Download per unit of output

Cost Theory
EA Session 7
July 13, 2007
Prof. Samar K. Datta
Overview
• Short run costs
• Long run costs & economies
of scale
• Economies of scope &
product transformation
curve
SHORT RUN COSTS
• Marginal Cost (MC) is the cost of expanding output by one
unit => MC = dTC/dQ
• Average Total Cost (ATC) is the cost per unit of output, or
average fixed cost (AFC) plus average variable cost (AVC)
=> ATC = TC/Q = TFC/Q + TVC/Q = AFC + AVC
• The relationship between the production function and cost
can be exemplified by:
– Increasing returns
• With increasing returns, output is increasing relative
to input and variable cost and total cost will fall
relative to output.
– Decreasing returns
• With decreasing returns, output is decreasing
relative to input and variable cost and total cost will
rise relative to output.
Cost Curves for a Firm
• The line drawn from
the origin to the
tangent of the
variable cost curve:
–
–
–
Its slope equals AVC
The slope of a point
on VC equals MC
Therefore, MC =
AVC at 7 units of
output (point A)
TC
P
400
VC
300
200
A
100
0
FC
1
2
3
4
5
6
7
8
9
10
11
12
13
Output
Cost Curves for a Firm
• Unit Costs
–
–
–
–
AFC falls
continuously
When MC < AVC or
MC < ATC, AVC &
ATC decrease
When MC > AVC or
MC > ATC, AVC &
ATC increase
When MC = AVC =
ATC then AVC and
ATC are at minimum
Cost
($ per
unit)
100
MC
75
50
ATC
AVC
25
AFC
0
1
2
3
4
5
6
7
8
Output (units/yr.)
9
10
11
PRODUCING A GIVEN OUTPUT AT
MINIMUM COST
Capital
per
year
Q1 is an isoquant
for output Q1.
Isocost curve C0 shows
all combinations of K and L
that cost C0.
K2
Isocost C2 shows quantity
Q1 can be produced with
combination K2L2 or K3L3.
However, both of these
are higher cost combinations
than K1L1.
CO C1 C2 are
three
isocost lines
A
K1
Q1
K3
C0
L2
L1
C1
L3
C2
Labor per year
THE INFLEXIBILITY OF SHORTRUN PRODUCTION
Capital
per
year
E
The long-run expansion
path is drawn as before..
C
Long-Run
Expansion Path
A
K2
Short-Run
Expansion Path
P
K1
Q2
Q1
L1
L2
B
L3
D
F
Labor per year
RETURNS TO SCALE
–
–
–
Constant Returns to Scale
• If input is doubled, output will double and
average cost is constant at all levels of
output.
Increasing Returns to Scale
• If input is doubled, output will more than
double and average cost decreases at all
levels of output.
Decreasing Returns to Scale
• If input is doubled, the increase in output
is less than twice as large and average
cost increases with output.
LONG-RUN AVERAGE AND
MARGINAL COST
Cost
($ per unit
of output
LMC
LAC
A
Output
ECONOMIES AND DISECONOMIES
OF SCALE
• Measuring Economies of Scale
Ec  ( C / C ) /( Q / Q )
Ec  ( C / Q ) /(C / Q )  MC/AC
• Therefore, the following is true:
– EC < 1: MC < AC
• economies of scale
– EC = 1: MC = AC
• constant economies of scale
– EC > 1: MC > AC
• diseconomies of scale
LONG-RUN COST WITH CONSTANT
RETURNS TO SCALE
Cost
($ per unit
of output)
With many plant sizes with minimum SAC = $10
the LAC = LMC and is a straight line
SAC1
SAC2
SMC1
SMC2
SAC3
SMC3
LAC =
LMC
$10
Q1
Q2
Q3
Output
LONG-RUN COST WITH ECONOMIES
AND DISECONOMIES OF SCALE
Cost
($ per unit
of output
SAC1
$10
The long-run
$8
cost curve is the
dark blue
portion of the
SAC curve which
represents the
minimum cost
for any level of
output, assuming
only three
discrete plant
sizes.
The long-run average cost curve is the
envelope of the firm’s short-run average
cost curves, assuming continually variable SAC3
plant size.
SAC2
A
LAC
B
SMC1
SMC3
LMC
SMC2
Q1
If the output is Q1 a manager
would chose the small plant
SAC1 and SAC $8.
Point B is on the LAC because
it is a least cost plant for a
given output.
Output
ECONOMIES OF SCOPE
• Economies of scope exist when the joint
output of a single firm is greater than the
output that could be achieved by two
different firms each producing a single
output.
–
–
Firms must choose how much of each to
produce.
The alternative combinations can be illustrated
using product transformation curves.
PRODUCT TRANSFORMATION CURVE
Each curve shows
combinations of output
with a given combination
of L & K.
Number
of tractors
O2
O1
O1 illustrates a low level
of output. O2 illustrates
a higher level of output with
two times as much labor
and capital.
Number of cars
ECONOMIES OF SCOPE
• The degree of economies of scope measures the
savings in cost and can be written:
C(Q1)  C (Q 2)  C (Q1, Q 2)
SC 
C (Q1, Q 2)
–
–
–
–
–
C(Q1) is the cost of producing Q1
C(Q2) is the cost of producing Q2
C(Q1Q2) is the joint cost of producing both
products
If SC > 0 -- Economies of scope
If SC < 0 -- Diseconomies of scope
DYNAMIC CHANGES IN COSTS –
THE LEARNING CURVE (optional)
• The learning curve measures the
impact of worker’s experience on the
costs of production.
• It describes the relationship
between a firm’s cumulative output
and amount of inputs needed to
produce a unit of output.
DYNAMIC CHANGES IN COSTS –THE
LEARNING CURVE (optional)
• The learning curve in the figure is
based on the relationship:
L  A  BN

N  cumulative units of output produced
L  labor input per unit of output
A, B and  are constants
A & B are positive and  is between 0 and 1
DYNAMIC CHANGES IN COSTS –THE
LEARNING CURVE (optional)
If N  1 :
•
–
L equals A + B and this measures labor
input to produce the first unit of output
If   0 :
•
–
Labor input remains constant as the
cumulative level of output increases, so
there is no learning
DYNAMIC CHANGES IN COSTS –
THE LEARNING CURVE (optional)
• If   0 and N increases :
–
L approaches A, and A represent
minimum labor input/unit of output
after all learning has taken place.
• The larger  :
–
The more important the learning
effect.
DYNAMIC CHANGES IN COSTS –THE
LEARNING CURVE (optional)
The chart shows a sharp drop
in lots to a cumulative amount of
20, then small savings at
higher levels.
Hours of labor
per machine lot
10
8
Doubling cumulative output causes
a 20% reduction in the difference
between the input required and
minimum attainable input requirement.
6
4
  0.31
2
0
10
20
30
40
50
Cumulative number of
machine lots produced
ECONOMIES OF SCALE VERSUS
LEARNING (optional)
Cost
($ per unit
of output)
Economies of Scale
A
B
Learning
C
LAC1
LAC2
Output