Please Read:
Cost Analysis and
Estimation
•“Economies
•“Economiesof
ofScale
Scaleand
andSoftware
SoftwareProduction”
Production”
•“Economies
•“Economiesof
ofScale
Scaleand
andScope
Scopein
inTelecommunications”
Telecommunications”
•“Economies
•“Economiesof
ofScale
Scalein
inAutomobile
AutomobileAccessories”
Accessories”
Chapter 9
7
8
Chapter 9
KEY CONCEPTS
Chapter 9 OVERVIEW
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„
„
„
„
What Makes Cost Analysis Difficult
Opportunity Cost
Incremental and Sunk Costs in Decision Analysis
Short-run and Long-run Costs
Short-run Cost Curves
Long-run Cost Curves
Minimum Efficient Scale
Firm Size and Plant Size
Learning Curves
Economies of Scope
Cost-volume-profit Analysis
9
„
„
„
„
„
„
„
„
„
„
„
„
„
„
„
historical cost
current cost
replacement cost
opportunity cost
explicit cost
implicit cost
incremental cost
profit contribution
sunk cost
cost function
short-run cost functions
long-run cost functions
short run
long run
planning curves
„
„
„
„
„
„
„
„
„
„
„
„
„
operating curves fixed cost
variable cost
short-run cost curve
long-run cost curve
economies of scale
cost elasticity
capacity
minimum efficient scale
multiplant economies of scale
multiplant diseconomies of scale
learning curve
economies of scope
cost-volume-profit analysis
breakeven quantity
10
What Makes Cost Analysis
Difficult?
„
„
Accounting and economic costs often differ.
„
„
Historical cost is the actual cash outlay.
Current cost is the present cost of previously
acquired items.
„
„
Cost of replacing productive capacity using
current technology.
Opportunity cost is foregone value.
Reflects second-best use.
Explicit and Implicit Costs
„
Replacement Cost
„
Opportunity Cost Concept
„
Historical Versus Current Costs
„
„
Opportunity Cost
Link Between Accounting and Economic
Valuations
„
„
11
„
Explicit costs are cash expenses.
Implicit costs are noncash expenses.
12
1
Incremental and Sunk Costs in
Decision Analysis
„
Incremental Cost
„
„
„
Incremental cost is the change in cost tied to
a managerial decision.
Incremental cost can involve multiple units of
output.
„
„
Short-run and Long-run Costs
At least one input is fixed in the short
run.
„ All inputs are variable in the long run.
„
Marginal cost involves a single unit of output.
„
Sunk Cost
„
„
How Is the Operating Period Defined?
Fixed and Variable Costs
Fixed cost is a short-run concept.
„ All costs are variable in the long run.
„
Irreversible expenses incurred previously.
Sunk costs are irrelevant to present decisions.
13
14
Production
Production and
and Cost
Cost Related
Related II
What Are Cost Functions?
„
„
„
Constant returns to the
variable input in the
production function…
All cost functions are a combination of two pieces of
information:
1) the production function.
2) the input prices.
Changes in either of these pieces of information will
change the cost function.
That is, cost functions get their shapes from the
shape of the production function and the input
prices.
15
results in a linear
variable cost function
16
Production
Production and
and Cost
Cost Related
Related IIII
17
Production
Production and
and Cost
Cost Related
Related III
III
Decreasing returns to
the variable input in
the production
function…
Increasing returns to
the variable input in
the production
function…
results in a curvilinear
variable cost function
which increases at an
increasing rate
results in a curvilinear
variable cost function
which increases at an
decreasing rate
18
2
Cost Curves
„
Cost = sum of (P
(Pinputs * Qinputs)
„
Qinputs includes fixed and variable inputs
„
Fixed Costs - sum of all Pi*Qi
Pi*Qi for fixed inputs
„
Variable Costs - sum of all Pi*Qi
Pi*Qi for variable
inputs
19
Short-Run
Short
Short-Run
Cost
Cost Curves
Curves
These
Thesecost
costfunctions
functionsare
areexactly
exactly
those
thoseininthe
the“Stack
“StackDiagram.”
