LESSON 13COST AND OUTPUT RELATIONSHIP
Learning outcomes After studying this unit, you should be able to: relate the concepts of production and costs define different types of cost relevant for production planning and control distinguish between economic costs and accounting costs identify the sources of costs indication of cost concept INTRODUCTION
In the previous chapter we have illustrated the concept of production. And in this lesson I am going to tell you about the cost and its related factors. You will also come to know about cost and output relationship. Cost and revenue are the two major factors that a profit maximising firm needs to monitor continuously. It is the level of cost relative to revenue that determines the firm’s overall profitability. In order to maximise profits, a firm tries to increase its revenue and lower its cost. While the market factors determine the level of revenue to a great extent, the cost can be brought down either by producing the optimum level of output using the least cost combination of inputs, or increasing factor productivities, or by improving the organisational efficiency. The firm’s output level is determined by its cost. The producer has to pay for factors of production for their services. The expenses incurred on these factors of production are known as the cost of production, or in short cost.
Product prices are determined by the interaction of the forces of demand and supply. The basic factor underlying the ability and willingness of firms to supply a product in the market is the cost of production. Thus, cost of production provides the floor to pricing. It is the cost that forms the basis for many managerial decisions like which price to quote, whether to accept a particular order or not, whether to abandon or add a product to the existing product line, whether or not to increase the volume of output, whether to use idle capacity or rent out the facilities, whether to make or buy a product, etc. However, it is essential to underline here that all costs are not relevant for every decision under consideration. The purpose of this unit is to explore cost and its relevance to decision-making. We begin by developing the important cost concepts, an understanding of which can aid managers in making correct decisions. We shall examine the difference between economic and accounting concepts of costs and profits. We shall then consider the concepts of short-run and long-run costs and show that they, in conjunction with the concepts of production studies in the preceding unit, can
give us a more complete understanding of the applications of cost theory to decision-making.
VARIOUS TYPES OF COSTS
There are different types of costs that a firm may consider relevant for decisionmaking under varying situations. The manner in which costs are classified or defined is largely dependent on the purpose for which the cost data are being outlined. Explicit and Implicit Costs The opportunity cost (or cost of the foregone alternative) of a resource is a definition cost in the most basic form. While this particular definition of cost is the preferred baseline for economists in describing cost, not all costs in decisionmaking situations are completely obvious; one of the skills of a good manager is the ability to uncover hidden costs. for dissimilar purposes. Traditionally, the accountants have been primarily connected with collection of historical cost data for use in reporting a firm’s financial behaviour and position and in calculating its taxes.They report or record what was happened, present information that will protect the interests of various shareholders in the firm, and provide standards against which performance can be judged. All these have only indirect relationship to decision-making. Business economists, on the other hand, have been primarily concerned with using cost data in decisions making. These purposes call for different types of cost data and classification. For example, the opportunity cost of a student’s doing a full time MBA could be the income that he would have earned if he had employed his labour resources on a job, rather than spending them in studying managerial economics, accounting, and so on. The time cost in money terms can be referred to as implicit cost of doing an MBA. The out-of-pocket costs on tuition and teaching materials are the explicit costs that a student incurs while attending MBA. Thus, the total cost of doing an MBA to a student is implicit costs (opportunity cost) plus the explicit (out-of-pocket) costs. Direct and Indirect Costs There are some costs which can be directly attributed to production of a given product. The use of raw material, labour input, and machine time involved in the production of each unit can usually be determined. On the other hand, there are certain costs like stationery and other office and administrative expenses, electricity charges, depreciation of plant and buildings, and other such expenses
that cannot easily and accurately be separated and attributed to individual units of production, except on arbitrary basis. When referring to the separable costs of first category accountants call them the direct, or prime costs per unit. The joint costs of the second category are referred to as indirect or overhead costs by the accountants. Direct and indirect costs are not exactly synonymous to what economists refer to as variable costs and fixed costs. Private Costs versus Social Costs Private costs are those that accrue directly to the individuals or firms engaged in relevant activity. External costs, on the other hand, are passed on to persons not involved in the activity in any direct way (i.e., they are passed on to society at large). While the private cost to the firm of dumping is zero, it is definitely positive to the society. It affects adversely the people located down current who are adversely affected and incur higher costs in terms of treating the water for their use, or having to travel