efficiencies or opportunities. But economies of scale have their limits.

Diseconomies of Scale

Diseconomies of scale come about when a business or organization becomes so big, or so inefficient, that the cost-per-unit of its products and services starts to rise A business can only grow so much before the benefits of growth begin to create additional costs and resources. Additional output becomes more expensive. Complexities take over and bureaucracies dominate. A good thing has turned sour. Thus, the goal for business and other organizations is to find the point of equilibrium in which economies of scale thrive and stave off the diseconomies.

4.13.1 External vs. Internal Factors

Economies and diseconomies of scale are frequently broken down by the respective factors leading to a certain level of scale. Some factors are internal, while other factors come from outside the business. Internal factors such as proprietary technology, unique training methods or a certain ethos can create outstanding economies of scale, while external factors such as higher interest rates, government regulation or consumer ambivalence can create difficult diseconomies of scale.

4.13.2 New Strategies

Newer forms of economies of scale have come about with technological advances and improved business practices. The extensive dependence upon computers and the use of the Internet allow small businesses to become efficient in ways previously thought impossible. Outsourcing business functions such as payroll or customer service can be a way to achieve greater output at less cost. Cost-sharing and grouping with other membership organizations, such as a chamber of commerce, similarly allow businesses to lower their costs, offer more products and increase income.

4.14 Empirical production function: Cobb-Douglas production function

Many studies have been undertaken to empirically study and statistically calculate the relationship between physical inputs and physical output. One of such empirical production functions is Cobb Douglas Production Function. It is intermediate between a linear and a fixed proportion production function. It is given by a formula ——

Q = ALαKβ

Where Q is total output,

L stands for quantity of labour,

K is quantity of capital,

A, α and β are positive constants.

Empirically it was found that, 75% increase in output can be attributed to increase in labour input and the remaining 25% was due to capital input. It was also found that the sum of exponents of Cobb-Douglas production function is equal to one. That is α + β is equal to one. This implies that it is a linearly homogenous production function.

4.14.1 Important features of Cobb-Douglas Production Function

1. Average Product of factors of production used up in this function depends upon the ratio in which the factors are combined for the production of commodity under consideration

2. Marginal Product of factors of production used up in this function also depends upon the ratio in which the factors are combined for the production of commodity under consideration

3. Cobb-Douglas production function is used in obtaining marginal rate of technical substitution ( the rate at which one input can be substituted for the other to produce same level of output) between two inputs.

4. As seen earlier, the sum of exponents of Cobb Douglas production function is equal to one. (α + β = 1). This is a measure of returns to scale. When α + β = 1, it is constant returns to scale, α + β > 1, it indicates, increasing returns to scale and when α + β < 1, it indicates diminishing returns to scale.

4.15 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.

The TC curve is drawn by taking output on the hori­zontal axis and total cost on the vertical axis

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.

4.16 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.

Historical and Replacement Costs:

The historical cost is the actual cost of an asset incurred at the time the asset was acquired. It means the cost of a plant at a price originally paid for it. In contrast, replacement cost means the price that would have to be paid currently for acquiring the same plant. So historical costs are the past costs and replacement costs are the present costs.

Price changes over time cause a difference between historical costs and replacement costs. For example, suppose that the price of a machine in 1995 was Rs. 1, 00,000 and its present price is Rs. 2, 50,000, the actual cost of Rs. 1, 00,000 is the historical cost while Rs. 2, 50,000 is the replacement cost.

The concept of replacement cost is very useful for the management. It projects a true picture while the historical cost gives poor projection to the management. Historical cost of assets is used for accounting purposes, in the assessment of net worth of the firm, while the replacement cost is used for business decision regarding the renovation of the firm.

Past Costs and Future Costs:

Past costs are the costs which have been actually incurred in the past. They are beyond the control of the management because they are already incurred. These costs can be evaluated with retro­spective effect. On the contrary, future costs refer to the costs that are reasonably expected to be incurred in some future periods.