Diagram.”
Figure 9.1
20
Total
Total Cost
Cost Function
Function for
for aa Production
Production System
System
Exhibiting
Exhibiting Increasing,
Increasing, Then
Then Decreasing,
Decreasing,
Returns
Returns to
to Scale
Scale
Total Cost
Total cost (TC) = TFC + TVC
(vertical addition of TFC and TVC curves)
„
Total
TotalCost
CostFunction
Function
Total
TotalProduct
ProductFunction
Function
Figure 9.2
21
22
Total
Total Cost
Cost Curve
Curve Derived
Derived
Total
Total Cost
Cost Curve
Curve Derived
Derived
Cost
CostFunction
Function
Production
ProductionFunction
Function
Production
ProductionFunction
Function
Each
Eachunit
unitof
of
labor
laborcosts
costs
$160
$160
24
25
3
Total Cost Curve Derived
Cost
CostFunction
Function
Variable
Variablecost
costcurve
curve
isis derived
derived from
fromthe
the
production
production function
function
and
and an
an assumption
assumption
about
about the
the price
price of
of
the
the input
input (labor’s
(labor’s
price
price isis $160
$160per
per
unit
unit in
in this
this
example).
example).
Production
ProductionFunction
Function
Quantity
of Output
The “Stack
Diagram”
Diagram”
Shows the
Relationship
Between
Production
and Cost!
(short(short-run)
Stage
III
Stage
II
DAR
Q2
DMR
Q3
Q = bX + c X 2 - dX 3
•
(A)
•
X3 X2
MP X
AP X
Units of Variable Input (X)
X1
• •
AP X = b + cX - d X 2
$
TC = a + bQ - c Q2 + d Q3
X3 X2
X1
TVC = bQ - c Q2 + d Q3
(B)
Units of Variable Input (X)
MP X = b + 2cX - 3d X 2
•
(C)
•
•
Q3
•
TFC = a
Q2
Q1
Quantity of Output
MC = b - 2cQ + 3d Q2
$
ATC = a + b - cQ + d Q2
Q
AVC = b - cQ + d Q2
(D)
AFC = a
Q
Q3
26
Stage
I
Q1
Q2
Quantity of Output
Q1
27
Marginal and Average Cost Curves
Long-run Cost Curves
Economies of Scale
„ Long-run cost curves show minimum
cost in an ideal environment.
„
28
29
The Effect of Scale
(This is the Long Run!)
„
Effect of Scale
if you expect 10 customers, you will
build a smaller facility than if you
expect 100 customers
„
„
30
In shortshort-run,
run, firm takes size as a given,
and tries to solve the problem of the
"optimal combination of inputs."
In longlong-run,
run, when nothing is fixed,
optimal size might be larger or smaller
31
4
The
The shape
shape of
of the
the LRAC
LRAC
•Why Does It Decline At First?
•Greater Specialization
•Ability to Use More Advanced Technologies
•Opportunity to Take Advantage of Lower Costs
•Lower Administrative Costs Per Unit
•Advances in Management Technology
•Why Does It Eventually Increase?
•“People Problems”
32
33
Key
Key Steps
Steps In
In Estimating
Estimating Cost
Cost
Functions
Functions
Real Long Run Average Cost Data
• Definition of Cost
• relevant cost data
• Correction for Price Level Changes
• perhaps using separate price indices
• Relating Cost to Output
• distinguish costs that vary (and those that don’t vary)
• Matching Time Periods
• Controlling Product, Technology, and Plant
• fixed definition of product, technology, and scale
• Length of Period and Sample Size
• large number of observations desired but...
34
35
Evidence
Evidence of
of Economies
Economies and
and
Diseconomies
of
Scale
Diseconomies of Scale
Cost Elasticity and Economies
of Scale
„
•Increasing Returns to Scale
εC < 1 means falling AC, increasing
returns.
„ εC = 1 means constant AC constant
returns.
