Theory of CostTheory of Cost

Cost Function – Derived FunctionCost Function – Derived Function

C= f(X, T, PC= f(X, T, Pff, K), K)

Where C is total costWhere C is total cost X is the outputX is the output

T is technologyT is technology

PPf f is price of FOPis price of FOP

K is fixed factor (capital)K is fixed factor (capital)

Cost ConceptsCost Concepts

Opportunity Cost & Actual ConceptsOpportunity Cost & Actual Concepts Business Costs & Full CostsBusiness Costs & Full Costs Explicit & Implicit or Imputed CostsExplicit & Implicit or Imputed Costs Out-of-Pocket & Book CostsOut-of-Pocket & Book Costs Fixed & Variable CostsFixed & Variable Costs Total, Average & Marginal CostsTotal, Average & Marginal Costs Short-Run and Long-Run CostsShort-Run and Long-Run Costs Incremental Costs and Sunk CostsIncremental Costs and Sunk Costs Historical & Replacement CostsHistorical & Replacement Costs Private & Social CostsPrivate & Social Costs

Opportunity Cost & Actual Opportunity Cost & Actual ConceptsConcepts

Opportunity cost refers to the expected returns Opportunity cost refers to the expected returns from the second best use of resources which from the second best use of resources which are foregone due to the scarcity of resources.are foregone due to the scarcity of resources.

Actual cost are those which are actually Actual cost are those which are actually incurred by the firm in the payment for labour, incurred by the firm in the payment for labour, material , machinery, equipment etc.material , machinery, equipment etc.

Business cost and full costBusiness cost and full cost

All the expenses which are incurred to carry out a All the expenses which are incurred to carry out a business. The concept of business cost is similar to business. The concept of business cost is similar to actual cost.actual cost.

Full cost includes business cost, opportunity cost and Full cost includes business cost, opportunity cost and normal profit. Normal profit is the necessary normal profit. Normal profit is the necessary minimum earning which the firm must receive to minimum earning which the firm must receive to remain in the present occupation.remain in the present occupation.

Explicit & Implicit or Imputed CostsExplicit & Implicit or Imputed Costs

Explicit costsExplicit costs = payments to non-owners of a firm for the = payments to non-owners of a firm for the supply of their resources (wages paid to labour, costs of supply of their resources (wages paid to labour, costs of electricity, the rental charges for plant usage, the cost of electricity, the rental charges for plant usage, the cost of other raw materials used in the production process, etc.)other raw materials used in the production process, etc.)

Implicit costsImplicit costs = the opportunity costs of using the resources = the opportunity costs of using the resources already owned by the firm, where no payment is made to already owned by the firm, where no payment is made to outsiders (use of the factory by giving up renting out for outsiders (use of the factory by giving up renting out for the same purpose, input of the owner / manager to give up the same purpose, input of the owner / manager to give up the opportunity to earn a salary at another firm)the opportunity to earn a salary at another firm)

Out of Pocket and Book costOut of Pocket and Book cost

The items of expenditure which involves cash The items of expenditure which involves cash payments or cash transfers are known as out of payments or cash transfers are known as out of pocket cost. All the explicit cost like wages, pocket cost. All the explicit cost like wages, rent, interest etc fall in this category.rent, interest etc fall in this category.

Certain cost which do not involve cash Certain cost which do not involve cash payment but a provision is made while payment but a provision is made while calculating profit and loss a/c are known as calculating profit and loss a/c are known as book cost. Eg. Unpaid interest on the owner’s book cost. Eg. Unpaid interest on the owner’s own fundown fund

Short run and Long run costShort run and Long run cost

Short run cost are the cost which vary with Short run cost are the cost which vary with variation in the output, the size of the firm variation in the output, the size of the firm remaining the same.remaining the same.

Long run cost are the cost incurred on fixed Long run cost are the cost incurred on fixed assets like plant & machinery etc.assets like plant & machinery etc.

Historical and Replacement costHistorical and Replacement cost

Historical cost refers to the cost of the asset Historical cost refers to the cost of the asset acquired in the pastacquired in the past

Replacement cost refers to the outlay which Replacement cost refers to the outlay which has to be made for the replacement of old has to be made for the replacement of old asset.asset.