They involve forecasting for control of expenses, appraisal of capital expenditure decisions on new projects as well as expansion programmes and profit-loss projections through proper costing under assumed cost conditions.

The management is more interested in future costs because it can exercise some control over them. If the management considers the future cost too high, it can either plan to reduce them or find out sources to meet them. These costs are also called avoidable costs or controllable costs.

Business Costs and Full Costs:

Business costs are the costs which include all the payments and contractual obligations made by the firm together with the book cost of depreciation on plant and equipment. They are relevant for the calculation of profits and losses in business, and for legal and tax purposes.

In contrast, full costs consist of opportunity costs and normal profit. Opportunity costs are the expected earnings from the next best use of the firm’s resources. Normal profit is the minimum profit required for the existence of a firm.

Common Production Costs and Joint Costs:

Sometimes, two or more than two products emerge from a common production process and from a single raw material. For example, the same piece of leather may be used for slippers or shoes. Such products present some peculiar and important problems for the management. They are identifiable as separate products only at the end of the process. So the costs incurred upto this point are common costs. Thus, common costs are the costs which cannot be traced to separate products in any direct manner.

When an increase in the production of one product results in an increase in the output of another product, such products are joint products and their costs are joint costs. For example, when gas is produced from coal, coke and other products also emerge automatically. Likewise, wheat and straw, cotton and cotton seeds may be its other examples.

Shutdown Costs and Abandonment Costs:

Shutdown costs are the costs that are incurred in the case of a closure of plant operations. If the operations are continued, these costs can be saved. These costs include all types of fixed costs, the costs of sheltering plant and equipment, lay-off expenses, employment and training of workers when the operation is restarted.

On the other hand, abandonment costs are the costs which are incurred because of retiring altogether a plant from use. These costs are related to the problem of disposal of assets. For example, the costs are related to the discontinuance of tram services in Delhi.

These concepts of costs are very important for the management when they have to make deci­sions regarding the continuance of existing plant, suspension of its operations or its closure.

Out-of-Pocket Costs and Book Costs:

The costs which include cash payments or cash transfers that may be recurring or non-recurring are called out-of-pocket costs. All the explicit costs such as rent, wages, interest, transport charges, etc. are out-of-pocket costs. They are also called explicit costs.

Book costs are the actual business costs which enter into book accounts but are not paid in cash. They are considered while finalising the profit and loss accounts. For example, depreciation which does not require current cash payments. They are also called imputed costs. Book costs may be converted into out-of-pocket costs. If a factor of production is owned, that is book cost. But, if it is hired, that is out-of-pocket cost.

Urgent Costs and Postponable Costs:

Urgent costs are those costs that are necessary for the continuation of the firm’s activities. The cost of raw materials, labour, fuel, etc. may be its examples which have to be incurred if production is to take place. The costs which can be postponed for some time, i.e., whose postponement does not affect the operational efficiency of the firm are called postponable costs. For example, maintenance costs which can be postponed for the time-being. This distinction of cost is very useful during war and inflation.

Escapable Costs and Unavoidable Costs

Escapable costs are the costs which can be reduced by contraction in business activities. Here, net effect on costs is important. However, it is difficult to estimate indirect effects such as the closure of an unprofitable business unit which will reduce costs but will increase the other related expenses like transportation charges, etc. On the other hand, unavoidable costs are the costs which do not vary with changes in the level of production, but they are unavoidable such as fixed costs.

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.

4.17 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

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.

Cost Function in the Short-Run

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.

The SAVC curve is U-shaped

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.

Each SAC curve represents a plant of a particular size which is suitable for a particular range of output. The firm will, therefore, make use of the various plants up to that level where the short-run average costs fall with increase in output. It will not produce beyond the minimum short-run average cost of producing various outputs from all the plants used together.

Let there be three plants represented by their short-run average cost curves SAC1 SAC2 and SAC3 in Figure 4. Each curve represents the scale of the firm. SAС1depicts a lower scale while the movement from SAC2 to SA Сshows the firm to be of a larger size. Given this scale of the firm, it will produce up to the least cost per unit of output. For producing ON output, the firm can use SAC1or SAC2 plant.