a great deal to fetch potable water. If these external costs were included in the production costs of the producing firm a true picture of real, or social costs of the output would be obtained. Ignoring external costs may lead to an inefficient and undesirable allocation of resources in society. Relevant Costs and Irrelevant Costs The relevant costs for decision-making purposes are those costs which are incurred as a result of the decision under consideration and which are relevant for the business purpose. The relevant costs are also referred to as the incremental costs. There are three main categories of relevant or incremental costs. These are the present-period explicit costs, the opportunity costs implicitly involved in the decision, and the future cost implications that flow from the decision. For example, direct labour and material costs, and changes in the variable overhead costs are the natural consequences of a decision to increase the output level. Many decisions will have implications for future costs, both explicit and implicit. If a firm expects to incur some costs in future as a consequence of the present analysis, such future costs should be included in the present value terms if known for certain. Economic Costs and Profits Accounting profits are the firm’s total revenue less its explicit costs. But according to economists profit is different. Economic profits are total revenue less all costs (explicit and implicit, the latter including a normal profit required to retain resources in a given line of production). Therefore, when an economist says that a firm is just covering its costs. It is meant that all explicit and implicit costs are being met, and that, the entrepreneur is receiving a return just large enough to retain his or her talents in the present line of production. If a firm’s total receipts exceed all its economic costs, the residual accruing to the entrepreneur is called an economic, or pure profit. In short: Economic Profit = Total Revenue-Opportunity Cost of all Inputs
This is depicted in the following figure : Economic Profits Total Revenue Economic or Opportunity Cost (Explicit plus implicit costs, including a normal profit)
Accounting Profit Accounting Costs
An economic profit is not a cost, because by definition it is a return in excess of the normal profit required to retain the entrepreneur in a particular line of production. Separable and Common Costs Costs can also be classified on the basis of their tractability. The costs that can be easily attributed to a product, a division, or a process are called separable costs, and the rest are called non-separable or common costs. The separable and common costs are also referred to as direct and indirect costs. The distinction between direct and indirect costs is of particular significance in a multiproduct firm for setting up economic prices for different products. Fixed and Variable costs Fixed costs are those costs which in total do not vary with changes in output. Fixed costs are associated with the very existence of a firm’s rate of output is zero. Such costs as interest on borrowed capital, rental payments, a portion of depreciation charges on equipment and buildings, and the salaries of top management and key personnel are generally fixed costs. On the other hand, variable costs are those costs which increase with the level of output. They include payment for raw materials, charges on fuel and electricity, wages and salaries of temporary staff, depreciation charges associated with wear and tear of this distinctions true only for the short-run. It is similar to the distinction that we made in the previous unit between fixed and variable factors of production under the short-run production analysis. The costs associated with fixed factors are called the fixed costs and the ones associated with variable factors, the variable costs. Thus, if capital is the fixed factor, capital rental is taken as the fixed cost and if labour is the variable factor, wage bill is treated as the variable cost. Activity :a) Can you give specific examples of: Implicit costs: ................................................... .............................................................................. ...................................................... ................................................ ..................... Social costs: ................................................... .............................................................................. ...................................................... ................................................. ......................
Directcosts: ................................................... .............................................................................. ...................................................... ................................................. ........................ IndirectCosts: ................................................... .............................................................................. ...................................................... ............................................... .................... Sunkcosts: ................................................... .............................................................................. ...................................................... ................................................. ........................ .. . Traceablecosts: ................................................... .............................................................................. ...................................................... ............................................ ................. Commoncosts: ................................................... .............................................................................. ...................................................... .............................................. ...................
