Cost n output relation

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Cost n output relation

  1. 1. 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 INTRODUCTIONIn theprevious chapterwe have illustrated the concept of production. And in thislesson I amgoing to tell youabout the cost and its related factors. You will also come toknow aboutcost and outputrelationship. Cost and revenue are the two majorfactors that a profit maximising firm needs to monitor continuously. It is thelevel of cost relative torevenue that determines the firm’s overall profitability. Inorder to maximise profits, afirm tries to increase its revenue and lower its cost. Whilethe market factors determinethe level of revenue to a great extent, the cost can bebrought down either byproducing the optimum level of output using the leastcost combination of inputs, or increasing factor productivities, or by improving theorganisational efficiency. The firm’s output level is determined by its cost. The producer has to pay for factors of production fortheir services. The expenses incurred on these factors of production are known as the costof production, or in short cost.Product prices are determined by the interaction of the forces of demandand supply. The basic factor underlying the ability and willingness of firms tosupply a product in the market is the cost of production. Thus, cost of productionprovides the floor to pricing. It is the cost that forms the basis for manymanagerial decisions like which price to quote, whether to accept a particularorder 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 idlecapacity or rent out the facilities, whether to make or buy a product, etc.However, it is essential to underline here that all costs are notrelevant for every decision under consideration.
  2. 2. 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 canaid managers in making correct decisions. We shall examine the difference betweeneconomic and accounting concepts of costs and profits. We shall then consider theconcepts of short-run and long-run costs and show that they, in conjunctionwith the concepts of production studies in the preceding unit, can
  3. 3. give us a more complete understanding of the applications of cost theoryto decision-making.VARIOUS TYPES OF COSTSThere are different types of costs that a firm may consider relevant for decision-making under varying situations. The manner in which costs are classifiedor defined is largely dependent on the purpose for which the cost dataare being outlined.Explicit and Implicit CostsThe opportunity cost (or cost of the foregone alternative) of a resource is adefinition cost in the most basic form. While this particular definition of cost is thepreferred baseline for economists in describing cost, not all costs in decision-making situations are completely obvious; one of the skills of a good manager is theability to uncover hidden costs. for dissimilar purposes. Traditionally, theaccountants have been primarily connected with collection of historical cost data foruse in reporting a firm’s financial behaviour and position and in calculating itstaxes.They report or record what was happened, present information that willprotect the interests of various shareholders in the firm, and providestandards against which performance can be judged. All these have onlyindirect relationship to decision-making. Business economists, on the otherhand, have been primarily concerned with using cost data in decisionsmaking. 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 bethe income that he would have earned if he had employed his labour resourceson a job, rather than spending them in studying managerialeconomics, accounting, and so on. The time cost in money terms can bereferred to as implicit cost of doing an MBA.The out-of-pocket costs on tuition and teaching materials are the explicitcosts that a student incurs while attending MBA. Thus, the total cost of doing anMBA to a student is implicit costs (opportunity cost) plus the explicit (out-of-pocket) costs.Direct and Indirect CostsThere are some costs which can be directly attributed to production of agiven product.The use of raw material, labour input, and machine time involved inthe production of each unit can usually be determined. On the other hand, there arecertain costs like stationery and other office and administrative expenses,electricity charges, depreciation of plant and buildings, and other such expenses
  4. 4. that cannot easily and accurately be separated and attributed to individual unitsof production, except on arbitrary basis. When referring to the separable costs offirst category accountants call them the direct, or prime costs per unit. The jointcosts of the second category are referred to as indirect or overhead costs by theaccountants. Direct and indirect costs are not exactly synonymous to whateconomists refer to as variable costs and fixed costs.Private Costs versus Social CostsPrivate costs are those that accrue directly to the individuals or firms engaged inrelevant activity. External costs, on the other hand, are passed on to persons notinvolved in the activity in any direct way (i.e., they are passed on to societyat large). While the private cost to the firm of dumping is zero, it is definitely positiveto the society. It affects adversely the people located down current who areadversely 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 wereincluded in the production costs of the producing firm a true picture of real, or socialcosts of the output would be obtained. Ignoring external costs may lead to aninefficient and undesirable allocation of resources in society.Relevant Costs and Irrelevant CostsThe relevant costs for decision-making purposes are those costs which areincurred as a result of the decision under consideration and which are relevantfor the business purpose. The relevant costs are also referred to asthe incremental