COST ANALYSIS

Firms make decisions in their quest for profit. Firms in perfectly competitive industries make three specific decisions.

1.      How much output to supply.

2.      Which production technique/technology to use?

3.      What quantity of each input to demand?

All these decisions are made in non-competitive industries as well. Because firms in perfectly competitive markets are price-takers in both input and output markets, many decisions depend on prices over which firms have no control. Cost functions are derived functions. They are derived from the production function, which focuses on the cost of production. To calculate costs, a firm must know two things: the quantity and combination of inputs it needs to produce its output and how much these inputs cost.

Accounting Cost Concepts

Opportunity Cost and Actual Cost

The opportunity cost measures the value of the opportunity that is lost or sacrificed when the choice of one course of action requires that an alternative course of action be given up. Opportunity costs are not measured in accounting records, and they are not relevant in many alternative choice problems but they are significant in certain situations. In general, if accepting an alternative requires that facilities or other resources must be devoted to that alternative that otherwise could be used for some other purpose, there is an opportunity cost, and it is measured by the profit that would have been earned had the resources been devoted to the other purpose. For example, the opportunity cost of a college education is the income you could have earned by working full time. If a firm purchases a new piece of equipment for Rs.5000, it does so because it expects that equipment to generate more profit. There is an opportunity cost, however, because that Rs.5000 could have been deposited in an interest-earning account.

Opportunity costs are by their very nature “iffy”. In most situations, it is extremely difficult to estimate what, if any, additional profit could be earned if the resources in question were devoted to some other use. Actual costs are the costs actually a firm incurs for payment of wages, purchase of raw material, procurement of plant and machinery, construction of building, equipment, travel and transport, the expenses on advertisement. The total money expenses, recorded in the books of accounts are the actual costs.

Explicit and Implicit Costs 

Economic costs are categorized into two parts: explicit and implicit costs. Explicit costs refers to the payment made to the factors hired from outside the firm, while implicit costs stands for the payments made for the self-owned resources used in the production. The implicit costs incurred in producing a specific commodity consist of the amounts that could be earned in the best alternative use of the entrepreneur’s time and money. The only difference between the two is in terms of amount spent on hired factor or on self-owned ones.

Business Costs and Full Cost

A firm’s business costs are its total money expenses as computed by ordinary accounting methods. These expenses “include all payments and contractual obligations made by the firm together with the book cost of depreciation on plant and equipment”. The full cost includes business costs, opportunity cost of the firm and normal profits. The opportunity costs of the firm include interest on the funds invested in the firm by its owners and the value of the labour services of the entrepreneur, if working in the firm and receiving no salary as a business expense. Normal profits are an additional amount, sufficient, but just sufficient, to induce the entrepreneur to continue to produce the same product, given the uncertainties faced.

Out-of-Pocket and Books Cost

Out-of-pocket costs refer to costs that involve immediate payments to outsiders as opposed to books costs that do not require current cash expenses. For example, payment of wages and salaries to the employees are out-of-pockets costs while salary of the owner, if not paid, is a book cost. The cost of owner’s own fund and depreciation cost are other examples of book costs. The out-of-pocket costs are also called explicit costs and correspondingly book costs are called implicit or imputed costs. Books costs can be converted into out-of-pocket costs by selling assets and leasing them back from the buyer. So, the difference between these two kinds of cost is in terms of ownership. A factor of production owned by a firm, its cost is a book cost if it is hired it is an out-of-pocket cost.  Both implicit and explicit costs are actual costs of a business firm and so both these must be recorded and considered for all decisions. Small firms very often ignore implicit costs and to that extent they overestimate their profits.

