Description
It explains theory of production which lays foundation for theory of supply.
THEORY OF
PRODUCTION
? Production theory forms the foundation for
the theory of supply
? Managerial decision making involves four
types of production decisions:
1. Whether to produce or to shut down
2. How much output to produce
3. What input combination to use
4. What type of technology to use
? Production involves transformation of
inputs such as capital, equipment, labor,
and land into output - goods and services
?Production theory can be divided into
short run theory or long run theory.
Long run and short run:
? The Long Run is distinguished from the short
run by being a period of time long enough for
all inputs, or factors of production, to be
variable as far as an individual firm is
concerned
? The Short Run, on the other hand, is a period
so brief that the amount of at least one input
is fixed
? The length of time necessary for all inputs to
be variable may differ according to the nature
of the industry and the structure of a firm
Production Function
A production function is a table or a mathematical
equation showing the maximum amount of output
that can be produced from any specified set of
inputs, given the existing technology. The total
product curve for different technology is given
below.
x
Q
Q = output
x = inputs
Production Function continued
Q = f(X
1
, X
2
, …, X
k
)
where
Q = output
X
1
, …, X
k
= inputs
For our current analysis, let’s reduce the
inputs to two, capital (K) and labor (L):
Q = f(L, K)
DEFINITIONS:
? In the short run, capital is held constant.
? Average product is total product divided by
the number of units of the input
? Marginal product is the addition to total
product attributable to one unit of variable
input to the production process fixed input
remaining unchanged.
? MP = TP
N
– TP
N-1
Short run
labour Total product Average
product
Marginal
product
1 10 10 10
2 24 12 14
3 39 13 15
4 52 13 13
5 61 12.2 9
6 66 11 5
7 66 9.4 0
8 64 8 -2
Marginal and Average product:
? Marginal product at any point is the slope of
the total product curve
? Average product is the slope of the line
joining the point on the total product curve to
the origin.
? When Average product is maximum, the
slope of the line joining the point to the origin
is also tangent to it.
P: Maximum Average Product
Q & R : Same Average Product
? Both AP and MP first rise, reach a maximum
and then fall.
? MP = AP when AP is maximum.
? MP may be negative if Variable input is used
too intensively.
?Law of diminishing marginal
productivity states that in the short run if
one input is fixed, the marginal product of the
variable input eventually starts falling
Law of Diminishing Returns
(Diminishing Marginal Product)
Holding all factors constant except one, the law of
diminishing returns says that:
? As additional units of a variable input are
combined with a fixed input, at some point the
additional output (i.e., marginal product) starts to
diminish
? e.g. trying to increase labor input without also
increasing capital will bring diminishing returns
Three stages of production:
? Stage 1: Till average product becomes
maximum
? Stage 2: till MP =zero
? Stage 3: MP is negative
Three Stages of Production in Short
Run
AP,MP
X
Stage I
Stage II
Stage III
AP
X
MP
X
Long run production:
? Section 2:
Production in the Long-Run
? All inputs are now considered to be variable
(both L and K in our case)
? How to determine the optimal combination of
inputs?
To illustrate this case we will use production
isoquants.
An isoquant is a curve showing all possible
combinations of inputs physically capable of
producing a given fixed level of output.
fig
Units
of K
40
20
10
6
4
Units
of L
5
12
20
30
50
Point on
diagram
a
b
c
d
e
a
Units of labour (L)
U
n
i
t
s
o
f
c
a
p
i
t
a
l
(
K
)
An isoquant
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
b
c
d
Isoquants and the Production Function
? Isoquant is a curve that shows the various
combinations of two inputs that will produce a given
level of output
? Slope of an isoquant indicates the rate at which
factors K and L can be substituted for each other while
a constant level of production is maintained.
