Cost Analysis 483j4o

Topic 3.2 Analysis of Costs

& Cost Estimation (Pl. read the prescribed chapter & cases given in it before coming for the class) Ref: Ch. 7

The Nature of Costs • Explicit Costs – ing (or Historical) Costs • Economic Costs – Implicit Costs – Opportunity (or Alternative) Costs • Relevant Costs – Incremental Costs (vs MC) • Sunk Costs are Irrelevant (why?)

Explicit vs. implicit costs • Explicit costs include the ordinary items that an ant would include as the firms expenses

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

Opportunity costs

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

Short run A 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 Functions Total Cost = TC = f(Q) Total Fixed Cost = TFC Total Variable Cost = TVC

TC = TFC + TVC

Total costs for firm X

Output TFC TVC TC (Q) (Rs) (Rs) (Rs)

100

0 1 2 3 4 5 6 7

80

60

0 10 16 21 28 40 60 91

12 12 12 12 12 12 12 12

TC

12 22 28 33 40 52 72 103

TVC

40

20

TFC 0 0

1

2

3

4

5

6

7

8

Short-Run Cost Functions Average Total Cost (ATC)= TC/Q Average Variable Cost (AVC)=TVC/Q

Average Fixed Cost (AFC)= TFC/Q

ATC = AFC + AVC Marginal Cost = TC/Q =TVC/Q

Costs (Rs)

TC 12 22 28 33 40 52 72 103

35 30 25 20

Q TVC AVC 0 0 1 10 10 22 2 16 8 14 3 21 7 11 4 28 7 10 8 10.4 5 40 6 60 10 12 14.7 7 91 13

AC

AC AVC

15 10 5

AFC

0 0

1

2

3

4

5

6

7

Q

Q TC MC AC 0 12 10 22 1 22 6 14 2 28 5 11 3 33 7 10 4 40 12 10.4 5 52 20 12 6 72 31 14.7 7 103

Costs (Rs) 35 30 25 20 15

MC

AC AVC

10 5

AFC

0 0

1

2

3

4

5

6

7

Q

Case Study 7-1 (p 293): Per Unit Cost curves in the cultivation of corn Note: MC starts to rise very sharply in Figure 7.2. True for many other cases, e.g. - Traveling costs (in of travel time) rise steeply at the rush hours on highways, used by Singapore Traffic authorities to restrict the use of car in these hours and recently London Traffic Police has also done so and NDMC also is planning this to decongest C.P.; - Landing costs (in of landing time) at airports also rise rapidly during peak hours.

Short-Run Cost Functions Q 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

AFC $60 30 20 15 12

AVC $20 15 15 20 27

ATC $80 45 35 35 39

MC $20 10 15 35 55

SR Cost Functions: Homework Assignment Q 0 0 1 2 2 4 3 6 4 8 10 5

TFC $60 60 60 60 60 60

TVC $0 20 30 45 80 135

TC $60 80 90 105 140 195

AFC $60 30 20 15 12

AVC $20 15 15 20 27

ATC $80 45 35 35 39

MC $20 10 15 35 55

Find AFC, AVC, & ATC, and MC

Fixed, variable, and total costs: Media Corp. OUTPUT 0 1 2 3 4 5 6 7 8 9 10 11 12

FC TFC

VC TVC

2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000

0 100 180 280 392 510 650 800 960 1140 1340 1560 2160

TC 2000 2100 2180 2280 2392 2510 2650 2800 2960 3140 3340 3560 4160

Average and marginal costs: Media Corp. OUTPUT 0 1 2 3 4 5 6 7 8 9 10 11 12

AFC

AVC

ATC

MC

2000.0 1000.0 666.7 500.0 400.0 333.3 285.7 250.0 222.2 200.0 181.8 166.7

100.0 90.0 93.3 98.0 102.0 108.3 114.3 120.0 126.7 134.0 141.8 180.0

2100.0 1090.0 760.0 598.0 502.0 441.7 400.0 370.0 348.9 334.0 323.6 346.7

100 80 100 112 118 140 150 160 180 200 220 600

Short-Run Cost Functions: Only L is variable factor

We can rewrite Average Variable Cost as AVC = TVC/Q = w/APL

And Marginal Cost (MC) as MC =TC/Q = TVC/Q =

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 curves

Costs

(a) Economies of scale: Decreasing Cost Industry NATURAL MONOPOLY

LRAC

O

Output

Alternative long-run average cost curves (b) Diseconomies of scale: Increasing Cost Industry

Costs

LRAC

O

Output

Alternative long-run average cost curves

Costs

(c) Constant costs: Constant Cost Industry

O

LRAC

Output

Costs

Alternative long-run average cost curves (a) Economies of scale

LRAC

(c) Constant costs

(b) Diseconomies of scale O

Output

A typical long-run average cost curve

Costs

LRAC

O

Output

Costs

A typical long-run average cost curve

O

Economies of scale

Constant costs

Diseconomies of scale

LRAC

Output

Case Study 7-2 (p 298): The Long Run Average cost Curve in Electricity Generation LRAC for 114 electricity producing firms in US Fig 7.5 It is an L shaped curve. The lowest point is reached at output of 32 billion kwh. Beyond this point they are faced with increasing cost.

So what they do beyond this?