Incremental cost and sunk costIncremental cost and sunk cost Incremental cost refers to the total additional cost Incremental cost refers to the total additional cost

associated with the decision to expand the output.associated with the decision to expand the output. Sunk cost are the cost that cannot be altered , Sunk cost are the cost that cannot be altered ,

increased or decreased by varying the rate of output. increased or decreased by varying the rate of output. These are the cost that cannot be recovered. For eg. These are the cost that cannot be recovered. For eg. Amortization of past expenses like depreciation , Amortization of past expenses like depreciation , expenditure on a highly specialized equipment expenditure on a highly specialized equipment designed to order for a plant that can neither be sold designed to order for a plant that can neither be sold to any other firm nor can be used for any alternative to any other firm nor can be used for any alternative purpose.purpose.

Private cost and social costPrivate cost and social cost

Private cost refers to the cost of production Private cost refers to the cost of production incurred and provided for by the individual incurred and provided for by the individual firm engaged in production of the firm engaged in production of the commodity. It includes both explicit and commodity. It includes both explicit and implicit cost.implicit cost.

Social cost refers to the cost of producing Social cost refers to the cost of producing the commodity to the society as the whole. the commodity to the society as the whole. It takes into consideration all those cost It takes into consideration all those cost borne by the society directly or indirectly.borne by the society directly or indirectly.

Traditional Theory – Short Run Traditional Theory – Short Run CostCost

TC = TFC + TVCTC = TFC + TVC

Total fixed cost:Total fixed cost: costs that do not vary with output and must be paid costs that do not vary with output and must be paid even if output is zero. These types of costs are beyond managerial even if output is zero. These types of costs are beyond managerial control. Examples: Depreciation of machinery, rent, mortgage control. Examples: Depreciation of machinery, rent, mortgage payments, interest payments on loans, and monthly connection fees for payments, interest payments on loans, and monthly connection fees for utilities. utilities. The level of total fixed costs is the same at all levels of output The level of total fixed costs is the same at all levels of output (even when output equals zero). (even when output equals zero).

Total variable cost:Total variable cost: costs that vary as output changes. If a firm uses costs that vary as output changes. If a firm uses more inputs to produce output, total variable costs will rise. These more inputs to produce output, total variable costs will rise. These types of costs are within management control. Examples: labour costs, types of costs are within management control. Examples: labour costs, raw material costs, and running expenses such as fuel, ordinary repair raw material costs, and running expenses such as fuel, ordinary repair & routine maintenance. Variable costs are equal to zero when no & routine maintenance. Variable costs are equal to zero when no output is produced and increase with the level of output.output is produced and increase with the level of output.

Fig. : Total Cost CurvesFig. : Total Cost Curves

TVC

TFC

Cost

Output

TC

Explanation for the total cost curveExplanation for the total cost curve

Total fixed costs are the same at all levels of output, a Total fixed costs are the same at all levels of output, a graph of the total fixed cost curve is a horizontal line.graph of the total fixed cost curve is a horizontal line.

The total variable cost curve increases as output The total variable cost curve increases as output increases. Initially, it is expected to increase at a increases. Initially, it is expected to increase at a decreasing rate (since marginal productivity increases decreasing rate (since marginal productivity increases initially, the cost of additional units of output initially, the cost of additional units of output decline). As the level of output rises, however, decline). As the level of output rises, however, variable costs are expected to increase at an variable costs are expected to increase at an increasing rate (as a result of the law of diminishing increasing rate (as a result of the law of diminishing marginal returns). marginal returns).

TC, TVC, TFCTC, TVC, TFC The table below contains a listing The table below contains a listing

of a hypothetical set of total fixed of a hypothetical set of total fixed cost and total variable cost cost and total variable cost schedules. As this table indicates, schedules. As this table indicates, total fixed costs are the same at total fixed costs are the same at each possible level of output. each possible level of output. Total variable costs are expected Total variable costs are expected to rise as the level of output rises.to rise as the level of output rises.

As the table below indicates, we As the table below indicates, we can use the TFC and TVC can use the TFC and TVC schedules to determine the total schedules to determine the total cost schedule for this firm. Note cost schedule for this firm. Note that, at each level of output, TC = that, at each level of output, TC = TFC + TVC. TFC + TVC.