Economic Cost and Normal Profit

The economic cost in the production of a good refers to the payments it must make to all the factors of production employed by a firm in the production of that good. The factors of production includes all the resources owned by a firm as well as those hired from outside. Normal profit is not profit but an item of economic cost. Particularly, it stands for the opportunity cost of entrepreneur’s time. It is a profit that is just sufficient to ensure that a firm remains in business. In the theory of markets, firms’ cost curves include normal profit as an integral part of supply cost. If the level of profit earned in a particular market is too low to generate a return on capital employed comparable to that obtainable in other equally risky markets, then the firm’s resources will be transferred to some other use.

Analytical Cost Concepts

Variable and Fixed Costs

Variable costs are items of cost that vary directly and proportionately with volume. Fixed costs do not vary at all with volume. Building depreciation, property taxes, supervisory salaries, and occupancy costs often behave in this fashion. These costs increase because of the passage of time, rather than because of the volume within a specified period of time

Total, Average and Marginal Cost

Total Cost (TC) includes all cash payments made to hired factors of production and all cash charges imputed for the use of the owner’s factors of production in acquiring or producing a good or service. For example, a shoe- makers total cost includes the amount spent on leather, thread, rent for the workshop, interest on borrowed capital, wages and salaries of employees and the charges for his services and his own funds invested in the business. Average Cost (AC) is the cost per unit of output obtained by dividing the total cost by the total quantity produced.

                                          AC = Total Cost/Output

 Marginal Cost (MC) is the extra cost of producing one additional unit.

                                     MC = Δ Total Cost / Δ Output

Short Run and Long-Run Costs

The terms short-run and long- run costs are classifications of costs involving time. Short run is defined as period during which at least one element of factor inputs is in fixed supply; the fixed factor input is plant and equipment. In the long run all factor inputs are variable. The short and long run do not refer to any fixed units of calendar time. Corresponding to this period classification, there are short run and long-run costs. 

A short run cost is the cost which varies with output when fixed plant and capital equipment remain the same while a long run cost is that which varies with output when all factor inputs, including plant and equipment vary. Long-run cost assumes variable plant size and it actually consists of short run cost curves for various plant sizes. This is because; in the long run all costs are variable. The plant may be fixed today, but in future decision may be made to increase its size to any desired level within the range of possible alternatives. Both short-run and long- run costs are useful in decision- making. Short run cost is concerned to a decision to produce more or less with a given plant. If the firm is considering an increase in plant size, it necessarily should examine the long-run cost of expansion. Long-run cost analysis is useful in investment decision.

Incremental Costs & Sunk Costs

Marginal cost holds the attention of the rational decision maker. Suppose, however, that the decision maker cannot even in imagination vary the output by one unit more or less. For many different kinds of practical reasons, outputs are often variable only in batches, or in more or less definite increments of some size. Incremental cost, the cost of an extra batch, is therefore, often the closest practical approximation to marginal cost. Rational business decisions, accordingly, can be made on the basis of incremental cost, which is compared with incremental revenue, the extra revenue from the same-sized batch of output.

Historical and Replacement Costs

The historical cost of an asset refers to the actual cost incurred for the acquisition of an asset whereas replacement cost refers to the outlay that has to be made for replacing an old asset. Historical cost of assets is used for accounting purposes in the assessment of the net-worth of the firm. The replacement cost appears in business decisions regarding the renovation of the firm. 

 Private and Social Costs

        

T co  The private cost stand for the price that an entrepreneur must pay to get the resources used in production of a commodity. For example, in order to produce a commodity X, the entrepreneur pays a certain amount to purchase resources, uses them, and sells the commodity. The entrepreneur can compare the receipts from sales with the cost of the resources and determine whether there is an accounting profit.

Social costs refer to the cost a society incurs when its resources are used to produce a given commodity. The social cost of using a bundle of resources to produce a unit of commodity X is the number of units of commodity Y that must be sacrificed in the process. Resources are applied to produce both X and Y. Those resources used to produce X cannot be used to produce Y. Therefore, the sacrifice in terms of commodity Y is social costs. For example, a society could have a greater output of automobiles if only small compact cars were produced. Larger, more luxurious cars required more of almost of every input. But in their private evaluation schemes, some members of the society may attach much greater significance to luxury cars than to compact cars. Balancing the relative resource cost of a commodity with its relative social desirability entails knowledge of both social valuations and social costs.