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

LTC/Q Long-Run Marginal Cost (LMC) =

 LTC/Q

Long-run average and marginal costs

LRMC

Costs

LRAC

O

Output

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

Case Study 7-3 (p 302): The Shape of the Long Run Average cost Curve in various U.S. Industries Hospitals, Commercial Banking (demand deposits & installment loans), Electric Power, Airlines, Railroads, Trucking Big firms normally have been found to have economies of scale compared to small firms as shown in Table 7-2 (Transport sector being the exception where the difference is not very much)

Long-run costs

Relationship between short-run and long-run AC curves

Deriving long-run average cost curves

Costs

SRAC1

1st factory

O

Output

Deriving long-run average cost curves

SRAC1

Costs

SRAC2

2nd factory

O

Output

Deriving long-run average cost curves

SRAC1

Costs

SRAC2 SRAC3

3rd factory

O

Output

Deriving long-run average cost curves

SRAC1

Costs

SRAC2 SRAC3

SRAC5 SRAC4

5th factory 4th factory

O

Output

Deriving long-run average cost curves

SRAC1

SRAC2 SRAC3

SRAC5 SRAC4

Costs

LRAC

O

Output

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

Costs

LRAC

LRAC curve: is envelope of the SRAC curves O

Output

Derivation of Long-Run Cost Curves

Other Possible Shapes of the LAC Curve

Learning Curves

Minimizing Costs Internationally • Foreign Sourcing of Inputs, e.g. auto components, BPO etc.

• New International Economies of Scale, e.g. global markets • Immigration of Skilled Labor, e.g. software, security professionals

• Brain Drain

Case Study 7-5 (p 307): Even the IBM PC and the Boeing 777 are not all American Table 7-3 gives the break up of IBM PC’s manufacturing cost Distribution in the U.S. and Outside the U.S. Only about 28% of IBM PC is sourced from the U.S. Almost 72 % of it is outsourced from Abroad of which - 62 % is by foreign owned firms - 38 % is U.S. owned plants abroad

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 e.g. Just in Time cost mgmt

Case Study 7-6 (p 311): Firm Architecture and Organizational Competitiveness based on a survey of 16 key business issues conducted by American Management Association (AMA)

Cost-Volume-Profit Analysis Total 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

Cost-Volume-Profit Analysis P = 10 TFC = 200 AVC = 5 QBE = 40

Target Profit Break even Analysis

QBE() = (TFC+ ) / (P - AVC)  is like TFC here NOTE: Only valid under the assumption of constant prices and AVC

Operating Leverage Operating Leverage = TFC/TVC Degree of Operating Leverage = DOL

% Q( P  AVC ) DOL   %Q Q( P  AVC )  TFC

Computing the DOL Calculating the DOL for a single product or a single-product firm. DOLQ units

= =

Q (P - V ) Q (P - V) - FC Q Q - QBE

Operating Leverage:

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

Case Study 7-7 (p 317): Breakeven Analysis for Lockheed Martin and Europe’s Airbus Industrie - How Breakeven Analysis was used to get govt. guarantee for the wide body aircraft by Lockheed Martin but by excluding the fixed costs of developing the technology and construction costs to build the Aircraft. - Airbus Industrie also had to be subsidized by 26 billion dollars and for 25 years by West European governments on the basis of Breakeven analysis.

Empirical Estimation Long-Run Cost Curves • Cross-Sectional Regression Analysis • Engineering Method • Survival Technique

Key steps in Empirical Cost estimation process 1. Definition of costs: Opportunity Costs Must be Extracted from ing Cost Data 2. Costs Must be Apportioned Among Products 3. Costs Must be Matched to Output Over Time 4. Costs Must be Corrected for Inflation 5. Controlling product, technology, and plant

Minimum efficient scale The smallest output at which long-run average cost is a minimum. Average cost

Qmes

Quantity of output

Engineering Method Relates inputs to output in technical manner, tends to ignore the istrative and other aspects of costs. Due to this not commonly used

The survival technique • Classify the firms in an industry by size (e.g small and large) & compute the percentage of industry output coming from each size class at various times • If the share of one class diminishes over time, it is assumed to be inefficient • These firms are then operating below minimum efficient scale

Economies of scope Exist when the cost of producing two (or more) products tly is less than the cost of producing each one alone.

S=

C(Q1) + C(Q2) - C(Q1+ Q2) C(Q1+ Q2)

Empirical Estimation Functional Form for Short-Run Cost Functions Linear Approximation

Theoretical Form 2

TVC  aQ  bQ  cQ

3

TVC  a  bQ

TVC 2 AVC   a  bQ  cQ Q

a AVC   b Q

MC  a  2bQ  3cQ

MC  b

2

Average Cost of Unit Q = C = aQb Estimation Form: log C = log a + b Log Q

Empirical Estimation Theoretical Form

Linear Approximation

Empirical Estimation Actual LAC versus empirically estimated LAC’

Case Study 4 & 3 - Black Gold - Production Function & Cost Functions in Oil Pipelines

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

If average variable cost is increasing with increases in output, total fixed cost will A) increase with increases in output. B) decrease with increases in output. C) remain unchanged with increases in output. D) increase initially and then decrease with increases in output. E) decrease initially and then

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

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

The Jefferson Company’s total cost function is

TC = 984 - 1200 Q + Q

3

 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

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

AC = 2551 – 100.Q + 2.Q

2

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

TVC = 0.14 + 0.80 Q + 0.036 W Adj-R-square = 0.92, DW = 1.9, F = 78.6 a) if W =10, derive AVC, & MC Function for the Firm? b) What are the shapes of AVC and MC? c) Why did Anderson fit a linear rather than a quadratic or cubic TVC function? Was this choice right? Why

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