AC = AFC + AVCAC = AFC + AVC

Average costs: costs per unit of outputAverage costs: costs per unit of output Average fixed cost = TFC divided by quantity Average fixed cost = TFC divided by quantity

produced.produced. AFC = TFC / QAFC = TFC / Q as output rises AFC falls continuously (resembles a as output rises AFC falls continuously (resembles a

rectangular hyperbola)rectangular hyperbola) Average variable cost = TVC divided by quantity Average variable cost = TVC divided by quantity

producedproduced AVC = TVC / QAVC = TVC / Q usually average variable cost is U-shaped, with usually average variable cost is U-shaped, with

AVC falling initially and then rising as it becomes AVC falling initially and then rising as it becomes more costly to produce additional units of output.more costly to produce additional units of output.

Average total costs = AFC + AVC = TC/QAverage total costs = AFC + AVC = TC/Q

Fig. : Average costsFig. : Average costs

Cost

Output

ATC

AVC

AFC

Average CostsAverage Costs

Marginal CostMarginal Cost

Marginal Cost (MC):Marginal Cost (MC):

Change in total costs due to a unit change in Change in total costs due to a unit change in output.output.

MC is the slope of TC curve. With an inverse MC is the slope of TC curve. With an inverse S-shape of TC, MC curve will be U shape.S-shape of TC, MC curve will be U shape.

Q

TCMC

Fig.: Average and marginal costsFig.: Average and marginal costs

Cost

Output

ATC

MC

Relationship between MC & Relationship between MC & ATCATC

If the MC is less than the ATC, then the ATC must be If the MC is less than the ATC, then the ATC must be falling. This follows from the fact that if you add a falling. This follows from the fact that if you add a quantity to the average costs that is less than the quantity to the average costs that is less than the average, the average must fall. average, the average must fall.

If the MC exceeds the ATC, the ATC must be rising. If the MC exceeds the ATC, the ATC must be rising. This follows from the fact that you are adding a This follows from the fact that you are adding a quantity to the average costs that is greater than the quantity to the average costs that is greater than the average. Hence the average must rise. average. Hence the average must rise.

It should also be noted that when MC cuts the ATC It should also be noted that when MC cuts the ATC and the AVC at their minimum points. and the AVC at their minimum points.

Fig .: Traditional Theory Cost Fig .: Traditional Theory Cost

Cost

Output

ATC

AVC

MC

AFC

Traditional Theory -Long run Traditional Theory -Long run costs/Envelope Curvecosts/Envelope Curve

The firm plans in the long run, when all inputs The firm plans in the long run, when all inputs are variableare variable

The LRAC is often called the firm’s planning The LRAC is often called the firm’s planning curve.curve.

The long run average cost (LRAC) is derived The long run average cost (LRAC) is derived from short run cost curves. Each point of from short run cost curves. Each point of LRAC corresponds to a point on short run cost LRAC corresponds to a point on short run cost curve, which is tangent to LRAC.curve, which is tangent to LRAC.

Long-Run Average Costs Long-Run Average Costs

The LRAC is a curve that is tangent to the set The LRAC is a curve that is tangent to the set of SRACs. When the LRAC curve falls the of SRACs. When the LRAC curve falls the tangency points are to the left of the minimum tangency points are to the left of the minimum points on the SRAC and when the LRAC points on the SRAC and when the LRAC curve is rising the tangency points are to the curve is rising the tangency points are to the right of the minimum points of the SRAC right of the minimum points of the SRAC curves. curves.

With a great variety of plant sizes, the With a great variety of plant sizes, the corresponding short-run average total cost corresponding short-run average total cost curves trace a smooth LRAC curve. curves trace a smooth LRAC curve.

Fig. :The LRAC or ‘the firm’s planning Fig. :The LRAC or ‘the firm’s planning curve’curve’

Cost

Output

SRATCs SRATCmSRATCl

40

30

6 12

The plant size selected in the long-run depends on the expected level of production

Fig. : The LRAC with unlimited Fig. : The LRAC with unlimited plant sizeplant size

Cost

Output

LRAC is tangent to the set of SRACs

LRAC

Fig. : Scale economiesFig. : Scale economiesCost

Output

Economies of scale

Constant returns to scale

Diseconomies of scale

Minimum efficient scale

•LRAC varies from industry to industry

•Usually economies dominate diseconomies

Economies of scaleEconomies of scale (a) internal economies(a) internal economies (b) external economies(b) external economies