costs.There are three main categories of relevant or incremental costs. These are thepresent-period explicit costs, the opportunity costs implicitly involved in thedecision, and the future cost implications that flow from the decision. Forexample, direct labour and material costs, and changes in the variable overheadcosts are the natural consequences of a decision to increase the output level.Many decisions will have implications for future costs, both explicit and implicit. Ifa firm expects to incur some costs in future as a consequence of thepresent analysis, such future costs should be included in the presentvalue terms if known for certain.Economic Costs and ProfitsAccounting profits are the firm’s total revenue less its explicit costs.But according to economists profit is different. Economic profits are total revenueless all costs (explicit and implicit, the latter including a normal profit required toretain resources in a given line of production). Therefore, when an economistsays that a firm is just covering its costs. It is meant that all explicit and implicitcosts are being met, and that, the entrepreneur is receiving a return just largeenough to retain his or her talents in the present line of production. If a firm’stotal receipts exceed all its economic costs, the residual accruing to theentrepreneur is called an economic, or pure profit. In short:Economic Profit = Total Revenue-Opportunity Cost of all Inputs
  5. 5. This is depicted in the following figure : Economic Profits Accounting ProfitTotal Revenue Economic or Opportunity Accounting Costs Cost (Explicit plus implicit costs, including a normal profit)An economic profit is not a cost, because by definition it is a return in excess ofthe normal profit required to retain the entrepreneur in a particular line ofproduction.Separable and Common CostsCosts can also be classified on the basis of their tractability. The costs that can beeasily attributed to a product, a division, or a process are called separablecosts, and the rest are called non-separable or common costs. The separableand common costs are also referred to as direct and indirect costs. Thedistinction between direct and indirect costs is of particular significance in a multi-product firm for setting up economic prices for different products.Fixed and Variable costsFixed costs are those costs which in total do not vary with changes inoutput. Fixed costs are associated with the very existence of a firm’s rate ofoutput is zero. Such costs as interest on borrowed capital, rental payments, aportion of depreciation charges on equipment and buildings, and thesalaries of top management and key personnel are generally fixed costs.On the other hand, variable costs are those costs which increase with the level ofoutput. They include payment for raw materials, charges on fuel and electricity,wages and salaries of temporary staff, depreciation charges associatedwith wear and tear of this distinctions true only for the short-run. It is similar tothe distinction that we made in the previous unit between fixed and variablefactors of production under the short-run production analysis. The costsassociated with fixed factors are called the fixed costs and the onesassociated with variable factors, the variable costs. Thus, if capital is thefixed factor, capital rental is taken as the fixed cost and if labour is the variablefactor, wage bill is treated as the variable cost.Activity :-a) Can you give specific examples of: Implicit costs:.............................................................................................................................. Social costs:...............................................................................................................................
  6. 6. Directcosts:................................................................................................................................ IndirectCosts:............................................................................................................................. Sunkcosts:.................................................................................................................................. Traceablecosts:.......................................................................................................................... Commoncosts:............................................................................................................................RELATIONSHIP BETWEEN PRODUCTION AND COSTSThe cost is closely related to production theory. A cost function is the relationshipbetween a firm’s costs and the firm’s output. While the production functionspecifies the technological maximum quantity of output that can beproduced from various combinations of inputs, the cost function combines thisinformation with input price data and gives information on various outputsand their prices. The cost function can thus be thought of as a combination ofthe two pieces of information i.e., production function and input pricesNow consider a short-run production function with only one variable input.The output grows at an increasing rate in the initial stages implying increasingretunes to the variable input, and then diminishing returns to the variableinput start. Assuming that the input prices remain constant, the aboveproduction function will yield the variable cost function which has a shapethat is characteristic of many variable cost function; increasing at a decreasingrate and then increasing at an increasing rate.Relationship between average product and average costs, and marginal productand marginal costs. For example.TVC = Pr. VAVC = TVC = Pr. V = PrQ Q Q/Vand MC = ∆TVC = Pr. ∆V= Pr ∆Q/∆∆Q ∆Q VWhere Pr stands for the price of the variable factor and V stands for amount ofvariable factor.You may note that Pr being given, AVC is inversely related to the
  7. 7. average product of the variable factors.