„ εC > 1 means rising AC, decreasing
returns.
„
•Soft Drink Industry
•Grain Production
•Decreasing Returns to Scale
•Electric Power Generation
36
Cost elasticity is εC = ∂C/C ÷ ∂Q/Q.
37
5
Minimum Efficient Scale
„
Competitive Implications of Minimum
Efficient Scale
„
„
Transportation Costs and MES
„
MES is the minimum point on the LRAC curve.
„
Terminal, line-haul and inventory costs can be
important.
High transport costs reduce MES impact.
Competition is most vigorous when:
„
„
„
MES is small in absolute terms.
MES is a small share of industry output.
Disadvantage to less than MES scale is
modest.
38
39
Firm Size and Plant Size
„
Multi-plant Economies and Diseconomies
of Scale
„
„
Multi-plant economies are cost advantages
from operating several plants.
Multi-plant diseconomies are cost
disadvantages from operating several plants.
Figure 9.5
40
41
Economics of Multi-plant
Operation: an Example
„
Plant Size and Flexibility
Figure 9.6
42
43
6
Firm Size and Plant Size
continued
Firm Size and Plant Size
There may be economies to multiplant operation
To Profit Maximize in the single plant firm:
Consider first a single plant firm:
MR =
∂TR
∂Q
MR = MC
Demand
DemandFunction
Function
P = $940 − $0.02Q
= $940 − $0.04Q
$940 − $0.04Q = $40Q + $0.02Q
Cost
CostFunction
Function
$0.06Q = $900
TC = $250,000 + $40Q + $0.01Q 2
MC =
∂TC
∂Q
Q = 15,000
= $40 + $0.02Q
Optimal
Optimalsingle
singleplant
plantsize
size
See
SeePg
Pg296
296
44
45
Firm Size and Plant Size
continued
Firm Size and Plant Size
continued
„
At
Atthis
thisProfit
ProfitMaximizing
MaximizingPoint
Point(15,000
(15,000units):
units):
P = $940 − $0.02Q
„
„
P = $940 − $0.02(15,000)
„
P = $640
and
π = $6,500,000
AC for a single plant must be examined
Assume same cost conditions apply
Assume no other multiplant economies or
diseconomies
Profits
Profitswith
withaasingle
singleplant
plant
46
47
Firm Size and Plant Size
continued
Now
Nowexamine
examinethe
thesame
samefirm
firmwhen
whenconsidering
consideringmultiple
multipleplants
plantsby
by
finding
findingthe
theminimum
minimumof
ofaverage
averagecost:
cost:
AC =
Firm Size and Plant Size
continued
This
Thisfirm
firm(considering
(consideringmultiplant
multiplantoperations)
operations)finds
findsminimum
minimumof
ofAC:
AC:
MC = AC
TC
Q
$40 + $0.02Q = $250,000Q −1 + $40 + $0.01Q
250,000Q −1 = 0.01Q
250,000
Q2 =
0.01
MES
MESPlant
Plant
Q = 5,000
TC = $250,000 + $40Q + $0.01Q 2
AC =
$250,000 + $40Q + $0.01Q 2
Q
AC = $250,000Q −1 + $40 + $0.01Q
48
To gain insight into whether multiple
plants might be reasonable
See
SeePg
Pg297
297
49
7
The Real Answer
Firm Size and Plant Size
continued
MC = $40 + $0.02Q
MC = $40 + $0.02(5,000)
But,
But,this
thisdoes
doesnot
notimply
implythat
thatthe
thefirm
firmshould
shoulduse
usethree
three5000
5000unit
unit
plants
plantsand
andproduce
produce15,000
15,000units
unitsto
tomaximize
maximizeprofits!
profits!
MC = $140
Profits
Profitswere
weremaximized
maximizedatatQ=15,000
Q=15,000under
underthe
theassumption
assumptionthat
that
both
bothmarginal
marginalcost
costand
andmarginal
marginalrevenue
revenuewere
wereequal
equalto
to$640.
$640.