The short-run average cost curves

The firm will, however, use the scale of plant represented by SAC3since the average cost of producing ON output is NB which is less than NA, the cost of producing this output on the SAC2 plant. If the firm is to pro­duce OL output, it can produce at either of the two plants. But it would be advantageous for the firm to use the plant SA C2 for the OL level of output.

But it would be more profitable for the firm to produce the larger output OM at the lowest aver­age cost ME from this plant. However, for output OH, the firm would use the SAСplant where the average cost HG is lower than HF of the SAC2 plant. Thus in the long-run in order to produce any level of output the firm will use that plant which has the minimum unit cost.

If the firm expands its scale by the three stages represented by SAC1SAC2and SAC3 curves, the thick wave-like portions of these curves form the long-run average cost curve. The dotted portions of these SAC curves are of no consideration during the long run because the firm would change the scale of plant rather than operate on them.

But the long-run average cost curve LAC is usually shown as a smooth curve fitted to the SAC curves so that it is tangent to each of them at some point, as shown in Figure 5, where SAC1,SAC2, SAC3, SAC4 and SAC5are the short-run cost curves. It is tangent to all the SAC curves but only to one at its minimum point.

The LAC is tangent to the lowest point E of the curve SAC3 in Figure 5 at OQ optimum output. The plant SAC3 which produces this OQ optimum output at the minimum cost QE is the optimum plant, and the firm produc­ing this optimum output at the minimum cost with this opti­mum plant is the optimum firm. If the firm produces less than the optimum output OQ, it is not working its plant to full capacity and if it produces beyond it is overworking its plants. In both the cases, the plants SAC2 and SAC4 have higher average costs of production than the plant SAC3

The short-run average cost curves

The LAC curve is known as the “envelope” curve because it envelopes all the SAC curves. According to Prof. Chamberlin, “It is composed of plant curves; it is the plant curve. But it is better to call it a “planning” curve because the firm plans to expand its scale of production over the long run.”

The long-run marginal cost (LMC) curve of the firm intersects SAC1and LAC curves at the minimum point E.

LAC Curve Flatter than SAC Curve:

Though the long-run average cost (LAC) curve is U-shaped, yet it is flatter than the short-run average cost (SAC) curve. It means that the LAC curve first falls slowly and then rises gradually after a minimum point is reached.

1. Initially, the LAC gradually slopes downwards due to the availability of certain economies of scale like the economical use of indivisible factors, increased specialisation and the use of technologi­cally more efficient machines or factors. The returns to scale increase because of the indivisibility of factors of production.

When a business unit expands, the returns to scale increase because the indivis­ible factors are employed to their maximum capacity. Further, as the firm expands, it enjoys internal economies of production. It may be able to install better machines, sell its products more easily, borrow money cheaply, procure the services of more efficient manager and workers, etc. All these economies help in increasing the returns to scale more than proportionately.

2. After the minimum point of the long-run average cost is reached, the LAC curve may flatten out over a certain range of output with the expansion of the scale of production. In such a situation, the economies and diseconomies balance each other and the LAC curve has a disc base.

3. With further expansion of scale, the diseconomies like the difficulties of coordination, manage­ment, labour and transport arise which more than counterbalance the economies so that the LAC curve begins to rise. This happens when the indivisible factors become inefficient and less productive due to the over expansion of the scale of production. Moreover, when supervision and coordination become difficult, the per unit cost increases. To these internal diseconomies are added external diseconomies of scale.

These arise from higher factor prices or from diminishing productivities of factors. As the indus­try continues to expand, the demand for skilled labour, land, capital, etc. rises. Transport and marketing difficulties also emerge. Prices of raw materials go up. All these factors lead to diminishing returns to scale and tend to raise costs.

Conclusion:

The LAC curves first falls and then rises more slowly than the SAC curve because in the long run all costs become variable and few are fixed. The plant and equipment can be altered and adjusted to the output. The existing factors can be worked fully and more efficiently so that both the average fixed costs and average variable costs are lower in the long run than in the short run. That is why, the LAC curve is flatter than the SAC curve.

