Topic 3.2Topic 3.2Analysis of CostsAnalysis of Costs

& & Cost EstimationCost Estimation

(Pl. read the prescribed chapter & cases (Pl. read the prescribed chapter & cases given in it before coming for the class)given in it before coming for the class)

Ref: Ch. 7Ref: Ch. 7

The Nature of The Nature of CostsCosts• Explicit CostsExplicit Costs

– Accounting (or Historical) CostsAccounting (or Historical) Costs• Economic CostsEconomic Costs

– Implicit CostsImplicit Costs– Opportunity (or Alternative) Opportunity (or Alternative)

CostsCosts• Relevant CostsRelevant Costs

– Incremental Costs (Incremental Costs (vs MCvs MC))•Sunk Costs are IrrelevantSunk Costs are Irrelevant ( (why?why?))

Explicit vs. implicit costs

• Explicit costs include the ordinary items that an accountant would include as the firms expenses

• Implicit costs include opportunity costs of resources owned and used by the firm’s owner

Opportunity costsOpportunity costsThe value of the other products that the The value of the other products that the resources used in production could have resources used in production could have produced at their next best alternative. It is produced at their next best alternative. It is a subset of Implicit costsa subset of Implicit costs

Short runA period of time so short that

the firm cannot alter the quantity of some of its inputs

•Typically some inputs are fixed inputs in the short run, e.g. plant and equipment, skilled labor etc. & •Fixed inputs determine/restrict the scale of the firm’s operation (output)

Short-Run Cost Short-Run Cost FunctionsFunctions

Total Cost = TC = f(Q)Total Fixed Cost = TFCTotal Variable Cost =

TVC

TC = TFC + TVC

Total costs for firm XTotal costs for firm X

0

20

40

60

80

100

0 1 2 3 4 5 6 7 8

TC

TVC

TFC

Output(Q)

01234567

TFC(Rs)

1212121212121212

TVC(Rs)

010162128406091

TC(Rs)

12222833405272

103

Short-Run Cost Short-Run Cost FunctionsFunctions

Average Total Cost (ATC)= TC/QAverage Variable Cost (AVC)=TVC/QAverage Fixed Cost (AFC)= TFC/Q

ATC = AFC + AVCMarginal Cost = TC/Q =TVC/Q

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7

AFCAFC

TCTC ACAC1212 2222 22222828 14143333 11114040 101052 52 10.410.472 72 1212103 103 14.714.7

QQ

Costs (Rs)

AVCACAC

QQ TVCTVC AVCAVC0 0 00 --11 10 10 101022 16 16 8833 21 21 7 74 4 28 28 7755 40 40 8866 60 60 101077 91 91 1313

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7

1010 66 55 77121220203131

MCMC --222214141111101010.410.4121214.714.7

QQ

Costs (Rs)

AFCAFC

QQ

Costs (Rs)

AVCACAC

QQ TC TC MCMC ACAC0 0 1212 11 2222 22 28 28 33 33 33 44 40 40 55 52 52 66 72 72 77 103 103

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7

Case Study 7-1 (p 293): Case Study 7-1 (p 293): Per Unit Cost curves in the cultivation of cornPer Unit Cost curves in the cultivation of corn

Note: MC starts to rise very sharply in Figure 7.2. Note: MC starts to rise very sharply in Figure 7.2.

True for many other cases, e.g. True for many other cases, e.g. - - Traveling costsTraveling costs (in terms of travel time) rise steeply (in terms of travel time) rise steeply at the rush hours on highways, used by Singapore at the rush hours on highways, used by Singapore Traffic authorities to restrict the use of car in these Traffic authorities to restrict the use of car in these hours and recently London Traffic Police has also hours and recently London Traffic Police has also done so and NDMC also is planning this to decongest done so and NDMC also is planning this to decongest C.P.;C.P.;- - Landing costsLanding costs (in terms of landing time) at airports (in terms of landing time) at airports also rise rapidly during peak hours.also rise rapidly during peak hours.