MR = MC
However,
However,ififthe
thefirm
firmuses
uses5,000
5,000size
sizeplants
plantsthe
themarginal
marginalcosts
costswill
will
be
belowered
loweredand
andthe
thenew
newprofit
profitmaximizing
maximizinglevel
levelof
ofproduction
productionwill
will
be
begreater
greaterthan
than15,000!
15,000!
$940 − $0.04Q = $140
Q = 20,000
Use
Use44plants
plantsof
of5,000
5,000unit
unitcapacity
capacityand
andprofits
profitswill
willequal
equal$8,000,000
$8,000,000
50
See
Seepage
page298
298
51
Learning Curves
„
Learning Curve Concept
„
„
„
„
Learning causes an inward shift in the LRAC
curve.
Learning curve advantages are often mistaken
for economies of scale effects.
Learning Curve Example
Strategic Implications of the Learning
Curve Concept
„
When learning results in 20% to 30% cost
savings, it becomes a key part of competitive
strategy.
52
Figure 9.10
53
Economies of Scope
„
Economies of Scope Concept
„
„
„
„
„
Scope economies are cost advantages that
stem from producing multiple outputs.
Big scope economies explain the popularity of
multi-product firms.
Without scope economies, firms specialize.
Cost-volume-profit Charts
„
„
Cost-volume-profit analysis shows effects of
varying scale.
Breakeven analysis shows zero profit points of
cost coverage.
Exploiting Scope Economies
„
54
Cost-volume-profit Analysis
Scope economics often shape competitive
strategy for new products.
55
8
Approach to Profit
Maximization
Firm Goal: Maximize Profit
Profit(π) =
Total Revenue minus Total Cost
„
MC = MR
π = TR - TC
„
56
Set marginal cost equal to marginal revenue
ΔTC
ΔTP
ΔTR
MR =
ΔTP
MC =
Why?
57
Breakeven
Breakeven and
and Operating
Operating Leverage
Leverage
(Firm
A)
(Firm A)
Linear
-VolumeCost
Volume-Profit Chart
Linear CostCost-Volume-Profit
Chart
Figure 9.13a
Figure 9.12
59
60
Breakeven
Breakeven and
and Operating
Operating Leverage
Leverage
(Firm
(Firm B)
B)
Breakeven
Breakeven and
and Operating
Operating Leverage
Leverage
(Firm
C)
(Firm C)
Figure 9.13b
61
Figure 9.13c
Once
Oncebreakeven
breakevenisisachieved,
achieved,profits
profitsrise
risefaster
fasterin
incas
cas“C”
“C”than
thanin
incase
case
“A”
“A”or
or“B.”
“B.”
62
9
Generalized Break-even
(Assumptions?)
Profit Maximization Using Breakeven Analysis (Three Steps)
„
„
„
63
The derivative of TC (which is the slope
of total cost) is called marginal cost.
cost.
The derivative of TR (which is the slope
of total revenue) is called marginal
revenue.
revenue.
When the slopes of total revenue and
total cost are equal, profit is maximized:
i.e.,
MR = MC.
64
Where Would This Competitive Firm Choose to
Operate?
Two Important Points
„
Produce where MC = MR
„
We will see that:
MC curve is the supply curve
(above average variable cost)
65
66
π and the Shutdown Point
Profit in the Graph
π = TR - TC
< -divide by Q
Avg. π = AR − ATC; but AR = Price
Avg. π = P − ATC
π and the shutdown points
Shutdown Point:
The shutdown point is the intersection of marginal cost and
average variable cost.
67
68
10
The Supply Curve is
the Marginal Cost Curve
Shutdown Point
„
Short run (Lower)(or ... MC = AVC)
when MC below AVC
Why?
„ With a shutdown losses are equal TFC
„ If operation is continued, losses are greater
(not even variable costs can be covered)
„ You must at least cover your variable costs
(and perhaps contribute to fixed costs)
„
„
For a Competitive Firm
69
70
Nursing Cost Estimate
„
See data on page 317
71
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