1517 cost-theory and estimation of cost

Chapter 8Chapter 8
The Theory
and
Estimation of
Cost
Managerial Economics:
Economic Tools for Today’s
Decision Makers, 4/e By Paul
Keat and Philip Young

2003 Prentice Hall Business Publishing Managerial Economics, 4/e Keat/Young
Before We Start…Group Presentation
• So popular?
Q = aL
b
K
1-borc
• b+c > 1 IRTS
• b+c = 1 CRTS
• b+c < 1 DRTS
• Short Run Analysis: MPK = c Q/K
& MPL = b Q/L
• b & c are elasticities of K & L
factors
• LogQ=loga+blogL+clogK + dlogT
where T  technology

The Theory and
Estimation of Cost
• Definition of Cost
• The Short Run Relationship Between
Production and Cost
• The Short Run Cost Function
• The Long Run Relationship Between
Production and Cost
• The Long Run Cost Function
• The Learning Curve

Definition of Cost
• A cost is relevant if it is affected by a
management decision.
• Historical cost is incurred at the time of
procurement
• Replacement cost is necessary to replace
inventory
• Are historical costs relevant?

Definition of Cost
• There are two types of cost associated
with economic analysis
• Opportunity cost is the value that is
forgone in choosing one activity over the
next best alternative
• Out-of-pocket cost is actual transfer of
value that occur
• Which cost is relevant?

Definition of Cost
• There are two types of cost associated
with time
• Incremental cost varies with the range
of options available in the decision
making process.
• Sunk cost does not vary with decision
options.
• Is sunk cost relevant?

SR Relationship Between
Production and Cost
• A firm’s cost structure is related to its
production process.
• Costs are determined by the production
technology and input prices.
• Assuming that the firm is a “price taker” in
the input market.

Production and Cost
• Total variable cost
(TVC) is associated
with the variable
input
• Assume w=$500
per unit (price-
taker)
Total
Input
(L) Q (TP) MP
TVC
(wL)
0 0 0
1 1,000 1,000 500
2 3,000 2,000 1,000
3 6,000 3,000 1,500
4 8,000 2,000 2,000
5 9,000 1,000 2,500
6 9,500 500 3,000
7 9,850 350 3,500
8 10,000 150 4,000
9 9,850 -150 4,500

Production and Cost
• TP and TVC are mirror images of
each other
Kings Dominion
Example

Production and Cost
• Total cost (TC) is the cost associated
with all of the inputs. It is the sum of
TVC and TFC.
• TC=TFC+TVC
• Marginal Costs
• Average Costs
Tool Set for
Production Cost
Analysis
vs.
Production Process
Analysis

Production and Cost
• Marginal cost (MC) is the change in
total cost associated a change in output.
Q
TC
MC
∆
∆
=
Q
TVC
Q
TVC
Q
TFC
Q
TVCTFC
Q
TC
MC
∆
∆
+=
∆
∆
+
∆
∆
=
∆
+∆
=
∆
∆
= 0
)(

Production and Cost
• Add marginal
cost to the
table
Total
Input
(L) Q MP
TVC
(wL) MC
0 0 0
1 1,000 1,000 500 0.50
2 3,000 2,000 1,000 0.25
3 6,000 3,000 1,500 0.17
4 8,000 2,000 2,000 0.25
5 9,000 1,000 2,500 0.50
6 9,500 500 3,000 1.00
7 9,850 350 3,500 1.43
8 10,000 150 4,000 3.33
9 9,850 -150 4,500

Production and Cost
• Observe that:
• When MP is
increasing,
MC is
decreasing.
• When MP is
decreasing,
MC is
increasing.
Total
Input
(L) Q MP
TVC
(wL) MC
0 0 0
1 1,000 1,000 500 0.50
2 3,000 2,000 1,000 0.25
3 6,000 3,000 1,500 0.17
4 8,000 2,000 2,000 0.25
5 9,000 1,000 2,500 0.50
6 9,500 500 3,000 1.00
7 9,850 350 3,500 1.43
8 10,000 150 4,000 3.33
9 9,850 -150 4,500

Production and Cost
• The relationship between MP and
MC is
MP
w
MP
w
Q
L
w
Q
Lw
Q
TVC
MC =•=
∆
∆
•=
∆
∆•
=
∆
∆
=
1
Law of diminishing returns implies that
MC will eventually increase! Why?

The Short Run Cost Function
• Average total cost (ATC) is the
average per-unit cost of using all of the
firm’s inputs (TC/Q)
• Average variable cost (AVC) is the
average per-unit cost of using the firm’s
variable inputs (TVC/Q)
• Average fixed cost (AFC) is the average
per-unit cost of using the firm’s fixed
inputs (TFC/Q)

• Add ATC = AFC + AVC to the table

• ATC = AFC + AVC

• Production cost graph or map is

• Important Map Observations
• AFC declines steadily over the range of
production. Why?
• In general, ATC is u-shaped. Why?
• MC intersects the minimum point (q*) on
ATC. Why?

• Important Map Observations
• What is the economic significance of q*?

• Average total cost (ATC) is the
average per-unit cost of using all of the
firm’s inputs (TC/Q)
• At Q* - ATC is minimized or inputs
are used most efficiently given the
production function
Going at 55 MPH

• A change in input
prices will shift the
cost curves.
• If fixed input costs
are reduced then
ATC will shift
downward. AVC
and MC will remain
unaffected. Computer Chip
Case

• A change in input
prices will shift
the cost curves.
• If variable input
costs are reduced
then MC, AVC,
and AC will all
shift downward.
Airline Industry
Case

• Yahoo Group
Discussion
• What is different
about dot.com
businesses?
Irrational
Exuberance

The LR Relationship Between
Production and Cost
• In the long run, all inputs are variable.
• What makes up LRAC?

The Long-Run Cost Function
• LRAC is made up
for SRACs
• SRAC curves
represent various
plant sizes
• Once a plant size is
chosen, per-unit
production costs are
found by moving
along that particular
SRAC curve

• The LRAC is the lower envelope of all
of the SRAC curves.
• Minimum efficient scale is the lowest
output level for which LRAC is
minimized
Is LRAC a function of market size?
What are implications?

• Reasons for Economies of Scale…
Increasing returns to scale
Specialization in the use of labor and capital
• Economies in maintaining inventory
• Discounts from bulk purchases
• Lower cost of raising capital funds
• Spreading promotional and R&D costs
Management efficiencies

• Reasons for Diseconomies of Scale…
 Decreasing returns to scale
 Input market imperfections
 Management coordination and control
problems

The Learning Curve
• Measures the
percentage decrease in
additional labor cost
each time output
doubles.
• An “80 percent” learning
curve implies that the
labor costs associated
with the incremental
output will decrease to
80% of their previous
level.

The Learning Curve
• A downward slope in the learning
curve indicates the presence of the
learning curve effect
• Why? Workers improve their
productivity with practice
• The learning curve effect shifts the
SRAC downward

Production Cost Homework
• Page 378
• Problem 10

1517 cost-theory and estimation of cost

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