RELATIONSHIP BETWEEN PRODUCTION AND COSTS The cost is closely related to production theory. A cost function is the relationship between a firm’s costs and the firm’s output. While the production function specifies the technological maximum quantity of output that can be produced from various combinations of inputs, the cost function combines this information with input price data and gives information on various outputs and their prices. The cost function can thus be thought of as a combination of the two pieces of information i.e., production function and input prices Now consider a short-run production function with only one variable input. The output grows at an increasing rate in the initial stages implying increasing retunes to the variable input, and then diminishing returns to the variable input start. Assuming that the input prices remain constant, the above production function will yield the variable cost function which has a shape that is characteristic of many variable cost function; increasing at a decreasing rate and then increasing at an increasing rate. Relationship between average product and average costs, and marginal product and marginal costs. For example. TVC = Pr. V ∴
AVC = TVC = Pr. V = Pr Q Q Q/V
and MC = ∆TVC = Pr. ∆V = ∆Q ∆Q
Pr ∆Q/∆V
Where Pr stands for the price of the variable factor and V stands for amount of variable factor. You may note that Pr being given, AVC is inversely related to the average product of the variable factors.
In the same way, given the wage rage, MC is inversely related to the marginal product of labour. We shall explore this relationship in greater detail subsequently. SHORT-RUN COST FUNCTIONS During short run some factors are fixed and others are variable.The short-run is normally defined as a time period over which some factors of production are fixed and others are variable. Needless to emphasize here that these periods are not defined by some specified length of time but, rather, are determined by the variability of factors of production. Thus, what one firm may consider the long-run may correspond to the short-run for another firm. Long run and short run costs of every firms varies. In the short-run, a firm incurs some costs that are associated with variable factors and others that result from fixed factors. The former are called variable costs and the latter represent fixed costs. Variable costs (VC) change as the level of output changes and therefore can be expressed as a function of output (Q), that is VC = f (Q). Variable costs typically include such things as raw material, labour, and utilities. In Column 3 of Table 1, we find that the total of variable costs changes directly with output. But note that the increases in variable costs associated with each one-unit increase in output are not constant. As production begins, variable costs will, for a time, increase by a decreasing amount, this is true through the fourth unit of the output. Beyond the fourth unit, however, variable costs rise by increasing amount for each successive unit of output. The explanation of this behaviour of variable costs lies in the law of diminishing returns. The following table will give you an idea about all Table I Total and Average-Cost Schedules for an Individual Firm in the Short-Rum (Hypothetical Data in Rupees) Total cost data, per week Average-cost data, per week (1) (2) (3) (4) (5) (6) (7) (8) Total Total Total Total Average Average Average Marginal Product Fixed variable cost fixed variable total cost Cost cost (TC) cost cost cost (MC) (TFC) (TVC) TC = (AFC) (AVC) (ATC) MC = TFC + AFC = AVC = ATC = change TVC TFC/Q TVC/Q TC/Q in TC change in Q 0 100 0 100 1 100 90 190 100.00 90.00 190.00 90 2 100 170 270 50.00 85.00 135.00 80
3 4 5 6 7 8 9 10
100 100 100 100 100 100 100 100
240 300 370 450 540 650 780 930
340 400 470 550 640 750 880 1030
33.33 25.00 20.00 16.67 14.29 12.50 11.11 10.00
80.00 75.00 74.00 75.00 77.14 81.25 86.25 86.67 93.00
113.33 100.00 94.00 91.67 91.43 93.75 97.78 103.00
70 60 70 80 90 110 130 150
Total Cost Total cost is the sum of fixed and variable cost at each level of output. It is shown in column 4 of Table-1. At zero unit of output, total cost is equal to the firm’s fixed cost. Then for each unit of production (through 1 to 10), total cost varies at the same rate as does variable cost. Per Unit, or Average Costs Besides their total costs, producers are equally concerned with their per unit, or average costs. In particular, average cost data is more relevant for making comparisons with product price, AVERAGE COST: COST : AC =TC/Q Where TC =total cost ; AC = average cost Q = quantity Average Fixed Costs Average fixed cost (AFC) is derived by dividing total fixed cost (TFC) by the corresponding output (Q). That is TFC AFC = -----Q While total fixed cost is, by definition, independent of output, AFC will decline so long as output increases. As output increases, a given total fixed cost of Rs. 100 is obviously being spread over a larger and larger output. This is what business executives commonly refer to as ‘spreading the overhead’. We find in Figure-III that the AFC curve is continuously declining as the output is increasing. The shape of this curve is of an asymptotic hyperbola. Average Variable Costs Average variable cost (AVC) is found by dividing total variable cost (TVC) by the corresponding output (Q): TVC