Similarly, the LMC curve is flatter than the SMC curve because all costs are variable and there are few fixed costs. In the short-run, the marginal cost is related to both the fixed and variable costs. As a result, the SMC curve falls and rises more swiftly than the LMC curve. The LMC curve bears the usual relation to the LAC curve. It first falls and is below the LAC curve. Then rises and cuts the LAC curve at its lowest point E and is above the latter throughout its length, as shown in Figure 6.

LAC curve

 4.18 The Modern Theory of Costs

The modem theory of costs differs from the traditional theory of costs with regard to the shapes of the cost curves. In the traditional theory, the cost curves are U-shaped. But in the modem theory which is based on empirical evidences, the short-run SAVC curve and the SMC curve coincide with each other and are a horizontal straight line over a wide range of output. So far as the LAC and LMC curves are concerned, they are L-shaped rather than U-shaped. We discuss below the nature of short- run and long-run cost curves according to the modem theory.

(1) Short-Run Cost Curves:

As in the traditional theory, the short-run cost curves in the modem theory of costs are the AFC, SAVC, SAC and SMC curves. As usual, they are derived from the total costs which are divided into total fixed costs and total variable costs.

But in the modem theory, the SAVC and SMC curves have a saucer-type shape or bowl-shape rather than a U-shape. As the AFC curve is a rectangular hyperbola, the SAC curve has a U-shape even in the modem version. Economists have investigated on the basis of empirical studies this behaviour pattern of the short-run cost curves.

According to them, a modern firm chooses such a plant which it can operate eas­ily with the available variable direct factors. Such a plant possesses some reserve capacity and much flexibility. The firm installs this type of plant in order to produce the maximum rate of output over a wide range to meet any increase in demand for its product.

The saucer-shaped SAVC and SMC curves are shown in Figure 7. To begin with, both the curves first fall upto point A and the SMC curvelies below the SAVC curve. “The falling part of the SAVC shows the reduction in costs due to the better utilisation of the fixed factor and the consequent increase in skills and productiv­ity of the variable factor (labour).

The saucer-shaped SAVC and SMC curves

With better skills, the wastes in raw materials are also being reduced and a better utilisation of the whole plant is reached.” So far as the flat stretch of the saucer-shaped SAVC curve over Q:1Q2range of output is concerned, the empirical evidence reveals that the operation of a plant within this wide range exhibits constant returns to scale.

The reason for the saucer-shaped SAVC curve is that the fixed factor is divisible. The SAV costs are constant over a large range, up to the point at which all of the fixed factor is used. Moreover, the firm’s SAV costs tend to be constant over a wide range of output because there is no need to depart from the optimal combination of labour and capital in those plants that are kept in operation.

Thus there is a large range of output over which the SAVC curve will be flat. Over that range, SMC and SAVC are equal and are constant per unit of output. The firm will, therefore, continue to produce within Q1Qreserve capacity of the plant, as shown in Figure 7.

After point B, both the SAVC and SMC curves start rising. When the firm departs from its normal or the load factor of the plant in order to obtain higher rates of output beyond Q2, it leads to higher SAVC and SMC. The increase in costs may be due to the over­time operations of the old and less efficient plant leading to frequent breakdowns, wastage of raw materials, reduction in labour productivity and increase in labour cost due to overtime operations. In the rising portion of the SAVC curve beyond point B, the SMC curve lies above it.

The short-run average total cost curve (SATC or SAC) is obtained by adding vertically the average fixed cost curve (AFC) and the SAVC curve at each level of output. The SAC curve, as shown in Figure 8, continues to fall up to the OQ level of output at which the reserve capacity of the plant is fully exhausted.