Diseconomies of scaleDiseconomies of scale (a) internal – managerial and labour (a) internal – managerial and labour

inefficiencyinefficiency (b) external (b) external

Reasons for Economies of Scale…Reasons for Economies of Scale… Increasing returns to scaleIncreasing returns to scale Specialization in the use of labor and capitalSpecialization in the use of labor and capital

Economies in maintaining inventoryEconomies in maintaining inventory Discounts from bulk purchasesDiscounts from bulk purchases Lower cost of raising capital fundsLower cost of raising capital funds Spreading promotional and R&D costsSpreading promotional and R&D costs

Management efficienciesManagement efficiencies

Reasons for Diseconomies of Scale…Reasons for Diseconomies of Scale… Decreasing returns to scale Input market imperfections Management coordination and control

problems

Long Run Marginal CostLong Run Marginal Cost

LRMC is derived from SRMC, but does not LRMC is derived from SRMC, but does not envelope them.envelope them.

LRMC is formed from points of intersections LRMC is formed from points of intersections of SRMC curves with vertical lines drawn of SRMC curves with vertical lines drawn from point of tangency of corresponding SAC from point of tangency of corresponding SAC curve and LRAC curve.curve and LRAC curve.

At the minimum point we have At the minimum point we have

SACSACBB = SMC = SMCBB = LAC = LMC = LAC = LMC

SAC1

SMC1

SMC2

SAC2

SMC3

SAC3

LMC

LAC

Break Even Analysis/Profit Break Even Analysis/Profit Contribution AnalysisContribution Analysis

Linear Cost & Revenue FunctionLinear Cost & Revenue Function

Break Even Analysis/Profit Break Even Analysis/Profit Contribution AnalysisContribution Analysis

Non Linear Cost & Revenue FunctionNon Linear Cost & Revenue Function

Modern Theory of CostModern Theory of Cost

Need for Reserve CapacityNeed for Reserve Capacity To meet seasonal & cyclical fluctuations in demand.To meet seasonal & cyclical fluctuations in demand. To give flexibility for repair of broken down To give flexibility for repair of broken down

machinery.machinery. To increase output as demand increases.To increase output as demand increases. To give flexibility for minor alterations of the product To give flexibility for minor alterations of the product

due to change in taste of customers.due to change in taste of customers. Some reserve capacity on organizational & Some reserve capacity on organizational &

administrative level will also be required.administrative level will also be required.

Difference b/w Reserve Capacity & Difference b/w Reserve Capacity & Excess CapacityExcess Capacity

Excess capacity arises from U-shaped costs by Excess capacity arises from U-shaped costs by the traditional theory of the firm. While the traditional theory of the firm. While reserve capacity arises from the saucer shaped reserve capacity arises from the saucer shaped cost of modern theory of firm.cost of modern theory of firm.

The traditional theory assumes that each plant The traditional theory assumes that each plant is designed to produce optimally only single is designed to produce optimally only single level of output. While the reserve capacity level of output. While the reserve capacity makes it possible to have constant SAVC makes it possible to have constant SAVC within a certain range of output.within a certain range of output.

Difference b/w Reserve Capacity & Difference b/w Reserve Capacity & Excess CapacityExcess Capacity

The modern theory with change in output cost The modern theory with change in output cost does not change while in traditional theory the does not change while in traditional theory the cost also changes.cost also changes.

In figure the firm produces an output of X In figure the firm produces an output of X smaller than Xsmaller than XMM thus (X thus (XMM-X )is the excess -X )is the excess capacity which leads to increase in cost. The capacity which leads to increase in cost. The range of output Xrange of output X11XX2 2 reflects the plant reserve reflects the plant reserve capacity which does not leads to increase in capacity which does not leads to increase in cost.cost.

Difference b/w Excess & Reserve CapacityDifference b/w Excess & Reserve Capacity

AVC

C

0 XX XMExcess Capacity X1

X2

C

0

Reserve Capacity

AVC

Short – Run Cost Curve under Short – Run Cost Curve under Modern Theory of CostModern Theory of Cost

Long Run Cost under Modern Long Run Cost under Modern Theory (L-Shaped LAC Curve)Theory (L-Shaped LAC Curve)