? The slope is called Marginal Rate of Technical
Substitution (MRTS)
Properties of Isoquants
? There is a different isoquant for every output rate
the firm could possibly produce with isoquants
farther from the origin indicating higher rates of
output
? Along a given isoquant, the quantity of labor
employed is inversely related to the quantity of
capital employed ? isoquants have negative
slopes
Properties of Isoquants
? Isoquants do not intersect. Since each isoquant
refers to a specific rate of output, an intersection
would indicate that the same combination of
resources could, with equal efficiency, produce
two different amounts of output
? Isoquants are usually convex to the origin ? any
isoquant gets flatter as we move down along the
curve
Substitutability of Inputs
? Three general types of shapes that an
isoquant might have are:
• The isoquants are right angles, indicating
that inputs a and b must be used in fixed
proportions and therefore are not
substitutable
e.g Yeast and flour for a specific type of bread
Substitutability of Inputs
b) Perfect Substitutes – in this case input a can be
substituted for input b at a fixed rate as indicated by
the straight line isoquants (which have a constant
slope and MRS)
Ie. Honey and brown sugar are often nearly perfect
substitutes, Natural gas and fuel oil are close
substitutes in energy production
Isoquant Maps for Perfect Substitutes
and Perfect Complements
Substitutability of Inputs
c) Imperfect Substitutes – and the rate at which input b
can be given up in return for one more unit of input a
while maintaining the same level of output (the MRS)
diminished as the amount of input a being used
increases
Ie. In farming, harvestors and labour for harvesting
grain provide an example of a diminishing MRS, and
in general capital and labour are imperfect
substitutes.
The Marginal Rate
of Technical Substitution
Marginal Rate of Technical Substitution
? The absolute value of the slope of the isoquant is
the marginal rate of technical substitution, MRTS,
between two resources
? Thus, the MRTS is the rate at which labor
substitutes for capital without affecting output ?
when much capital and little labor are used, the
marginal productivity of labor is relatively great and
the marginal productivity of capital relatively small
? one unit of labor will substitute for a relatively
large amount of capital
Law of Diminishing Marginal
Rate of Technical Substitution:
Table 7.8 Input Combinations
for Isoquant Q = 52
Combination L K
A 6 2
B 4 3
C 3 4
D 2 6
E 2 8
AL AK MRTS
-2 1 2
-1 1 1
-1 2 1/2
0 2
Marginal Rate of Technical Substitution
? If labor and capital were perfect substitutes in
production, the rate at which labor substituted for
capital would remain fixed along the isoquant ?
the isoquant would be a downward sloping
straight line
? Summary
? Isoquants farther from the origin represent higher
rates of output
? Isoquants slope downward
? Isoquants never intersect
? Isoquants are bowed toward the origin
Marginal Rate of Technical Substitution
? Anywhere along the isoquant, the marginal rate of
technical substitution of labor for capital equals
the marginal product of labor divided by the
marginal product of capital, which also equals the
absolute value of the slope of the isoquant
? MRTS = MP
L
/ MP
C
Isocost Lines
? Isocost lines show different combinations of
inputs which give the same cost
? At the point where the isocost line meets the
vertical axis, the quantity of capital that can be
purchased equals the total cost divided by the
monthly cost of a unit of capital ? TC / r
? Where the isocost line meets the horizontal axis,
the quantity of labor that can be purchased
equals the total cost divided by the monthly cost
of a unit of labor ? TC / w
? The slope of the isocost line is given by
? Slope of isocost line = -(TC/r)/(TC/w) = -w/r
Choice of Input Combinations
? The profit maximizing firm wants to produce its
chosen output at the minimum cost ? it tries to
find the isocost closest to the origin that still
touches the chosen isoquant.
Isocost Line - is a line that shows the various
combinations of two inputs that can be bought for a
given dollar cost.
The equation for an isocost line is:
C = P
L
+ P
K
Maximizing Output for a given cost
r
w
MP
MP
MRTS
K
L
LK
= =
Minimizing Cost subject to given Output
Expansion Path
? If we imagine a set of isoquants representing
each possible rate of output, and given the
relative cost of resources, we can then draw
isocost lines to determine the optimal
combination of resources for producing each rate
of output
? Expansion Path leads to Total Cost Curve
? An expansion path is a long-run concept
(because all inputs can change)
? Each point on the expansion path
represents a cost-minimizing combination
of inputs
? Given input prices, each point represents
a total cost of producing a given level of
output when the entrepreneur can choose
any input combination he or she want
Expansion Path
? If the relative prices of resources change, the
least-cost resource combination will also change
? the firm’s expansion path will change
? For example, if the price of labor increases,
capital becomes relatively less expensive ? the
efficient production of any given rate of output
will therefore call for less labor and more capital
Returns to Scale
? Is large scale production more efficient than
small scale production for a certain market?
