Lecture 5
Technological Change
What would be the impact of technological change on output?
Capital
How would an isoquant move?
50
40
A
30
B
20
300
C
200
10
100
1
2
3
4
5
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6
7
Labor
Lecture 5
But productivity can increase without technological change!
Note however,
that we are NOT
producing more
Capital
K
C2
C
Q
C1
B
B’
I
A’
C’
A
L2
L1
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Labor
Lecture 5
Total Factor Productivity
A Better Measure for Technological Change
Total factor productivity measure, relates changes in output to all
inputs. In the case of our example to labor AND capital.
Take for instance a production function:
Q   ( bL  cK )
Where Q is the quantity of output, L is quantity of labor, b is a labor related
rate, c is a capital related rate such as unit price (both constants)
We divide the quantity by the sum of
all the weighted inputs to get a ratio α
In general:

Q
n
w I
i 1
i i

Q
bL  cK
Where wi is the weight
associated with the ith
input Ii
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Lecture 5
Cost
• Historical cost
• Opportunity cost
• Explicit cost
• Implicit cost
• Short-run cost
• Long-run cost
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Lecture 5
Historical V Opportunity Cost
Historical cost: The amount – in currency – that the entity paid for a
good or service
(The “I don’t believe I paid for that” cost)
Opportunity cost: The value of the highest valued good or service
you could have procured if you had not selected the present option
(The “I could have had a V8” cost)
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Lecture 5
Explicit V Implicit Cost
Explicit Cost: Ordinary items that accountants include as accountable
costs, e.g. payroll, cost of materials, etc.
Implicit Cost: The hidden –usually unaccounted for – charges, e.g.
owner’s time
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Lecture 5
Short-run V Long-run Cost Function
Short-run: The
immediate time frame
during which the entity
(firm) cannot change the
quantity of at least some
of the inputs.
Long-run: The time frame
during which the entity (firm)
has had time to adjust to give
itself the ability to change the
quantity of at least one of the
inputs.
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Lecture 5
Short-run Cost Function
As the firm is unable to alter the quantities of some inputs such as plant and
equipment – or sometimes even labor – short run functions are characterized by:
Fixed costs
Total cost (TC)
Cost
As well as, of course,
Total variable cost (TVC)
Variable costs
Total fixed cost (TFC)
Total cost in the short-run is therefore:
TC=TFC+TVC
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Output
Lecture 5
Average and Marginal Cost
Average fixed cost (AFC): is total fixed cost per
unit of output (and it DOES change!)
Average variable cost (AVC): is total variable cost
per unit of output
Average total cost (ATC): the sum of the two, or
total cost per unit of output
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TFC
AFC 
Q
TVC
AVC 
Q
TC
ATC 
Q
Lecture 5
Cost
Marginal
Cost=dTC/dQ
Average
Total Cost
Average
Variable
Cost
Average
Fixed Cost
Output
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Lecture 5
Marginal Cost
The addition to total cost resulting from the addition of the last unit of output
TVC  TFC TVC

0
Q
Q
TVC
MC 
Q
MC 
We know that TVC is the product of the price of the
variable unit (W) and the quantity of variable input (U)
TVC  WU
TVC  WU
We also know that the change of the variable
input U wrt quantity is the marginal product of that
variable input
U
1
MC  W
W
Q
MP
So what variable price W should you pay for your
input (say some raw material)?
W  MP  MC
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Lecture 5
Example:
ABCO has a total cost function as below:
TC  100  50Q  11Q2  Q3
The firm’s marginal cost function will be:
dTC
MC 
 50  22Q  3Q 2
dQ
The firm’s average variable cost function will be:
TVC 100  50Q  11Q 2  Q 3
AVC 

 50  11Q  Q 2
Q
Q
Note that marginal cost always equals average variable cost when
AVC is at a minimum.
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Lecture 5
dAVC
 11  2Q  0
dQ
Q  5.5
MC  50  22( 5.5 )  3( 5.5 )2  19.75
AVC  50  11( 5.5 )  ( 5.5 )2  19.75
Note also that marginal cost always equals average total cost when ATC is at
a minimum.
TC 100  50Q  11Q 2  Q 3 100
ATC 


 50  11Q  Q 2
Q
Q
Q
dATC
 ( 100 / Q 2 )  11  2Q  0
dQ
Q  6.64
MC  36.11
ATC  36.11
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Lecture 5
Long-run Cost Function
In the long-run, the organization has had the time to adjust, may be expand
equipment capacity, install new equipment, open a new plan or catch up with
technology. Nothing – no input – is frozen and the organization can PLAN for
a new set of future short-run situations.
Imagine…… that an
organization wishes to expand
output. Let us say, it has the
choice of opening three types of
plants – three years from now.
Average
Cost
C1
C2
C3
The short-run average cost
function for each plant is given
Output
Quantity
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Lecture 5
Average Cost
C1
C2
C3
Q1
Q2
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Output Quantity
Lecture 5
Average Cost
Long-run
Average
Cost
Function
Short-run Average
Cost Functions
Output Quantity
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Lecture 5
Given the long-run average cost,
we can calculate the long-run
total cost:
LRTC  LRAC  Q
Given the long-run total cost, we
can calculate the long-run
marginal cost:
dLRTC
LRMC 
dQ
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Lecture 5
Example:
Q  4 ( KL )
Ephemer Industries has the production function:
Q2
TC  8L  2K 
 2K
2K
as
As Ephemer pays $8 for hour of labor and $2
for unit of capital, it’s total cost is:
Q2
L
16 K
Q2
TCS 
 20
20
In the short-run K is fixed at K=10, thus:
Where TCS is short-run total cost.
Short-run Average Cost will be:
ACS 
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TCS Q 20


Q
20 Q
Lecture 5
And the short-run marginal cost is:
MCS 
dTCS Q

dQ
10
In the long-run, in input is fixed.
We wish to determine the optimum
amount of capital input to be used to
produce Q units per months, we
minimize the total cost function
Substituting, we have
dTC
Q2

20
dK
2K 2
Q
K
2
Q2
Q2
TC 
 2K 
Q
2K
Q
TC  2Q
This implies that the long-run average cost equals $2 per unit
produced.
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Lecture 5
Economies of Scope
Economies of scope exist when the cost of producing two (or more)
products jointly is less than the sum cost of producing each one alone
To determine if economies of scope are available to us, we calculate:
S
C( Q1 )  C( Q2 )  C( Q1  Q2 )
C( Q1  Q2 )
S represents the percent savings due to economies of scope
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Lecture 5
Break-Even Analysis
Profit ensues when all costs are covered
Break-even analysis will find the point where total cost and total
revenue are equal
$
Total Cost
Total
Revenue
Quantity
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Lecture 5
Example:
Makeabuck Inc. has the total cost function:
The firm’s total revenue is:
TC  1000  25Q
TR  PQ  75Q
How many units of product must the firm will make and sell to start making a profit ?
TC  TR  1000  25Q  75Q
1000  50Q
Q  1000 / 50  20
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