cost theory

Department of Business Administration

FALL 2010-

11

Cost Theory and Estimation

by

Assoc. Prof. Sami Fethi

The Nature of Costs







Explicit Costs



Accounting Costs

Economic Costs



Implicit Costs



Alternative or Opportunity Costs

Relevant Costs



Incremental Costs



Sunk Costs are Irrelevant

CH 7: Cost Theory

© 2004, Managerial Economics, Dominick Salvatore

2

© 2010/11, Sami Fethi, EMU, All Right Reserved .

CH 7: Cost Theory

The Nature of Costs

•

Costs are incurred as a result of production.

•

Economists define cost in terms of opportunities that are sacrificed when a choice is made. Therefore, economic costs are simply benefits lost .

•

Accountants define cost in terms of resources consumed. Accounting costs reflect changes in stocks (reductions in good things, increases in bad things) over a fixed period of time.


3


CH 7: Cost Theory

Explicit Costs

 Explicit costs are actual expenditures of the firm to hire, rent, or purchase the inputs it requires in production. These includes the wages to hire labor, the rental price of capital , equipment , and buildings , and the purchase price of raw materials and semi finished products .


4


CH 7: Cost Theory

Implicit Costs

 Implicit costs refers to the value of the inputs that are owned and used by the firm in its own production activity.

These includes the highest salary that the entrepreneur could earn in his or her best alternative employment and the highest return that the firm could receive from investing its capital in the most rewarding alternative use or renting its land and buildings to the highest bidder.


5


CH 7: Cost Theory

Economic Costs

 Economic cost refers the sum of explicit and implicit costs.

These costs must be distinguished from accounting costs, which refer only to the firm’s actual expenditures , or explicit cost , incurred for purchased or hired inputs.


6


CH 7: Cost Theory

Alternative or Opportunity Costs

 The cost to the firm of using a purchased or owned input is equal to what the input could earn in its best alternative use.

•

The firm must include the alternative or opportunity costs because the firm cannot retain a hired input if it pays a lower price for the input than another firm.


7


Relevant and Irrelevant Costs

CH 7: Cost Theory

 Relevant Costs: The costs that should be considered in making a managerial decision; economic or opportunity costs.

 Incremental costs: the total increase in costs for implementing a particular managerial decision.

•

Irrelevant or Sunk Costs: The cost that are not affected by a particular managerial decision.


8


Short-Run Cost Functions

CH 7: Cost Theory

 In short-run period, some of the firm’s inputs are fixed and some are variable, and this leads to fixed and variable costs.

 Total costs is the cost of all the productive resources used by the firm. It can be divided into two separate costs in the short run.


9


Total fixed and variable costs

CH 7: Cost Theory

 Total Fixed Costs: The total obligations of the firm per time period for all the fixed inputs the firm uses.

 Total Variable Costs: The total obligations of the firm per time period for all the variable inputs the firm uses.


10



CH 7: Cost Theory

Total Cost = TC = f(Q)

Total Fixed Cost = TFC

Total Variable Cost = TVC

TC = TFC + TVC


11


CH 7: Cost Theory

Average Costs

 Average total cost (also called average cost ) equals total cost per unit of output produced

ATC = TC/Q

 Average fixed cost equals fixed cost divided by quantity produced

AFC = FC/Q

 Average variable cost equals variable cost divided by quantity produced

AVC = VC/Q


12


CH 7: Cost Theory

Average Costs and Marginal Cost

 Average total cost is also the sum of average fixed cost and average variable cost.

ATC = AFC + AVC

 Marginal (incremental) cost is the increase in total cost resulting from a one-unit increase in output.

Marginal decisions are very important in determining profit levels.

MC = ΔTC/ΔQ


13


CH 7: Cost Theory


•

The marginal cost curve, average variable cost curve and average total cost curves are generally U-shaped.

•

The U-shape in the short run is attributed to increasing and diminishing returns from a fixedsize plant, because the size of the plant is not variable in the short run.

14

© 2010/11, Sami Fethi, EMU, All Right Reserved . © 2004, Managerial Economics, Dominick Salvatore

CH 7: Cost Theory


•

The marginal cost and average cost curves are related

 When MC exceeds AC , average cost must be rising

 When MC is less than AC , average cost must be falling

•

This relationship explains why marginal cost curves always intersect average cost curves at the minimum of the average cost curve.

15


CH 7: Cost Theory

$

Graphical Presentation

MC will intersect the AVC at the minimum of the AVC [always

].

ATC

AVC

ATC*

AVC* TC = ATC* x Q**

TVC = AVC* x Q*

R

J

MC will intersect the ATC at the minimum of the ATC

.

The vertical distance between

ATC and AVC at any output is the AFC. At Q** AFC is RJ.

