Transcript Document 7516089

Managerial Economics
in a Global Economy
Chapter 7
Cost Theory and Estimation
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
The Nature of Costs
 Explicit Costs

Accounting Costs: actual expenditures on resources
 Economic Costs


Implicit Costs: returns on inputs owned by the firm
Opportunity Costs (Economic Costs): costs of all the inputs, whether
owned by the firm or not.
 Example 1.
 Suppose that a firm purchased raw materials by 100, kept in
the inventory.
 If the price fell to 60.
 Accountant cost = 100
 Economic Cost (relevant) = 60
 We can’t sell by more than 60.
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Example 2.
 A machine purchased for 1000. If we use a linear depreciation
for 10 years.


After 10 years, the accounting value = zero.
Suppose that after 10 years, the firm can sell the machine for 120.
 The economic cost of the machine at year 11 = 120.
 We can sell it at that value.
 Relevant Costs

Incremental Costs: the change in total costs from implementing a
particular managerial decision, e.g., introducing a new product line,
undertaking a new advertising campaign, or the production of a
previously purchased component.

Sunk Costs are Irrelevant: the costs that are not affected by the
decision, they are irrelevant or Sunk Costs.
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Short-Run Cost Functions
 Total Cost = TC = f(Q)

Total Fixed Cost = TFC

Total Variable Cost = TVC
 TC = TFC + TVC
 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
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Short-Run Cost Functions
Q
0
1
2
3
4
5
TFC
$60
60
60
60
60
60
Managerial Economics
TVC
$0
20
30
45
80
135
TC
$60
80
90
105
140
195
AFC
$60
30
20
15
12
Prof. M. El-Sakka
AVC
$20
15
15
20
27
ATC
$80
45
35
35
39
MC
$20
10
15
35
55
CBA. Kuwait University
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
 Average Variable Cost
 AVC = TVC/Q = w/APL




Note that AVC = TVC/Q = wL/Q
But APL = Q/L
and
By substitution
AVC = w . 1/APL
1/APL = L/Q
= w/APL
 Marginal Cost
 TC/Q = TVC/Q = w/MPL






Note that
MC = TVC/ Q = w (L) / Q
But
MPL = Q / L
and
1/MPL = L / Q
Since w is constant and by substitution;
MC = W . 1/MPL = w/MPL
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
 Long-Run Total Cost = LTC = f(Q)
 Long-Run Average Cost = LAC = LTC/Q
 Long-Run Marginal Cost = LMC = LTC/Q
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Derivation of Long-Run Cost Curves
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Relationship Between Long-Run and Short-Run Average Cost Curves
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Possible Shapes of the LAC Curve
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Plant Size and Economies of Scale
Theoretical LAC
Economies of Scale




Diseconomies of Scale
Reasons of economies of scale:
Specialization
Technological reasons (diameter of pipes)
Financial Reasons



Quantity discounts
Interest discounts
Advertising discounts
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Economies of Scope
 Lowering costs when a firm produces tow or more products
together than producing each one alone
 S = {C(Q1) + C(Q2) – C(Q1+Q2)} / C(Q1+Q2)

(scope)
 e.g.,
 If Q1+Q2 = 15
 If C(Q1) = 12 and C(Q2) = 6 then;
 S = ((12+6)) – 15 / 15 = .2
 There is a 20% saving in costs the bigger the economies of
scope
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Learning Curve
 Shows the decline in the average input cost of
production with rising cumulative total outputs over
time.
 Average Cost of Unit Q = C = aQb
 C = average input cost
 a = average cost of the first unit of output
 b = negative
 Note:
 If b is high, the faster is the decline in input cost
 If b is small the smaller is the decline in input cost
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
The Learning Curve
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Estimation Form:
 log C = log a + b Log Q
 e.g., if estimated regression is:
 Log C = 3 – 0.3 log Q
At Q = 100
 Log C = 3 – 0.3 log(100)
= 3 – 0.3(4.605)
= 3 – 1.382
= 1.616
At Q = 200
Log C = 3- 0.3 log(200)
= 3 – 0.3(5.2989)
= 3 – 1.589
= 1.411
Average costs is going down as output is increasing over time.
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Cost-Volume-Profit Analysis (Break Even)
 Note:
• Total Revenue = TR = (P)(Q)
• Total Cost = TC = TFC + (AVC)(Q)
• Breakeven Volume TR = TC
• Or:
• (P)(Q) = TFC + (AVC)(Q)
• QBE = TFC/(P - AVC)
• Target output
• QT = (TFC + ΠT) / (P – AVC)
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
 Cost-Volume-Profit Analysis
P = 40
TFC = 200
AVC = 5
QBE = 40
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
e.g., Break even output
 If TFC = 200
P = 10
AVC = 5
 QBE= (200/(10-5) = 40
 Since P = 10
 TR = 10(40) = 400
 TC = TFC + P(AVC) = 200 + 40(5) = 400
e.g., target output
 If the firm wants to earn 100 as a target profit what is the
target output



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

QT = (200 + 100) / (10-5) = 60
Note that
TR = 10(60) = 600
TC = 200 + 5(60) = 500
Π = TR – TC = 600 – 500 =100
Which is the target profit
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
 Operating Leverage
 Operating Leverage = TFC/TVC
Degree of Operating Leverage = DOL
%
Q( P  AVC )
DOL 

%Q Q( P  AVC )  TFC
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
TC’ has a higher DOL
than TC and therefore a
higher QBE
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
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
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Empirical Estimation
Functional Form for Short-Run Cost Functions
Theoretical Form
Linear Approximation
TVC  aQ  bQ2  cQ3
TVC  a  bQ
TVC
2
AVC 
 a  bQ  cQ
Q
a
AVC   b
Q
MC  b
MC  a  2bQ  3cQ 2
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Theoretical Form
Managerial Economics
Linear Approximation
Prof. M. El-Sakka
CBA. Kuwait University
Empirical Estimation long-Run Cost Curves
 Cross-Sectional Regression Analysis
 Engineering Method
 Survival Technique
Actual LAC versus empirically estimated LAC’
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University