COST – OUTPUT RELATIONS

               The cost theory deals with the behaviour of cost in relation to a change in output. It considers cost output relations such that the total cost varies with variation in output. From the business decision-makers point of view the absolute change in total cost is not important, but the direction of change in the average and marginal costs is of special significance. The direction of change in marginal and average costs is a matter of cost function. A cost function is a symbolic statement of technological relationship between the cost and output. A common form of cost function may be stated as:

                                             TC f (Q)                                                                  

                                                ΔTC / ΔQ > 0

The more specific form of cost function is relevant to the time chosen for cost analysis – short run or long run. In the short run, some cost remain fixed, while all costs are variable in the long run. Thus on the basis of time, there are two kinds of cost functions (a) short run cost functions and (b) long run cost functions. Accordingly cost output relationship is analyzed in the short and long run framework.

Costs in the Short Run

Total Cost

In the theory of the firm total costs are divided into two groups: total fixed costs and total variable cost:

                   TC= TFC + TVC
Total Fixed Cost

The fixed costs include salaries of administrative staff, depreciation (wear and tear) of machinery, expenses for building, depreciation and repair, expenses for land maintenance and depreciation (if any). Normal profit, which is a lump sum including a percentage return on fixed capital and allowance for risk may also be treated as fixed cost. A straight line parallel to the output axis graphically denotes the total fixed cost in the following figure.

Total Variable Costs

The variable costs include: the raw materials, the cost of direct labor, the running expenses of fixed capital, such as fuel, ordinary repairs and routine maintenance. The total variable cost of the firm has broadly an inverse-S shape (Fig.6.2) that reflects the law of variable proportions. At the initial stages of production with a given plant, as more of the variable factor(s) is employed, its productivity increases and the average variable cost falls. This continues until the optimal combination of the fixed and variable factors is reached. Beyond this point as increased quantities of the variable factor(s) are combined with the fixed factor(s) the productivity of the variable factor(s) declines and the average variable cost rises.                                

 

By adding the TFC and TVC we obtain 
the total cost of the firm (Fig.)

Average Cost
The AC is obtained by dividing the TC by the corresponding level of output:

AC=TC/Q                                                          

      = TFC + TVC/ Q

                              = AFC + AVC   The shape of the AC is similar to that of the AVC (both being U-shaped). Initially the AC declines, it reaches a minimum at the level of optimal operation of the plant and subsequently rises again.

The U- shape of both the AVC and the AC reflects the law of variable proportions or law of eventually decreasing returns to the variable factor{s) of production. The average cost of a firm in the short run always declines to a minimum; then it rises. How much it declines depends on the proportion of fixed to total costs. If the proportion of fixed costs is high, the decline in average cost is rapid. An authorhas explained the behaviour of the average cost in terms of designed capacity. The output whose average cost is the minimum carries the standard definition of capacity output. Capacity here does not mean maximum output but rather the designed output. A plant is designed to produce so many units a week or a month at a minimum cost per unit. In the short run, the plant may be operated below or above the designed output. If a plant is operated at 80 percent of the designed output, the

If a plant is operated at 80 percent of the designed output, then 80 percent is its rate of capacity utilization. Average cost is higher for outputs below and above the designed, or capacity, output. Thus  the average cost curve is always U-shaped. The two sides of the U can be either steep or so nearly flat that the curve looks more like the profile of a shallow saucer. If the capacity output, the minimum cost output, happens also to be physical limit that cannot be exceeded, the AVC and MC curves rise vertically at the capacity output. The curves of average variable cost and of marginal cost need not have a smooth U-shape. In fact both curves can be horizontal over a wide range of output.

Average Fixed Cost. 