AVC = -----Q AVC declines initially, reaches a minimum, and then increases again, AFC + AVC = ATC ∆ ATC --------- = MC ∆Q Average Total Costs
Average total cost (ATC) can be found by dividing total cost (TC) by total output (Q) or, by adding AFC and AVC for each level of output. That is: TC ATC = ----- = AFC + AVC Q These data are shown in column 7 of the above Table. Marginal Cost
Marginal cost (MC) is defined as the extra, or additional, cost of producing one more unit of output. MC can be determined for each additional unit of output simply by noting the change in total cost which that unit’s production entails: Change in TC ∆TC MC = ----------------------------------- = --------Change in Q ∆Q The marginal cost concept is very crucial from the manager’s point of view. Marginal cost is a strategic concept because it designates those costs over which the firm has the most direct control. More specifically, MC indicates those costs which are incurred in the production of the last unit of output and therefore, also the cost which can be “saved” by reducing total output by the last unit. Average cost figures do not provide this information. A firm’s decisions as to what output level to produce is largely influenced by its marginal cost. When coupled with marginal revenue, which indicates the change in revenue from one more or one less unit of output, marginal cost allows a firm to determine whether it is profitable to expand or contract its level of production. Relationship of MC to AVC and ATC
It is also notable that marginal cost cuts both AVC and ATC at their minimum (Figure III). When both the marginal and average variable costs are falling, average will fall at a slower rate. And when MC and AVC are both rising, MC will rise at a faster rate. As a result, MC will attain its minimum before the AVC. In other words, when MC is less than AVC, the AVC will fall, and when MC exceeds AVC, AVC will rise. This means (Figure III) that so long as MC lies below AVC, the latter will fall and where MC is above AVC,AVC will rise. Therefore, at the point of intersection where MC=AVC,AVC has just ceased to fall and attained its minimum, but has not yet begun to rise. Similarly, the marginal cost curve cuts the average total cost curve at the latter’s minimum point. This is because MC
can be defined as the addition either to total cost or to total cost or to total variable cost resulting from one more unit of output. However, no such relationship exists between MC and the average fixed cost, because the two are not related; marginal cost by definition includes only those costs which change with output, and fixed costs by definition are independent of output. Managerial Uses of the Short-Run Cost Concepts
As already emphasized the relevant costs to be considered for decision-making will differ from one situation to the other depending on the problem faced by the manager. In general, the total cost concept is quite useful in finding out the break-even quantity of output. The total cost concept is also used to find out whether firm is making profits or not. The average cost concept is important for calculating the per unit profit of a business firm. The marginal and incremental cost concepts are essential to decide whether a firm should expand its production or not. LONG-RUN COST FUNCTIONS Long-run total cost curves are derived from the long-run production functions in which all inputs are variable. Such a production function is represented by the five asquint curves showing five different levels of output. The five cost curves tangent to these is equates at the points A,B,C,D and E represent total cost on resources. Since the cost per unit of capital (v) and, labour (w) are assumed to be constant, these five cost curves are parallel to one another, and the distance between them is constant along the expansion path traced out by A,B,C,D and E. Taking the values for total cost and output from the expansion path of Figure V (the most efficient points), we can construct the following table for total cost and output:
Figure V EXPANSIONPATH AND RETURNS TO SCALE
LABOUR Output (Q) 50 125 250 300 325
Long-run Total Cost (LTC) 150 200 250 300 350
These points are graphed in Figure VI as the long-run total cost (LTC) curve. The points A,B,C,D and E correspond to the equilibrium points in Figure V. Note that the LTC curve at first increases at a decreasing rate, then at a constant rate, and finally at an increasing rate. The LTC curve starts from the origin implying thereby that in the longrun all costs are variable and if nothing is produced, no resources will be used (i.e., the firm will quit the industry altogether). Thus, the LTC curve is analogous to the short-run VC curve. Only difference is, while the shape of VC is due to the law of variable proportions in the short-run, the shape of LTC is due to the existence of increasing, constant, and decreasing returns to scale in the long-run.