Q* Q** Q

At Q* output, the AVC is at a minimum AVC* [also max of AP

L

].

At Q** the ATC is at a MINIMUM .


16


CH 7: Cost Theory

Relationship Between Marginal and Average Costs

If MC > ATC, then ATC is rising

If MC = ATC, then ATC is at its minimum

If MC < ATC, then ATC is falling

If MC > AVC, then AVC is rising

If MC = AVC, then AVC is at its minimum

If MC < AVC, then AVC is falling


17



CH 7: Cost Theory

Average Total Cost = ATC = TC/Q

Average Fixed Cost = AFC = TFC/Q

Average Variable Cost = AVC = TVC/Q

ATC = AFC + AVC

Marginal Cost =



TC/



Q =



TVC/



Q


18


CH 7: Cost Theory

Short-Run Cost Functions-Example

3

4

5

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

60 45 105 20 15 35 15

60 80 140 15 20 35 35

60 135 195 12 27 39 55

Average Total Cost = ATC = TC/Q

Average Fixed Cost = AFC = TFC/Q

Average Variable Cost = AVC = TVC/Q

ATC = AFC + AVC

Marginal Cost =



TC/



Q =



TVC/



Q


19


Graphical Presentation

CH 7: Cost Theory


20


CH 7: Cost Theory

Average Cost Curves-Graphical meaning

•

The average fixed cost curve slopes down continuously.

•

The average total cost curve is the vertical summation of the average fixed cost curve and the average variable cost curve

 The ATC curve is always higher than

AFC and AVC curves

•

While output gets big and AFC decline to zero, the AVC curve approaches the

ATC curve.

21


Wage Rate

Average Variable Cost

AVC = TVC/Q = w/AP

L

CH 7: Cost Theory

Marginal Cost



TC/



Q =



TVC/



Q = w/MP

L


22


CH 7: Cost Theory

Long-Run Cost Curves

•

The long run is the period of time during which:

 Technology is constant

 All inputs and costs are variable

 The firm faces no fixed inputs or costs

 The long run period is a series of short run periods.

[For each short run period there is a set of TP, AP, MP, MC, AFC, AVC, ATC, TC,

TVC & TFC for each possible scale of plant].

23


CH 7: Cost Theory


Long-Run Total Cost = The minimum total costs of producing various levels of output when the firm can build any desired scale of plant: LTC = f(Q)

Long-Run Average Cost = The minimum per-unit cost of producing any level of output when the firm can build any desire scale of plant: LAC = LTC/Q

Long-Run Marginal Cost = The change in long-run total costs per unit change in output: LMC =



LTC/



Q


24



CH 7: Cost Theory

Long-Run Total Cost = LTC = f(Q)

Long-Run Average Cost = LAC = LTC/Q

Long-Run Marginal Cost = LMC =



LTC/



Q


25


Derivation of Long-Run Cost Curves


CH 7: Cost Theory

From point A on the expansion path in the first panel with w=$ 10 and r=$ 10, the firm uses 4 units of labor 4L and 4 units of capital 4k and the minimum totalcost producing

1Q is $80. This is shown as point A’ and A’’ on the longrun total cost curve in the middle panel and bottom panel.

26


Relationship Between Long-Run and Short-

Run Average Cost Curves

CH 7: Cost Theory

The top panel of the figure is based on the assumption that the firm can build only four scales of plant

SAC1 etc.., while the bottom panel is based on the assumption that the firm can build many more or an infinite number of scales of plant. At A’’ min av cost of producing o/p is $80.

At B* the firm can produce 1.5Q at an av cost of $70 by using either SAC1 or SAC2 and so on..


27


Possible Shapes of the LAC Curve

CH 7: Cost Theory

The left panel shows a U-shaped LAC curve which indicates first decreasing and then increasing returns to scale. The middle panel shows a nearly Lshaped LAC curve which shows that economies of scale quickly give way to constant returns to scale or gently rising LAC. The right panel shows an LAC curve that declines continuously, as in the case of natural monopolies.


28


Learning Curves

CH 7: Cost Theory

The learning curve shows the decline in the average input cost of production with rising cumulative total outputs over time. The learning curve also shows that the average cost is about $

250 for producing the 100 th unit at point F etc..


29


CH 7: Cost Theory

Learning Curves

Average Cost of Unit Q = C = aQ b

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

The Learning curve can be express algebraically as follows:

(C is cost of the Q th unit of output)

 ln C = ln a + b ln Q

Linearized version, can be easily estimated and interpreted.

 ln C = 3 – 0.3 ln Q

If Q increases by 1%, then unit (average) costs decrease by 0.3%.