Average Fixed Cost (AFC) is Total Fixed Cost divided by the number of units of output (q)

  AFC =TFC/q 

                                                            Average Fixed Cost falls as output rises, because the same total is being spread over or divided by, a larger number of units. This phenomenon is sometimes called spreading overhead. The AFC curve is a rectangular hyperbola asymptotic to the axes- that is, the curve approaches the vertical and the horizontal at each end. For very small outputs, average fixed cost per unit is high, and for large outputs it is low. The AFC curve is a rectangular hyperbola because average fixed cost multiplied by output is always exactly the same amount. Thus AFC steadily declines as output expands.

                                                                                                     Average Variable Cost

The average variable cost is obtained by dividing the TVC with the corresponding level of output.

Accompanying figure  illustrates that the Average Variable Cost at each level of output is derived from the slope of a line drawn from the origin to the point on the TVC curve corresponding to the particular level of output. For example the AVC at q1 output is the slope of the ray Oa and at q 2 is the slope of the ray Ob, and so on. It is evident that the slope of a ray through the origin declines continuously until the ray becomes tangent to the TVC curve at a point c. To the right of this point the slope of rays through the origin starts increasing. Thus the AVC curve falls initially as the productivity of the variable factor(s) increases, attains a minimum when the plant is optimally operated and rises beyond that point. 

Marginal Cost

The most important of all cost concepts is that of marginal cost (MC). The marginal cost is defined as the change in TC that results from a unit change in output.  It is the addition to total cost when another unit of output is produced. Marginal cost is independent of the fixed-cost as one more unit causes nothing to be added to the fixed cost. Marginal cost is associated only with the variable costs. The area under a marginal cost curve is equal to total variable cost. Expressing mathematically,

MC= TC/ Q                                                   

In the short run, every firm is constrained by some fixed input that (1) leads to diminishing returns to variable inputs and (2) limits its capacity to produce. As a firm reaches that capacity, it becomes more costly to produce successively higher levels of output. Marginal costs finally increase with output in the short run.                     

In summary, in the short run the cost curves (AVC, AC and MC) are U-shaped, reflecting the law of variable proportions. In the short run with a fixed plant there is a phase of increasing productivity (falling unit costs) and a phase of decreasing productivity (increasing unit costs) of the variable factor(s). Between these two phases of plant operation there is a single point at which unit costs are at a minimum. When this point on the AC is reached the plant is utilized optimally.

The relationship between Average Cost and Average Variable Cost

Since AC = AFC + AVC, AVC is a part of AC. The U-shape of both the AVC and AC reflects the law of variable proportions. It is important to note that the minimum point of the AC occurs to the right of the minimum point of the AVC Fig.

because the AC includes AFC, and the AFC falls continuously with expansion in output. After the AVC has reached its lowest point and starts rising, its rise is over a certain range offset by the fall in the AFC, so that the AC continues to fall (over that range) in spite of the increase in AVC. But the rise in AVC eventually becomes greater than the fall in the AFC so that the AC starts increasing. The AVC approaches the AC asymptotically as output increases.

Figure illustrates that the AVC reaches it minimum at x while the AC is at its minimum at x’.  Between x and x’ the fall in AFC more than offsets the rise in AVC so that the AC continues to fall. Beyond x’ the increase in AVC is not offset by the fall in AFC, so average cost begins to rise

                                     The relationship between MC and AC

The average variable cost continues to decline so long as the marginal cost is below it, but it starts rising at the point where marginal cost crosses the average variable cost. The marginal cost will always rise more sharply than the average variable cost. Similar relation holds between marginal cost and average cost. Fig. illustrates the relationship between marginal cost and average cost.                

