Cost Theory and Estimation

An important consideration in decision making

Cost Theory and Estimation

Nature of Costs

Short-Run Cost Functions

Long-Run Cost Curves

Learning Curves

Cost-Volume-Profit Analysis

The New Economies of Scale

Supply-Chain Management

Empirical Estimation of Cost Functions

Nature of Costs • What is relevant?

A cost is relevant if it is

affected by a

management decision

• Opportunity cost

• Marginal cost

• Incremental cost

• Sunk cost http://article.wn.com/view/2014/06/24/Three_Graphs_that_Show_the_Chinese_Mobile_Technology_Revolut/

https://mrski-apecon-2008.wikispaces.com/Chapter+13+Emily+K

RevenueRevenue

Total

Opportunity

Costs

Explicit Costs

• The actual expenditures of the firm

• Accounting costs

Implicit Costs

• Value of the inputs owned

and used by the firm

• Economic costs

• Cost that does not require the

firm to give up money, but

rather opportunity

Nature of Costs

Implicit costs

https://mrski-apecon-2008.wikispaces.com/Chapter+13+Emily+K

The opportunity cost associated with choosing a particular decision is measured by the benefits foregone in the next-best alternative

Consider this…

Management Fees

Miscellaneous revenues

Less:

Office rent

Other office expenses

Staff wages (excluding self)

Profit

Php140,000

12,000

-36,000

-18,000

-24,000

74,000

Management Fees

Miscellaneous revenues

Less:

Office rent

Other office expenses

Staff wages (excluding self)

Interest rate @ 8%

Current value at job

Profit (Loss)

Php140,000

12,000

36,000

18,000

24,000

6,400

56,000

11,600

Consider this…

Management Fees

Miscellaneous revenues

Less:

Office rent

Other office expenses

Staff wages (excluding self)

Profit

Php140,000

12,000

-36,000

-18,000

-24,000

74,000

Management Fees

Miscellaneous revenues

Less:

Office rent

Other office expenses

Staff wages (excluding self)

Interest rate @ 8%

Current value at job

Profit (Loss)

Php140,000

12,000

36,000

18,000

24,000

6,400

80,000

(12,400)

The sunk cost is an expense that has already been incurred and cannot be recovered

Nature of Costs Incremental costs are associated with

a choice and therefore only ever

include forward-looking costs

sunk costs not included

Marginal costs refer to the cost to

produce one more unit of product or

service.

Marginal and Incremental

costs are used to help

management evaluate

different potential future

courses of action

Cost functions • Factors that determine costs

Short-Run

• Some of the firm’s

inputs are fixed

• Cost curves are

operating curves

TC = TFC + TVC

Short-Run(per-unit)

• ATC = TC/Q

• AVC = TVC/Q

• AFC = TFC/Q

= ATC - AVC

• MC = ΔTC/ΔQ

= ΔTVC/ ΔQ

AFC

Table 7-1 Short-Run total and Per-Unit Cost Schedules

Ch.7 Cost Theory and Estimation, Salvatore. P.283

Q TFC TVC TC AFC AVC ATC MC

0 $60 $0 $60 -- -- -- --

1 60 20 80 $60 $20 $80 $20

2 60 30 90 30 15 45 10

3 60 45 105 20 15 35 15

4 60 80 140 15 20 35 35

5 60 135 195 12 27 39 55

0 1 2 3 4 5

TFC $60 60 60 60 60 60

TVC $0 20 30 45 80 135

TC $60 80 90 105 140 195

$0

$50

$100

$150

$200

$250

1 2 3 4 5

AFC -- $60 30 20 15 12

AVC -- $20 15 15 20 27

ATC -- $80 45 35 35 39

MC -- $20 10 15 35 55

$0

$10

$20

$30

$40

$50

$60

$70

$80

$90

1 2 3 4 5

AFC -- $60 30 20 15 12

AVC -- $20 15 15 20 27

ATC -- $80 45 35 35 39

MC -- $20 10 15 35 55

$0

$10

$20

$30

$40

$50

$60

$70

$80

$90

AVC, ATC, and MC are

U-shaped

AFC continues to decline as

output increases

MC curve reaches its

minimum before intercepting

AVC and ATC curves at their

lowest points

Q1Q2 Q3

(1) AVC first declines, reaches a minimum

at Q2, and rises thereafter

• AVC at its minimum, MC = AVC

(2) ATC first declines, reaches a minimum

at Q3, and rises thereafter

• ATC at its minimum, MC = ATC

(3) MC first declines, reaches a minimum at

Q1, and rises thereafter

• MC equals both AVC and ATC at

their minimum values

• MC lies below AVC and ATC over

the range for which these curves

decline, but lies above them when

they are rising

Q TFC TVC TC AFC AVC ATC MC

0 $60 $0 $60 -- -- -- --

1 60 20 80 $60 $20 $80 $20

2 60 30 90 30 15 45 10

3 60 45 105 20 15 35 15

4 60 80 140 15 20 35 35

5 60 135 195 12 27 39 55

AVC = TVC = wL = w = w

Q Q Q/L APL

AVC

TVC

Q

w

L

APL

– average variable cost

– total variable cost

– output level

– wage rate

– quantity of labor used

– average physical product of labor

Q TFC TVC TC AFC AVC ATC MC

0 $60 $0 $60 -- -- -- --

1 60 20 80 $60 $20 $80 $20

2 60 30 90 30 15 45 10

3 60 45 105 20 15 35 15

4 60 80 140 15 20 35 35

5 60 135 195 12 27 39 55

MC = ΔTVC = Δ(wL) = w(ΔL) = w = w aΔQ ΔQ ΔQ ΔQ/ΔL MPL

MPL – marginal product of labor

Long-Run

• All inputs are variable

• Cost curves are

planning curves

LAC = LTCQ

LAC = LTC

Q

LMC = ΔLTC

ΔQ

• The U-shape of the LAC curve depends on

increasing, constant, and decreasing returns to

scale

• The relationship of the LMC-LTC is the same as the

short-run MC-ATC.