  8. 8. In the same way, given the wage rage, MC is inversely related to the marginalproduct of labour.We shall explore this relationship in greater detail subsequently.SHORT-RUN COST FUNCTIONSDuring short run some factors are fixed and others are variable.The short-run isnormally defined as a time period over which some factors of production are fixedand others are variable. Needless to emphasize here that these periods are notdefined by some specified length of time but, rather, are determined bythe variability of factors of production. Thus, what one firm may consider thelong-run may correspond to the short-run for another firm. Long run and shortrun costs of every firms varies.In the short-run, a firm incurs some costs that are associated with variable factorsand others that result from fixed factors. The former are called variable costs andthe latter represent fixed costs. Variable costs (VC) change as the level of outputchanges 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, andutilities. In Column 3 of Table 1, we find that the total of variable costs changesdirectly with output. But note that the increases in variable costs associated witheach one-unit increase in output are not constant. As production begins, variablecosts will, for a time, increase by a decreasing amount, this is true through the fourthunit of the output. Beyond the fourth unit, however, variable costs rise by increasingamount for each successive unit of output. The explanation of this behaviourof 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) MarginTotal Total Total Total Average Average Average alProduct 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 Q0 100 0 1001 100 90 190 100.00 90.00 190.00 90
  9. 9. 2 100 170 270 50.00 85.00 135.00 803 100 240 340 33.33 80.00 113.33 704 100 300 400 25.00 75.00 100.00 605 100 370 470 20.00 74.00 94.00 706 100 450 550 16.67 75.00 91.67 807 100 540 640 14.29 77.14 91.43 908 100 650 750 12.50 81.25 93.75 1109 100 780 880 11.11 86.25 97.78 13010 100 930 1030 10.00 86.67 103.00 150 93.00Total CostTotal cost is the sum of fixed and variable cost at each level of output. It is shownin column 4 of Table-1. At zero unit of output, total cost is equal to the firm’s fixedcost. Then for each unit of production (through 1 to 10), total cost varies at thesame rate as does variable cost.Per Unit, or Average CostsBesides their total costs, producers are equally concerned with their per unit, oraverage costs. In particular, average cost data is more relevant for makingcomparisons with product price,AVERAGE COST:AC =TC/Q WhereTC =total cost ; AC = average cost Q = quantityAverage Fixed CostsAverage fixed cost (AFC) is derived by dividing total fixed cost (TFC) bythe corresponding output (Q). That is TFCAFC = ----- - QWhile total fixed cost is, by definition, independent of output, AFC will decline solong as output increases. As output increases, a given total fixed cost of Rs. 100is obviously being spread over a larger and larger output. This is what businessexecutives commonly refer to as ‘spreading the overhead’. We find in Figure-IIIthat the AFC curve is continuously declining as the output is increasing.The shape of this curve is of an asymptotic hyperbola.Average Variable CostsAverage variable cost (AVC) is found by dividing total variable cost (TVC) by thecorresponding output (Q):
  10. 10. TVC
  11. 11. AVC = ----- - QAVC declines initially, reaches a minimum, and then increases again,AFC + AVC = ATC∆ ATC-------- - = MC∆QAverage Total CostsAverage 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: TCATC = ---- - = AFC + AVC QThese data are shown in column 7 of the above Table.Marginal CostMarginal cost (MC) is defined as the extra, or additional, cost of producing one moreunit of output. MC can be determined for each additional unit of outputsimply by noting the change in total cost which that unit’s production entails: Change in TC∆TCMC = ------------------ = -------- - Change in Q ∆QThe marginal cost concept is very crucial from the manager’s point of view. Marginalcost is a strategic concept because it designates those costs over which the firm has themost direct control. More specifically, MC indicates those costs which are incurred in theproduction of the last unit of output and therefore, also the cost which can be “saved” byreducing total output by the last unit. Average cost figures do not provide thisinformation. A firm’s decisions as to what output level to produce is largely influencedby its marginal cost. When coupled with marginal revenue, which indicates the change inrevenue from one more or one less unit of output, marginal cost allows a firm todetermine whether it is profitable to expand or contract its level of production.Relationship of MC to AVC and ATCIt is also notable that marginal cost cuts both AVC and ATC at theirminimum (Figure III). When both the marginal and average variable costs arefalling, average will fall at a slower rate. And when MC and AVC are both rising, MCwill rise at a faster rate. As a result, MC will attain its minimum before the AVC. Inother words, when MC is less than AVC, the AVC will fall, and when MC exceedsAVC, AVC will rise. This means (Figure III) that so long as MC lies below AVC, thelatter will fall and where MC is above AVC,AVC will rise. Therefore, at thepoint of intersection where MC=AVC,AVC has just ceased to fall and attained itsminimum, but has not yet begun to rise. Similarly, the marginal cost curve cuts theaverage total cost curve at the latter’s minimum point. This is because MC
  12. 12. can be defined as the addition either to total cost or to total cost or to totalvariable cost resulting from one more unit of output. However, no suchrelationship exists between MC and the average fixed cost, because the two are notrelated; marginal cost by definition includes only those costs which changewith output, and fixed costs by definition are independent of output.Managerial Uses of the Short-Run Cost ConceptsAs already emphasized the relevant costs to be considered for decision-makingwill differ from one situation to the other depending on the problem faced by themanager. In general, the total cost concept is quite useful in finding outthe break-even quantity of output. The total cost concept is also used tofind out whether firm is making profits or not. The average cost concept isimportant for calculating the per unit profit of a business firm. The marginaland incremental cost concepts are essential to decide whether a firmshould expand its production or not.LONG-RUN COST FUNCTIONSLong-run total cost curves are derived from the long-run production functions inwhich all inputs are variable. Such a production function is represented bythe five asquint curves showing five different levels of output. The five costcurves tangent to these is equates at the points A,B,C,D and E represent total coston resources. Since the cost per unit of capital (v) and, labour (w) are assumed tobe constant, these five cost curves are parallel to one another, and the distancebetween 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 andoutput: Figure V EXPANSIONPATH AND RETURNS TO SCALE
  13. 13. LABOU ROutput Long-run Total Cost(Q) (LTC) 50 150 125 200 250 250 300 300 325 350These points are graphed in Figure VI as the long-run total cost (LTC) curve. The pointsA,B,C,D and E correspond to the equilibrium points in Figure V. Note that the LTCcurve at first increases at a decreasing rate, then at a constant rate, and finally at anincreasing rate. The LTC curve starts from the origin implying thereby that in the long-run all costs are variable and if nothing is produced, no resources will be used (i.e., thefirm will quit the industry altogether). Thus, the LTC curve is analogous to the short-runVC curve. Only difference is, while the shape of VC is due to the law of variableproportions 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.