                                                                 The Learning Curve

The first batch of a new product produced with a new technology usually has higher unit cost than later batches do. When color TV sets first came out, most people seemed to think that the unit costs of making the sets would fall and thus make it possible for retail prices to be lower. The rapid pace of technology together with growing cultivation of analytical techniques, have caused close attention to be given to the costs of new products. The learning curve is a generalization about these costs. The expression itself is borrowed from psychology, which has found that any animal, a rat or a human, teams something at some rate by repeated trials. Also called a program function, a learning curve shows the decline in unit costs as the number of units produced increases. Experience in the aircraft industry has shown that a commonly found learning curve is an "80 percent curve". Such a curve means that with doubling of the cumulative number produced, costs fall to (about) 80 percent of their previous level. In practice, the cost figures employed are usually direct labor only, that is, just a part of variable costs. The process of learning is one of acquiring greater familiarity with the details of tasks, of modifying tools and procedures, and of improving coordination. The teaming curve need not be an 80 per cent; apparently its range is between about 75 and about 90 percent. Analysis of experience is firm enough that the curve can often be used for prediction. Thus, if a company gets an order to produce, say, ten thousand units of a totally new piece of equipment, analysts can make a good estimate of the cost of the ten thousandth unit after they know the costs of the one-hundredth one.

            LONG-RUN COSTS- THE 'ENVELOPE' CURVE 

The long run is defined as “a period of time of such length that all inputs are variable” The firm's production function has no fixed inputs; the firm has no fixed costs. It expands its output by building and operating a wholly new and larger plant. Input-output relations in the production function are those of returns to scale. Another important aspect of the long run is that the long run is a ‘planning horizon’. In this respect the long run cost curve is a guide to the entrepreneur in his decision to plan the future expansion of his output.

Long run average cost curve

The long-run average-cost curve is derived from short-run cost curves. Each point on the long run average cost curve corresponds to a point on a short-run cost curve, which is tangent to the long run curve at that point. In the following paragraphs we will discuss how the LAC is derived from the SRC curves.

Suppose that there are three plants operating with the average costs SAC₁

SAC_2, SAC₃ respectively shown in Fig.6.8.  If the firm plans to produce output X₁ it will choose the small plant. It will choose medium size plant if it plans to produce X₂ output and will choose the large size plant if it wishes to produces X₃ output_.  Now if the firm begins with the small plant and faces gradually increasing demand, it will produce with small size plant at lower costs (up to level X₁). X₁ is the firm’s lowest cost level of output beyond which average cost starts rising. But the firm will continue producing with small plant even beyond X₁’, a average cost for these levels of output on the small plant is still lower than that on the medium plant. It is only when the demand for its product reaches X₁” level, the firm chooses to either continue producing with a small plant or install the medium size plant. If the firm anticipates demand to rise beyond X₁” it will install the medium size plant which will produce output larger than X₁” at lower average cost than that of the small plant.  The firm faces a similar decision when it reaches the level X₂”. If the firms anticipates the demand to remain constant at X₂” , the firm chooses not to install the large plant as it involves a larger investment which is profitable only when the demand expands beyond X₂”.  

 Let us now assume that there is many plant sizes each suitable for a certain level of output as shown in Fig. We will have many intersecting point that are crucial for making a choice whether to continue with the existing plant or to install a larger plant. These points may be so close to each other that we get almost a continuous curve. It is known as the “long-run average cost curve” or the “Envelope Curve”. Each point of this curve shows the minimum (optimal) cost or the least cost of producing the corresponding level of output. It is also the planning curve of the firm on the basis of which the firm decides what plant to set up to produce optimally the expected output. The firm chooses the short-run plant that allows it to produce the anticipated output at the least possible cost. The U- shape of the long run average cost curve reflects the laws of returns to scale. The economies of scale exist only up to a certain size of plant, known as the “Optimum plant size” with which all possible economies of scale are fully exploited. Beyond the optimum plant size, dis-economies of scale rise from managerial inefficiencies. This causes the LAC to turn upward. In Fig. the point X_m is the point of optimum output and the responding plant is the optimum plant size.