The SAC curve

Beyond that output level, the SAC curve rises as output increases. The smooth and continuous fall in the SAC curve upto the OQ level of output is due to the fact that the AFC curve is a rectangular hyperbola and the SAVC curve first falls and then becomes horizontal within the range of reserve capacity. Beyond the OQ output level, it starts rising steeply. But the minimum point M of the SAC curve where the SMC curve intersects it, is to the right of point E of the SAVC curve. This is because the SAVC curve starts rising steeply from point E while the AFC curve is falling at a very low rate.

(2) Long-Run Cost Curves:

Empirical evidence about the long-run average cost curve reveals that the LAC curve is L-shaped rather than U-shaped. In the beginning, the LAC curve rapidly falls but after a point “the curve remains flat, or may slope gently downwards, at its right-hand end.” Economists have assigned the following reasons for the L-shape of the LAC curve.

1. Production and Managerial Costs:

In the long run, all costs being variable, production costs and managerial costs of a firm are taken into account when considering the effect of expansion of output on average costs. As output increases, production costs fall continuously while managerial costs may rise at very large scales of output. But the fall in production costs outweighs the increase in managerial costs so that the LAC curve falls with increases in output. We analyse the behaviour of production and managerial costs in explaining the L-shape of the LAC curve.

Production Costs:

As a firm increases its scale of production, its production costs fall steeply in the beginning and then gradually. The is due to the technical economies of large scale production enjoyed by the firm. Initially, these economies are substantial. But after a certain level of output when all or most of these economies have been achieved, the firm reaches the minimum optimal scale or mini­ mum efficient scale (MES).

Given the technology of the industry, the firm can continue to enjoy some technical economies at outputs larger than the MES for the following reasons:

(a) from further decentralisation and improvement in skills and productivity of labour; (b) from lower repair costs after the firm reaches a certain size; and

(c) by itself producing some of the materials and equipment cheaply which the firm ne

eds instead of buying them from other firms.

Managerial Costs:

In modern firms, for each plant there is a corresponding managerial set-up for its smooth operation. There are various levels of management, each having a separate management technique applicable to a certain range of output. Thus, given a managerial set-up for a plant, its mana­gerial costs first fall with the expansion of output and it is only at a very large scale output, they rise very slowly.

To sum up, production costs fall smoothly and managerial costs rise slowly at very large scales of output. But the fall in production costs more than offsets the rise in managerial costs so that the LAC curve falls smoothly or becomes flat at very large scales of output, thereby giving rise to the L-shape of the LAC curve.

In order to draw such an LAC curve, we take three short-run average cost curves SAC1 SA С2, and SAC3representing three plants with the same technol­ogy in Figure 9. Each SAC curve includes production costs, managerial costs, other fixed costs and a mar­gin for normal profits. Each scale of plant (SAC) is subject to a typical load factor capacity so that points A, В and С represent the minimal optimal scale of out­put of each plant.

SAC curve

By joining all such points as A, В and С of a large number of SACs, we trace out a smooth and continuous LAC curve, as shown in Figure 9. This curve does not turn up at very large scales of output. It does not envelope the SAC curves but intersects them at the optimal level of output of each plant.

2. Technical Progress:

Another reason for the existence of the L-shaped LAC curve in the modern theory of costs is technical progress. The traditional theory of costs assumes no technical progress while explaining the U-shaped LAC curve. The empirical results on long-run costs conform the widespread existence of economies of scale due to technical progress in firms.

The period between which technical progress has taken place, the long-run aver­age costs show a falling trend. The evidence of diseconomies is much less certain. So an upturn of the LAC at the top end of the size scale has not been observed. The L-shape of the LAC curve due to tech­nical progress is explained in Figure 10.

The L-shape of the LAC curve

Suppose the firm is producing OQ1 output on LAC1curve at a per unit cost of ОС1 If there is an increase in demand for the firm’s product to OQ2,with no change in technology, the firm will produce OQ2 output along the LAC1 curve at a per unit cost of ОС2. If, however, there is technical progress in the firm, it will install a new plant having LAC2 as the long-run average cost curve. On this plant, it produces OQ2 output at a lower cost OC2 per unit.