Short-Run Cost FunctionsShort-Run Cost FunctionsQ TFC TVC TC AFC AVC ATC MC0 $60 $0 $60 - - - -1 60 20 80 $60 $20 $80 $202 60 30 90 30 15 45 103 60 45 105 20 15 35 154 60 80 140 15 20 35 355 60 135 195 12 27 39 55

SR Cost Functions: SR Cost Functions: Homework AssignmentHomework Assignment

Q TFC TVC TC AFC AVC ATC MC0 $60 $0 $60 - - - -1 60 20 80 $60 $20 $80 $202 60 30 90 30 15 45 103 60 45 105 20 15 35 154 60 80 140 15 20 35 355 60 135 195 12 27 39 55

00224466881010

Find AFC, Find AFC, AVC, & ATC, AVC, & ATC,

and MCand MC

OUTPUT FC VC TC0 2000 0 20001 2000 100 21002 2000 180 21803 2000 280 22804 2000 392 23925 2000 510 25106 2000 650 26507 2000 800 28008 2000 960 29609 2000 1140 3140

10 2000 1340 334011 2000 1560 356012 2000 2160 4160

Fixed, variable, and total Fixed, variable, and total costs: Media Corp.costs: Media Corp.

TFC TVC

Average and marginal costs: Media Average and marginal costs: Media CorpCorp..

OUTPUT AFC AVC ATC MC01 2000.0 100.0 2100.0 1002 1000.0 90.0 1090.0 803 666.7 93.3 760.0 1004 500.0 98.0 598.0 1125 400.0 102.0 502.0 1186 333.3 108.3 441.7 1407 285.7 114.3 400.0 1508 250.0 120.0 370.0 1609 222.2 126.7 348.9 18010 200.0 134.0 334.0 20011 181.8 141.8 323.6 22012 166.7 180.0 346.7 600

Short-Run Cost Short-Run Cost Functions: Functions: Only L is variable Only L is variable

factorfactor

We can rewrite Average Variable Cost as

AVC = TVC/Q = w/APL

And Marginal Cost (MC) asMC =TC/Q = TVC/Q =

w/MPL

Long-run cost functions

•Often considered to be the firm’s planning horizon

•Describes alternative scales of operation when all inputs are variable

Alternative long-run average cost curvesAlternative long-run average cost curves

OutputO

Cos

ts(a) Economies of scale: Decreasing Cost Industry(a) Economies of scale: Decreasing Cost Industry

NATURAL MONOPOLYNATURAL MONOPOLY

LRAC

Alternative long-run average cost curvesAlternative long-run average cost curves

OutputO

Cos

ts

(b) Diseconomies of scale: Increasing Cost Industry(b) Diseconomies of scale: Increasing Cost Industry

LRAC

Alternative long-run average cost curvesAlternative long-run average cost curves

OutputO

Cos

ts

(c) Constant costs: Constant Cost Industry(c) Constant costs: Constant Cost Industry

LRAC

Alternative long-run average cost Alternative long-run average cost curvescurves

OutputO

Cos

ts (a)(a) Economies of scale Economies of scale

LRAC

(b)(b) Diseconomies of scale Diseconomies of scale

(c)(c) Constant costs Constant costs

A typical long-run average cost curveA typical long-run average cost curve

OutputO

Cos

ts

LRAC

A typical long-run average cost curveA typical long-run average cost curve

OutputO

Cos

ts

LRACEconomiesof scale

Constantcosts

Diseconomiesof scale

Case Study 7-2 (p 298): Case Study 7-2 (p 298): The Long Run Average cost Curve in The Long Run Average cost Curve in

Electricity GenerationElectricity Generation

LRAC for 114 electricity producing firms in US Fig 7.5 LRAC for 114 electricity producing firms in US Fig 7.5

It is an L shaped curve. The lowest point is reached at It is an L shaped curve. The lowest point is reached at output of 32 billion kwh. Beyond this point they are output of 32 billion kwh. Beyond this point they are faced with increasing cost. faced with increasing cost.

So what they do beyond this?So what they do beyond this?

Long-Run Cost CurvesLong-Run Cost CurvesLong-Run Total Cost (LTC) = f(Q)Long-Run Average Cost (LAC) =

LTC/QLong-Run Marginal Cost (LMC) =

LTC/Q

OutputO

Cos

ts

(d)(d) Initial economies of scale, then diseconomies of scale Initial economies of scale, then diseconomies of scale

Long-run average and marginal costsLong-run average and marginal costs

LRMC

LRAC

Case Study 7-3 (p 302): Case Study 7-3 (p 302): The Shape of the Long Run Average cost The Shape of the Long Run Average cost