Useful to make predictions for the future: how much does the average cost for the 100th unit as well as 200th:

 lnC =3 – 0.3ln100 = 2.4 ==> C = antilog of (2.4) =$251.19

 lnC =3 – 0.3ln200 =2.31==>C =antilog of (2.31) =$204.03

30

© 2004, Managerial Economics, Dominick Salvatore © 2010/11, Sami Fethi, EMU, All Right Reserved .

Cost-Volume-Profit Analysis

CH 7: Cost Theory

Cost-volume-profit or breakeven analysis examines the relationship among the TR, TC, and total profits of the firm at various levels of o/p. This technique is often used by business executives to determine the sales volume required for the firm to break even and the total profits and losses at other sales levels.

The analysis uses a cost-volume-profit chart in which the TR and TC curves are represented by straight lines and the break-even o/p (Q

B

) is determined at their intersection.


31


CH 7: Cost Theory


The slope of the total revenue TR curve refers to the product price of $10 per unit.

The vertical intercept of the total cost of

(TC) curve refers

TFC of $200, and the slope of the TC curve to the AVC of

$5. The break-even with TR=TC $400 at the output (Q) of $40 units per time period at the point B.


32


CH 7: Cost Theory


Total Revenue = TR = (P)(Q)

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

Breakeven Volume TR = TC

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

Q

BE

= TFC/(P - AVC)


33


CH 7: Cost Theory

Break-even o/p

Q

BE

= TFC/(P - AVC)

P = 40

TFC = 200

AVC = 5

Q

BE

= 40


34


CH 7: Cost Theory

Operating Leverage and the other concepts

Operating leverage: The ratio of the firm’s total fixed costs to its total variable costs.

Contribution margin per unit: The excess of the selling price of the product over the average variable costs of the firm (i.e. P-AVC) that can be applied to cover the fixed costs of the firm and to provide profits.

Degree of operating leverage (DOL): The percentage change in the firm’s profits divided by the percentage change in output or sales; the sales elasticity of profits.


35


CH 7: Cost Theory

Operating Leverage

Operating Leverage = TFC/TVC

Degree of Operating Leverage = DOL

DOL



%

%







Q



(



(



AVC

AVC )



)

TFC


36


CH 7: Cost Theory

Operating Leverage

 The intersection of TR and TC defines the break even quantity of Q

B

=40. With TC’, the break even quantity increases to

Q

B’

=45.

 TC’ has a higher DOL than TC and therefore a higher Q

BE


37


CH 7: Cost Theory

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


38


CH 7: Cost Theory

Empirical Estimation

TVC

Functional Form for Short-Run Cost Functions

Theoretical Form Linear Approximation

  2 

cQ

3

TVC a bQ

AVC



TVC

Q

MC

 

2

bQ



3

cQ

2

2 AVC

 a



Q b

MC

 b


39


CH 7: Cost Theory

Empirical Estimation

Theoretical Form Linear Approximation


40


CH 7: Cost Theory

Empirical Estimation Long-Run Cost Curves







Cross-Sectional Regression Analysis

Engineering Method

Survival Technique


41


Empirical Estimation-Example

CH 7: Cost Theory





A computer company wants to estimate the average variable cost fuction of producing hard disks. The firm believes that AVC varies with the level of output and wages. An analyst collects the monthly data over the past two years and deflates the variables using the relevant price indexes. Finally, he regresses

TVC fuction on output and wages as follows:

LnTVC=0.14+0.80LnQ+0.036LnW

(2.8) (3.8) (3.3) t-values

‾ R²=0.92 DW=1.9

F=125.8


42


Empirical Estimation-Example

CH 7: Cost Theory



Suppose W= $10, drive the AVC and MC.



What are the shapes of the AVC and MC curves of the firm?



Why did the analyst fit a linear rather than quadratic or cubic TVC function?



Was this application the right choice? Why?


43


The End

CH 7: Cost Theory

Thanks


44


cost theory

FALL 2010-

Cost Theory and Estimation

by

Assoc. Prof. Sami Fethi

Explicit Costs

Economic Costs

Relevant Costs

Total Cost = TC = f(Q)

Total Fixed Cost = TFC

Total Variable Cost = TVC

TC = TFC + TVC

•

•

Average Variable Cost

AVC = TVC/Q = w/AP

Marginal Cost

TC/

Q =

TVC/

Q = w/MP

•

Long-Run Total Cost = LTC = f(Q)

Long-Run Average Cost = LAC = LTC/Q

Long-Run Marginal Cost = LMC =

LTC/

Q

Total Revenue = TR = (P)(Q)

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

Breakeven Volume TR = TC

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

Q

= TFC/(P - AVC)

Operating Leverage = TFC/TVC

Degree of Operating Leverage = DOL

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

TVC

cQ

TVC a bQ

AVC

TVC

Q

MC

bQ

cQ

Cross-Sectional Regression Analysis

Engineering Method

Survival Technique

The End

Thanks

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