Similarly, if the firm decides to increase its output to OQ3 to meet further rise in demand technical progress may have advanced to such a level that it installs the plant with the LACcurve. Now it produces OQ3output at a still lower cost OCper unit. If the minimum points, L, M and N of these U- shaped long-run average cost curves LAC1, LAC2 and LACare joined by a line, it forms an L-shaped gently sloping downward curve LAC.

3. Learning:

Another reason for the L-shaped long- run average cost curve is the learning process. Learning is the product of experience. If experience, in this context, can be measured by the amount of a commodity produced, then higher the production is, the lower is per unit cost.

The consequences of learning are similar to increasing re­turns. First, the knowledge gained from working on a large scale cannot be forgotten. Second, learning increases the rate of productivity. Third, experience is measured by the aggregate output produced since the firm first started to produce the product.

Learning-by-doing has been observed when firms start producing new products. After they have produced the first unit, they are able to reduce the time required for production and thus reduce their per unit costs. For example, if a firm manufactures airframes, the fall observed in long-run average costs is a function of experience in producing one particular kind of airframe, not airframes in general.

One can, therefore, draw a “learning curve” which relates cost per airframe to the aggregate number of airframes manufactured so far, since the firm started manufacturing them. Figure 11 shows a learning curve LAC which relates the cost of producing a given output to the total output over the entire time period.

Growing experience with making the product leads to falling costs as more and more of it is produced. When the firm has exploited all learning possibilities, costs reach a minimum level, M in the figure. Thus, the LAC curve is L-shaped due to learning by doing.

learning curve

Relation between LAC and LMC Curves:

In the modern theory of costs, if the LAC curve falls smoothly and continuously even at very large scales of output, the LMC curve will lie below the LAC curve throughout its length, as shown in Figure 12.

Relation between LAC and LMC Curves

If the LAC curve is downward sloping up to the point of a minimum optimal scale of plant or a mini­mum efficient scale (MES) of plant beyond which no further scale economies exist, the LAC curve becomes horizontal. In this case, the LMC curve lies below the LAC curve until the MES point M is reached, and beyond this point the LMC curve coincides with the LA С curve, as shown in Figure 13.

LA С curve

Conclusion:

The majority of empirical cost studies suggest that the U-shaped cost curves postulated by the traditional theory are not observed in the real world. Two major results emerge predominantly from most studies. First, the SAVC and SMC curves are constant over a wide-range of output.

Second, the LAC curve falls sharply over low levels of output, and subse­quently remains practically constant as the scale of output increases. This means that the LAC curve is L-shaped rather than U-shaped. Only in very few cases diseconomies of scale were observed, and these at very high levels of output.

Economies of Scale and the LAC Curve:


The shape of the LAC curve depends fundamentally upon the internal economies and diseconomies of scale, while the shift in the LAC curve depends upon external economies and diseconomies of scale. The LAC curve first declines slowly and then rises gradually after a minimum point is reached.

Initially, the LAC curve slopes downwards due to the availability of certain internal economies of scale to the firm like the economical use of indivisible factors, increased speciali­sation, use of technologically more efficient machines, better managerial and marketing organisation, and ben­efits of pecuniary economies. All these economies lead to increasing returns to scale. It means that as output increases, the LAC curve declines, as shown in Figure 14 where the LAC curve falls gradually up to point M.

Economies of Scale and the LAC Curve

The economies of scale exist only up to this point which is the optimum point of the LAC curve. If the firm expands its output further than this optimum level, diseconomies of scale arise. The diseconomies of scale result from lack of coordination, inefficiencies in management, and problems in marketing, and in­creases in factor prices as the firm expands its scale.

As a result, there are decreasing returns to scale which turn the LAC curve upwards, as shown in the figure where the LAC curve starts rising from point M. Thus internal economies and diseconomies of scale are built into the shape of the LAC curve because they accrue to the firm from its own actions as it expands its output level. They relate only to the long run.

On the other hand, external economies and diseconomies of scale affect the position of the LAC curve. External economies of scale are external to a firm and accrue to it from actions of other firms when the output of the whole industry expands. They reflect interdependence among firms in an indus­try.