Relationship of Long-Run and

Short-Run Average Cost Curves

• Long-Run average cost curve shows

the minimum average cost of

producing any given level of output

• LAC curve is the tangent line to

each of the short-run average

curves

Returns to Scale

Constant returns to scale

Increasing returns to scale

Decreasing returns to scale INPUT OUTPUT

INPUT OUTPUT

INPUT OUTPUT

Returns to Scale

Constant returns to scale

Increasing returns to scale

Decreasing returns to scale

INPUT OUTPUT

INPUT OUTPUT

INPUT OUTPUT

Minimum Efficient Scale (MES)

•The lowest output at

which minimum

average cost can be

achieved

•Important in determining

how many firms a

particular market can

support

Economies of

Scope

• The cost of

producing multiple

goods is less than

the aggregate cost

of producing each

item separately

• An important source

of economies of

scope is transferable

know-how

Learning Curves

• As firms gain experience in the

production of a commodity or

service, their average cost of

production usually declines

• from many experiences gained

• used to forecast needs for

personnel, machinery, raw

materials and for scheduling

production

Cost-Volume-Profit

Analysis

• Breaking it even

and then some

Cost-Volume-Profit Analysis(CVP Analysis / breakeven analysis)

Examines the relationship among total revenue, total costs, and total profits of the firm at various levels of output

TR = (P)(Q)

TC = TFC + (AVC)(Q)

TR=TC

QB = TFC .

P-AVC

Solve:

(P)(QB) – (AVC)(QB) = TFC

(QB)(P-AVC) = TFC

Q

TR = (P)(Q)TC = TFC + (AVC)(Q)TR=TC(P) (QB) = TFC + (AVC) (QB)

QB = TFC .

P-AVC

Q

TFC = $200

P = $10

AVC = $5

Solve:

QB = $200 .

$10-$5

QB = 40

Contribution margin per unit

• Portion of the selling price

that can be applied to

cover fixed costs and

provide for profits

QT = TFC + πT .

P-AVC

Q

TFC = $200

P = $10

AVC = $5

Solve:

QT = $200 + $100 .

$10-$5

QT = 60

Operating Leverage (OL)

Refers to the ratio of the firms total fixed costs to total variable costs

Higher ratio = more leveraged

= profits are more sensitive to changes in output or sales

𝐷𝑂𝐿 =%∆𝜋

%∆𝑄=

∆𝜋/𝜋

∆𝑄/𝑄=

∆𝜋

∆𝑄.𝑄

𝜋

DOL – degree of operating leverage

Q

FC = $200

FC’ = $300

AVC = $5

AVC’ = $3.33

QB’ = 45

TC’ has a higher DOL

than TC and therefore

a higher QB

𝐷𝑂𝐿 =60($10 − $5)

60 $10 − $5 − $200=$300

$100= 3

Given:

Increase in output from 60 to 70 units

Find:

DOL with TC

𝐷𝑂𝐿 =60($10 − $5)

60 $10 − $5 − $200=$300

$100= 3

𝐷𝑂𝐿′ =60($10 − $3.33)

60 $10 − $3.33 − $300≅$400

$100= 4

The degree of operating leverage (DOL)

increases as the firm becomes more

leveraged or capital intensive

New Economies of ScaleMinimizing costs internationally

International trade in inputs

Foreign sourcing of inputs - requirement to remain competitive

New international economies of scale

Firms must constantly explore sources of cheaper inputs and

overseas production

Product development, purchasing, production, demand

management, order fulfillment

Immigration of skilled labor

Logistics or supply-chain management

Merging at the corporate level of the purchasing, transportation,

warehousing, distribution and customer services functions rather than

dealing with them separately at division levels

Development of new and much faster algorithms that greatly facilitate the

solution of complex logistic problems

Growing use of just-in-time inventory management

Increasing trend toward globalization of production and distribution

Empirical Estimation

of Cost Functions

• Planning for the long

haul

Empirical Estimation

Data Collection Issues

Opportunity costs must be extracted from accounting cost data

Costs must be apportioned among products

Costs must be matched to output over time

Costs must be corrected for inflation

𝐶 = 𝑓(𝑄, 𝑋1, 𝑋2, … , 𝑋𝑛)

Empirical EstimationFunctional Form for Short-Run Cost Functions

Theoretical Form

𝑀𝐶 = 𝑎 + 2𝑏𝑄 + 3cQ2

Empirical EstimationFunctional Form for Short-Run Cost Functions

Linear Approximation

Empirical EstimationEfficiency of Operation in Estimating the LAC curve

Architecture of Ideal Firm

Core Competencies

Outsourcing of Non-Core Tasks

Learning Organization

Efficiency and Flexibility

Location Near Markets

Agility in Responding to Market Forces

References

Salvatore, D. (2007). Managerial Economics In A Global Economy (Sixth ed.). New York: Oxford

University Press.

Samuelson, W. F., & Marks, S. G. (2010). Managerial Economics (Sixth ed.). New Jersey: John

Wiley & Sons, Inc.

Thomas, C. R., & Maurice, S. (2011). Managerial Economics Foundations of Business Analysis

and Strategy (Tenth ed.). New York: McGraw-Hill Co.

*Web site sources for other graphs