? Is a market better served by many small
firms or a few large ones?
? The returns to scale concept describes the
relationship between scale and efficiency.
Returns to Scale
? The returns to scale concept is an inherently
long run concept.
? Increasing returns to scale : a production
function for which any given proportional
change in all inputs leads to a more than
proportional change in output.
Returns to Scale
? Constant returns to scale : a production function for
which a proportional change in all inputs causes
output to change by the same proportion.
? Decreasing returns to scale : a production function for
which a proportional change in all inputs causes a
less than proportional change in output.
The Distinction between Diminishing
Returns and Decreasing Returns to
Scale
? Diminishing returns to scale is a short run
concept that refers to the case in which one
input varies while all others are held fixed.
? Decreasing returns to scale is a long run
concept that refers to the case in which all
inputs are varied by the same proportion.
fig
0
1
2
3
4
0 1 2 3
U
n
i
t
s
o
f
c
a
p
i
t
a
l
(
K
)
Units of labour (L)
200
300
400
500
600
a
b
c
R
Constant returns to scale
fig
0
1
2
3
4
0 1 2 3
U
n
i
t
s
o
f
c
a
p
i
t
a
l
(
K
)
Units of labour (L)
200
300
400
500
600
a
b
c
R
700
Increasing returns to scale (beyond
point b)
fig
0
1
2
3
4
0 1 2 3
U
n
i
t
s
o
f
c
a
p
i
t
a
l
(
K
)
Units of labour (L)
200
300
400
500
a
b
c
R
Decreasing returns to scale
(beyond point b)
Returns to Scale Shown on the Isoquant
Map
Economic Region of Production
? There are certain combinations of inputs that the firm
should not use in the long run no matter how cheap
they are (unless the firm is being paid to use them)
? These input combinations are represented by the
portion of an isoquant curve that has a positive slope
Economic Region of Production
? A positive sloped isoquant means that merely to
maintain the same level of production, the firm must
use more of both inputs if it increases its use of one
of the inputs
? The marginal product of one input is negative, and
using more of that input would actually cause output
to fall unless more of the other input were also
employed.
Economic Region of Production
? Ridge Lines – are lines connecting the points where
the marginal product of an input is equal to zero in
the isoquant map and forming the boundary for the
economic region of production
? Economic Region of Production – is the range in
an isoquant diagram where both inputs have a
positive marginal product. It lies inside the ridge lines
Homogeneous Production function:
? If both factors of production are increased by
proportion ?, and if new level of output Q*
can be expressed as a function of ? to any
power v, and the initial output ,
i.e. Q* = ?
V
Q
then the function is homogeneous and v is the
degree of homogeneity.
For example , check the function Q = 4L+3K
2
? If the production function is homogeneous ,
the expansion path is a straight line.
? Check the homogeneity of the following
functions:
? Q = 4L +3K
? Q= 4KL
? Q =4KL+K
A simple production function is the
Cobb-Douglas form
? Three parameters: A, o, and |
? The Cobb-Douglas production function has
CRS if o+|=1
? The Cobb-Douglas production function has
increasing (decreasing) returns to scale if
o+|>(<)1
? If o=|=½, we have the square root production
function
q A L K
o |
= ·
ISOCLINE:
? An isocline is a locus of points along which
MRTS is constant.
? An expansion path is also an isocline.
? An isocline is a straight line if the production
function is homogeneous
Cobb – Douglas Production Function:
? Q =AK
?
L
?
If
?
+
? =
1 , we have CRS
> 1 , we have IRS
< 1, we have DRS
Check Q = L
2
K
2
doc_667027364.ppt
It explains theory of production which lays foundation for theory of supply.
THEORY OF
PRODUCTION
? Production theory forms the foundation for
the theory of supply
? Managerial decision making involves four
types of production decisions:
1. Whether to produce or to shut down
2. How much output to produce
3. What input combination to use
4. What type of technology to use
? Production involves transformation of
inputs such as capital, equipment, labor,
and land into output - goods and services
?Production theory can be divided into
short run theory or long run theory.