Curve in various U.S. IndustriesCurve in various U.S. Industries

Hospitals, Commercial Banking (demand deposits & Hospitals, Commercial Banking (demand deposits & installment loans), Electric Power, Airlines, Railroads, installment loans), Electric Power, Airlines, Railroads, Trucking Trucking

Big firms normally have been found to have Big firms normally have been found to have economies of scale compared to small firms as shown economies of scale compared to small firms as shown in Table 7-2 (Transport sector being the exception in Table 7-2 (Transport sector being the exception where the difference is not very much)where the difference is not very much)

Long-run costsLong-run costs

Relationship between short-runRelationship between short-runand long-run and long-run ACAC curves curves

Deriving long-run average cost curvesDeriving long-run average cost curves

SRAC1

Cos

ts

OutputO

1st factory

Deriving long-run average cost curvesDeriving long-run average cost curves

SRAC1

SRAC2

Cos

ts

OutputO

2nd factory

Deriving long-run average cost curvesDeriving long-run average cost curves

SRAC1

SRAC3SRAC2

Cos

ts

OutputO

3rd factory

Deriving long-run average cost curvesDeriving long-run average cost curves

SRAC1

SRAC3SRAC2

SRAC4

SRAC5

Cos

ts

OutputO

5th factory

4th factory

Deriving long-run average cost curvesDeriving long-run average cost curves

SRAC1

SRAC3SRAC2

SRAC4

SRAC5

LRAC

Cos

ts

OutputO

Deriving a long-run average cost curve: choice of factory sizeDeriving a long-run average cost curve: choice of factory size

LRAC

Cos

ts

OutputO

LRAC curve: is envelope of the SRAC curves

Derivation of Long-Run Cost Curves

Other Possible Shapes of the LAC Curve

Learning CurvesLearning Curves

Minimizing Costs InternationallyMinimizing Costs Internationally• Foreign Sourcing of Inputs, Foreign Sourcing of Inputs,

e.g. auto components, BPO etc.e.g. auto components, BPO etc.• New International Economies of New International Economies of

Scale, Scale, e.g. global marketse.g. global markets• Immigration of Skilled Labor, Immigration of Skilled Labor,

e.g. software, security professionalse.g. software, security professionals• Brain DrainBrain Drain

Case Study 7-5 (p 307): Case Study 7-5 (p 307): Even the IBM PC and the Boeing 777 are not Even the IBM PC and the Boeing 777 are not

all Americanall American

Table 7-3 gives the break up of IBM PC’s Table 7-3 gives the break up of IBM PC’s manufacturing cost Distribution in the U.S. and manufacturing cost Distribution in the U.S. and Outside the U.S. Outside the U.S.

Only about 28% of IBM PC is sourced from the U.S. Only about 28% of IBM PC is sourced from the U.S. Almost 72 % of it is outsourced from Abroad of whichAlmost 72 % of it is outsourced from Abroad of which- 62 % is by foreign owned firms - 62 % is by foreign owned firms - 38 % is U.S. owned plants abroad- 38 % is U.S. owned plants abroad

Architecture of Ideal FirmArchitecture of Ideal Firm• Core CompetenciesCore Competencies• Outsourcing of Non-Core TasksOutsourcing of Non-Core Tasks• Learning OrganizationLearning Organization• Efficiency and FlexibilityEfficiency and Flexibility• Location Near MarketsLocation Near Markets• Agility in Responding to Market Agility in Responding to Market

Forces Forces e.g. Just in Time cost mgmte.g. Just in Time cost mgmt

Case Study 7-6 (p 311): Case Study 7-6 (p 311): Firm Architecture and Organizational Firm Architecture and Organizational

CompetitivenessCompetitiveness

based on a survey of 16 key business issues based on a survey of 16 key business issues conducted by American Management conducted by American Management

Association (AMA)Association (AMA)

Cost-Volume-Profit AnalysisCost-Volume-Profit AnalysisTotal Revenue = TR = (P)(Q)

Total Cost = TC = TFC + (AVC)(Q)

Breakeven Volume TR = TC

(P)(Q) = TFC + (AVC)(Q)

QBE = TFC/(P - AVC)(P - AVC) is called contribution margin per unit

P = 10

TFC = 200

AVC = 5

QBE = 40

Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis

Target Profit Break even AnalysisTarget Profit Break even Analysis

QBE() = (TFC+ ) / (P - AVC)

is like TFC here

NOTE:

Only valid under the assumption of constant prices and AVC

Operating LeverageOperating Leverage

Operating Leverage = TFC/TVC

Degree of Operating Leverage = DOL

% ( )% ( )

Q P AVCDOLQ Q P AVC TFC

Computing the DOLComputing the DOL

DOLDOLQ unitsQ units

Calculating the DOL for a single product or a Calculating the DOL for a single product or a single-product firm.single-product firm.