LONG-RUN TOTAL COST
Unit Costs in the Long-Run In the long-run, costs are not divided into fixed and variable components; all costs are variable. Thus, the only long-run unit cost functions of interest are long-run average cost (LAC) and long-run marginal cost (LMC). These are defined as follows : LTC LAC = ------Q ∆LTC
LMC = ----------∆ Q d (LTC) LMC = ----------dQ For the long-run total cost given in Figure VI, these unit costs can be presented in tabular form as follows: Output
Long Run Total
Long Run
Long Run
Q 0 50 125 250 300 325
Cost (LTC) 0 150 200 250 300 350
Average Cost (LAC) -3.00 1.60 1.00 1.00 1.08
Marginal Cost (LMC) -3.00 0.67 0.67 1.00 2.00
These LAC and LMC values are graphed in Figure VII. We see, both in the table and in the graph, that LAC and LMC are U-shaped and that they are equal at the minimum of LAC. The values of LMC are graphed at the midpoints of the output intervals they represent.
Figure VII Long-run average & marginal costs
Activity
a) Why are all costs variable in the long-run? ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ....................................... ................................................... .............................................................................. ...................................................... ................................................. ........................ .. .......................................
................................................... .............................................................................. ...................................................... ................................................. ........................ .. ....................................... b) Why is the LAC called an “enveloped curve”? Why cannot the LMC be can envelope as well? ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ....................................... ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ....................................... ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ....................................... c) What do you understand by “cost-efficiency”? “cost-efficiency ”? Draw a long-run cost diagram and explain.
b) Comment on the nature of costs involved in depreciation from both economic and accounting standpoints. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ..................................................... .......................... c) Distinguish between historical costs and replacement costs. Why is this distinction useful? ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ..................................................... .......................... d) Give examples to distinguish between ‘fixed overheads’ and ‘variable overheads’. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ..................................................... .......................... e) Can all ‘direct costs’ be treated as ‘variable costs’? ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. .............................................. ...................................................... ........ Activity Given Q = 100 + 0.L 2 – 0.0005 L 3
Where Q is output; L is labour. Suppose the wage rate is Rs. 10 and that 100 laborers are being employed. Find the AVC and MC. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. . ................................................... .............................................................................. ...................................................... ................................................. ........................ .. ................................................... .............................................................................. ...................................................... ................................................. ........................ .. .................................................. Activity 3
a) Fill in the blanks in the Table below. b) Take a separate graph paper and draw all the curves. Sort-run Cost-Schedules
Q 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
TFC 50 50 50
TVC
TC 55
8
AFC
AVC
ATC
MC
3
11.34
3
9.5 9.5
9 9.5
25
101
25 60.5
13 50 50 50 50
65 18 72.5 28 86
50 50 50 50 50 50 50 50
45 54.5 65.2
5 4.55 130
99.1 174.75 162 259.25 269.5
50 50
399 450
-Output O is measured in 000 units -All costs are measured in Rs. 000
2.5
22.5