  14. 14. 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 can beFor the long-run total cost given in Figure VI, these unit costs presentedin tabular form as follows:Output Long Run Total Long Run Long Run
  15. 15. Q Cost Average Cost Marginal Cost (LTC) (LAC) (LMC) 0 0 -- -- 50 150 3.00 3.00 125 200 1.60 0.67 250 250 1.00 0.67 300 300 1.00 1.00 325 350 1.08 2.00These LAC and LMC values are graphed in Figure VII. We see, both in the tableand in the graph, that LAC and LMC are U-shaped and that they are equal at theminimum of LAC. The values of LMC are graphed at the midpoints of the outputintervals they represent. Figure VII Long-run average & marginal costsActivitya) Why are all costs variable in the long-run?................................................................................................................................................................................................................................................................................................................................................
  16. 16. ........................................................................................................................................................................b) Why is the LAC called an “enveloped curve”? Why cannot the LMC be can envelope as well?........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3) What do you understand by “cost-efficiency”? Draw a long-run cost diagram and explain.2) Comment on the nature of costs involved in depreciation from both economicand accounting standpoints.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3) Distinguish between historical costs and replacement costs. Why is thisdistinction useful?............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................4) Give examples to distinguish between ‘fixed overheads’ and‘variable overheads’.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................5) Can all ‘direct costs’ be treated as ‘variable costs’?........................................................................................................................................................................................................................................................................................................................ Activity 2 3Given Q = 100 + 0.L – 0.0005 L
  17. 17. 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 1) Fill in the blanks in the Table below. 2) Take a separate graph paper and draw all the curves.Sort-run Cost-SchedulesQ TFC TVC TC AFC AVC ATC MC1 50 552 50 8 253 50 60.54 135 50 656 50 18 3 11.34 37 50 72.58 50 289 8610 50 45 5 9.5 911 50 54.5 4.55 9.5 9.512 50 65.213 50 13014 50 99.115 50 174.7516 50 16217 50 259.2518 269.519 50 39920 50 450 2.5 22.5 25 101-Output O is measured in 000 units-All costs are measured in Rs. 000
  18. 18. 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 1) Fill in the blanks in the Table below. 2) Take a separate graph paper and draw all the curves.Sort-run Cost-SchedulesQ TFC TVC TC AFC AVC ATC MC1 50 552 50 8 253 50 60.54 135 50 656 50 18 3 11.34 37 50 72.58 50 289 8610 50 45 5 9.5 911 50 54.5 4.55 9.5 9.512 50 65.213 50 13014 50 99.115 50 174.7516 50 16217 50 259.2518 269.519 50 39920 50 450 2.5 22.5 25 101-Output O is measured in 000 units-All costs are measured in Rs. 000
  19. 19. 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 1) Fill in the blanks in the Table below. 2) Take a separate graph paper and draw all the curves.Sort-run Cost-SchedulesQ TFC TVC TC AFC AVC ATC MC1 50 552 50 8 253 50 60.54 135 50 656 50 18 3 11.34 37 50 72.58 50 289 8610 50 45 5 9.5 911 50 54.5 4.55 9.5 9.512 50 65.213 50 13014 50 99.115 50 174.7516 50 16217 50 259.2518 269.519 50 39920 50 450 2.5 22.5 25 101-Output O is measured in 000 units-All costs are measured in Rs. 000

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