==QQ ( (PP - - VV))

QQ ( (PP - - VV) - ) - FCFC

== QQQQ - - QQBEBE

Operating Leverage:Operating Leverage:

TC’ has a higher DOL than TC and therefore a higher QBE

Case Study 7-7 (p 317): Case Study 7-7 (p 317): Breakeven Analysis for Lockheed Martin and Breakeven Analysis for Lockheed Martin and

Europe’s Airbus Industrie Europe’s Airbus Industrie

- How Breakeven Analysis was used to get govt. - How Breakeven Analysis was used to get govt. guarantee for the wide body aircraft by Lockheed guarantee for the wide body aircraft by Lockheed Martin but by excluding the fixed costs of developing Martin but by excluding the fixed costs of developing the technology and construction costs to build the the technology and construction costs to build the Aircraft.Aircraft.- Airbus Industrie also had to be subsidized by 26 - Airbus Industrie also had to be subsidized by 26 billion dollars and for 25 years by West European billion dollars and for 25 years by West European governments on the basis of Breakeven analysis.governments on the basis of Breakeven analysis.

Empirical EstimationEmpirical EstimationLong-Run Cost CurvesLong-Run Cost Curves

• Cross-Sectional Regression Cross-Sectional Regression AnalysisAnalysis

• Engineering MethodEngineering Method• Survival TechniqueSurvival Technique

Key steps in Empirical Key steps in Empirical Cost estimation processCost estimation process

1.1. Definition of costs: Definition of costs: Opportunity Costs Opportunity Costs Must be Extracted from Accounting Cost DataMust be Extracted from Accounting Cost Data

2.2. Costs Must be Apportioned Among Costs Must be Apportioned Among ProductsProducts

3.3. Costs Must be Matched to Output Over Costs Must be Matched to Output Over TimeTime

4.4. Costs Must be Corrected for InflationCosts Must be Corrected for Inflation5.5. Controlling product, technology, and Controlling product, technology, and

plantplant6.6. Length of period and sample sizeLength of period and sample size

Minimum efficient scaleMinimum efficient scaleThe smallest output at which long-run The smallest output at which long-run

average cost is a minimum.average cost is a minimum.

Quantity of outputQuantity of output

Average Average costcost

QQmesmes

Engineering Method

Relates inputs to output in technical manner, tends to

ignore the administrative and other aspects of costs. Due to

this not commonly used

The survival The survival techniquetechnique

• Classify the firms in an industry by Classify the firms in an industry by size (e.g small and large) & compute size (e.g small and large) & compute the percentage of industry output the percentage of industry output coming from each size class at coming from each size class at various timesvarious times

• If the share of one class diminishes If the share of one class diminishes over time, it is assumed to be over time, it is assumed to be inefficientinefficient

• These firms are then operating below These firms are then operating below minimum efficient scaleminimum efficient scale

Economies of scopeEconomies of scopeExist when the cost of producing Exist when the cost of producing

two (or more) products jointly two (or more) products jointly is less than the cost of is less than the cost of

producing each one alone.producing each one alone.

C(QC(Q11) + C(Q) + C(Q22) - C(Q) - C(Q11+ Q+ Q22))C(QC(Q11+ Q+ Q22))

S =

Empirical EstimationEmpirical EstimationFunctional Form for Short-Run Cost Functions

2 3TVC aQ bQ cQ

2TVCAVC a bQ cQQ

22 3MC a bQ cQ

Theoretical Form Linear Approximation

TVC a bQ aAVC bQ

MC bAverage Cost of Unit Q = C = aQb

Estimation Form: log C = log a + b Log Q

Empirical EstimationEmpirical EstimationTheoretical Form Linear Approximation

Empirical EstimationEmpirical EstimationActual LAC versus empirically estimated LAC’

Case Study 4 & 3 - Black Gold- Production Function & Cost

Functions in Oil Pipelines

Objective Type QuestionsObjective Type QuestionsLong-run average cost equals Long-run average cost equals long-run marginal cost wheneverlong-run marginal cost wheneverA) the average cost function A) the average cost function exhibits constant returns to scale.exhibits constant returns to scale.B) fixed costs are zero.B) fixed costs are zero.C) one of the factor has increasing C) one of the factor has increasing marginal returns.marginal returns.D) the cost of capital is near zero.D) the cost of capital is near zero.E) long-run marginal cost is at its E) long-run marginal cost is at its minimum.minimum.