They are realised by a firm when other firms in the industry make inventions and evolve specialisation in pro­duction processes thereby reducing its per unit cost. They also arise to firms in an industry from reductions in fac­tor prices. As a result, per unit cost falls and the LAC curve unfits downwards as shown by the shifting of the LAC curve to LAC in Figure 15.

LAC curve

On the contrary, external diseconomies shift the LAC curve upwards. External diseconomies arise solely through a rise in the market prices of factors used in an industry. When an industry expands, the increase in the demand for factors like labour, capital, equipment, raw materials, power, etc. rises and when the industry is unable to meet this demand due to shortages, per unit cost of firms rises. As a result, the LAC curve shifts upwards, as shown by the shifting of the LAC curve to LAC in Fig. 15.

Elasticity of Cost:

If output (Q) is produced at a total cost (T), the cost function is T=f (0. The elasticity of total cost is the ratio of the proportional change in total cost to the proportional change in output. It may be written as

Elasticity of Cost

Thus, cost elasticity (к) is equal to the ratio of marginal cost (dT/dQ) to average cost (T/Q). It follows from this that if MC< > AC, K< > 1. It means that when MOAC, k>1. Diagrammatically, when the MC curve is ris­ing and is above the AC curve, k>1, as shown by the area right to point E in Figure 16.

It is the case of decreasing returns. When MC = AC, к = 1, it is the point E where the MC curve cuts the AC curve from below in the figure. It is the case of constant returns. When MC < AC, к <1, shown as the area to the left of point E in the figure, where the MC curve is falling and is below the AC curve. It is the case of increasing returns.

Since the average cost and the marginal cost are de­rived from the total cost in relation to the output, the shapes of the AC curve and the MC curve can also be checked from the shape of the total cost curve. If P is the point on the total cost curve at a given output Q, then the average cost is to be read off as the gradient of OP and the marginal cost as the tangent at P.

This is shown in Figure 17. The figure, further, reveals that the elastic­ity of total cost increases continuously with increases in output from less than unity to greater than unity. At first, cost elastic­ity is less than unity for small outputs, and finally, it is greater than unity for large outputs. In other words, if we take к = 1 at some definite level of output, Q = a, then k< 1 for outputs Q < α, and к > 1 for outputs Q > a. This is illustrated in Figure 17.

The elastic­ity of total cost increases continuously with increases in output from less than unity to greater than unity

Elasticity of Average Cost:

The elasticity of total cost

Elasticity of Average Cost

The following results follow from this:

(1) If A: (the elasticity of total cost) is greater than, equal to or less than unity, the elasticity of average cost is greater than, equal to or less than zero-, and (2) the elasticity of total cost exceeds the elasticity of average cost by unity, i.e., E (T/Q) = к-1 or k-E (T/Q) =1.

Elasticity of Marginal Cost:

As we know, the elasticity of total cost is given by E (T) = dT/dQ. Q/T. Therefore, the marginal cost is (dT/dQ). Replacing T by dT/dQ.

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Elasticity of Productivity:

The output of a firm is determined by the various inputs used by it. Assuming all inputs (λ) are used in fixed proportions to produce output Q, then Q =f (λ). The elasticity of productivity is defined as the ratio of proportional change in output to the proportional change in inputs. It can be written as

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Elasticity of productivity helps in understanding the nature of production function in economic theory. If clip_image037 >1, it is the case of increasing returns because a small proportionate increase in inputs leads to more than proportionate increase in output.

If clip_image037[1] <1, it is the case of decreasing returns because a small proportionate increase in inputs leads to a less than proportionate increase in output. If clip_image037[2] =1, there are constant returns. Since the concept of elasticity of productivity is based on the assumption of fixed proportions of inputs used in production, total costs become proportional to the inputs employed.

Therefore, e is the inverse of the elasticity of total cost. But the basic difference between the elasticity of productivity and the elasticity of total cost arises from the fact that the inputs are used in fixed proportions only in the case of ɛ and not for k.