If average variable cost is If average variable cost is increasing with increases in increasing with increases in output, total fixed cost willoutput, total fixed cost will

A) increase with increases in A) increase with increases in output.output.B) decrease with increases in B) decrease with increases in output.output.C) remain unchanged with C) remain unchanged with increases in output.increases in output.D) increase initially and then D) increase initially and then decrease with increases in output.decrease with increases in output.E) decrease initially and then E) decrease initially and then increase with increases in output.increase with increases in output.

If there is only one variable input, If there is only one variable input, average variable cost can be average variable cost can be defined as thedefined as theA) output’s price divided by the input’s A) output’s price divided by the input’s average product.average product.B) output’s price divided by the input’s B) output’s price divided by the input’s marginal product.marginal product.C) price of the variable input divided by C) price of the variable input divided by its average product.its average product.D) price of the variable input divided by D) price of the variable input divided by its marginal product.its marginal product.E) price of the variable input multiplied E) price of the variable input multiplied by its marginal product.by its marginal product.

When average total cost is at its When average total cost is at its minimum,minimum,A) average variable cost is declining with A) average variable cost is declining with increases in output.increases in output.B) average variable cost plus average fixed B) average variable cost plus average fixed cost is declining with increases in output.cost is declining with increases in output.C) average total cost is equal to average C) average total cost is equal to average variable cost.variable cost.D) marginal cost is equal to average D) marginal cost is equal to average variable cost.variable cost.E) marginal cost is equal to average total E) marginal cost is equal to average total cost.cost.

The Jefferson Company’s total cost function is

TC = 984 - 1200 Q + Q3  where TC is the firm’s monthly total cost (in rupees), and Q is the firm’s monthly output. 1) What is Jefferson Company’s average total cost function and Marginal Cost? 2) At what level of output is the cost minimum and the level of minimum cost. 3) At what level of output is the AC and MC equal.4) What is TFC and AFC at the min AC?

The TomHoe Corporation (UK) has the following average cost (AC) function for its coffee shop

AC = 2551 – 100.Q + 2.Q2  

Where q is the units of output produced

a) What is the output level at which the marginal cost is minimum. b) At what level of output is the average and marginal cost equal c) What is the output level at which the average variable cost is minimum.

Questions: Questions: The Microsoft computer com. Wants to estimate The Microsoft computer com. Wants to estimate the AVC of producing computer diskettes. The firm believes the AVC of producing computer diskettes. The firm believes that AVC varies with level of output and wages. Alan that AVC varies with level of output and wages. Alan Anderson, chief of the research department of the company, Anderson, chief of the research department of the company, collects monthly data on output of disc produced, AVC and collects monthly data on output of disc produced, AVC and wage rates paid by the company over the last 2 years. He wage rates paid by the company over the last 2 years. He deflates costs and wages by their respective price indexes. deflates costs and wages by their respective price indexes. He gets following regression resultHe gets following regression result

TVC = 0.14 + 0.80 Q + 0.036 W TVC = 0.14 + 0.80 Q + 0.036 W Adj-R-square = 0.92, DW = 1.9, F = 78.6Adj-R-square = 0.92, DW = 1.9, F = 78.6

a) if W =10, derive AVC, & MC Function for the Firm?a) if W =10, derive AVC, & MC Function for the Firm?b) What are the shapes of AVC and MC?b) What are the shapes of AVC and MC?c) Why did Anderson fit a linear rather than a quadratic c) Why did Anderson fit a linear rather than a quadratic or cubic TVC function? Was this choice right? Whyor cubic TVC function? Was this choice right? Why

NEXT TOPIC: MARKETS

Perfect Competition &

Monopolye.g. Stock market, Wholesale Fruits/Veg. Mkts, ForEx Market,

Computer hardware marketElectricity Supply, Telecom, Railways, Airlines,

Public Transport