Long run and short run:
? The Long Run is distinguished from the short
run by being a period of time long enough for
all inputs, or factors of production, to be
variable as far as an individual firm is
concerned
? The Short Run, on the other hand, is a period
so brief that the amount of at least one input
is fixed
? The length of time necessary for all inputs to
be variable may differ according to the nature
of the industry and the structure of a firm
Production Function
A production function is a table or a mathematical
equation showing the maximum amount of output
that can be produced from any specified set of
inputs, given the existing technology. The total
product curve for different technology is given
below.
x
Q
Q = output
x = inputs
Production Function continued
Q = f(X
1
, X
2
, …, X
k
)
where
Q = output
X
1
, …, X
k
= inputs
For our current analysis, let’s reduce the
inputs to two, capital (K) and labor (L):
Q = f(L, K)
DEFINITIONS:
? In the short run, capital is held constant.
? Average product is total product divided by
the number of units of the input
? Marginal product is the addition to total
product attributable to one unit of variable
input to the production process fixed input
remaining unchanged.
? MP = TP
N
– TP
N-1
Short run
labour Total product Average
product
Marginal
product
1 10 10 10
2 24 12 14
3 39 13 15
4 52 13 13
5 61 12.2 9
6 66 11 5
7 66 9.4 0
8 64 8 -2
Marginal and Average product:
? Marginal product at any point is the slope of
the total product curve
? Average product is the slope of the line
joining the point on the total product curve to
the origin.
? When Average product is maximum, the
slope of the line joining the point to the origin
is also tangent to it.
P: Maximum Average Product
Q & R : Same Average Product
? Both AP and MP first rise, reach a maximum
and then fall.
? MP = AP when AP is maximum.
? MP may be negative if Variable input is used
too intensively.
?Law of diminishing marginal
productivity states that in the short run if
one input is fixed, the marginal product of the
variable input eventually starts falling
Law of Diminishing Returns
(Diminishing Marginal Product)
Holding all factors constant except one, the law of
diminishing returns says that:
? As additional units of a variable input are
combined with a fixed input, at some point the
additional output (i.e., marginal product) starts to
diminish
? e.g. trying to increase labor input without also
increasing capital will bring diminishing returns
Three stages of production:
? Stage 1: Till average product becomes
maximum
? Stage 2: till MP =zero
? Stage 3: MP is negative
Three Stages of Production in Short
Run
AP,MP
X
Stage I
Stage II
Stage III
AP
X
MP
X
Long run production:
? Section 2:
Production in the Long-Run
? All inputs are now considered to be variable
(both L and K in our case)
? How to determine the optimal combination of
inputs?
To illustrate this case we will use production
isoquants.
An isoquant is a curve showing all possible
combinations of inputs physically capable of
producing a given fixed level of output.
fig
Units
of K
40
20
10
6
4
Units
of L
5
12
20
30
50
Point on
diagram
a
b
c
d
e
a
Units of labour (L)
U
n
i
t
s
o
f
c
a
p
i
t
a
l
(
K
)
An isoquant
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
b
c
d
Isoquants and the Production Function
? Isoquant is a curve that shows the various
combinations of two inputs that will produce a given
level of output
? Slope of an isoquant indicates the rate at which
factors K and L can be substituted for each other while
a constant level of production is maintained.
? The slope is called Marginal Rate of Technical
Substitution (MRTS)
Properties of Isoquants
? There is a different isoquant for every output rate
the firm could possibly produce with isoquants
farther from the origin indicating higher rates of
output
? Along a given isoquant, the quantity of labor
employed is inversely related to the quantity of
capital employed ? isoquants have negative
slopes
Properties of Isoquants
? Isoquants do not intersect. Since each isoquant
refers to a specific rate of output, an intersection
would indicate that the same combination of
resources could, with equal efficiency, produce
two different amounts of output
? Isoquants are usually convex to the origin ? any
isoquant gets flatter as we move down along the
curve
Substitutability of Inputs
? Three general types of shapes that an
isoquant might have are:
• The isoquants are right angles, indicating
that inputs a and b must be used in fixed
proportions and therefore are not
substitutable
e.g Yeast and flour for a specific type of bread
Substitutability of Inputs
b) Perfect Substitutes – in this case input a can be
substituted for input b at a fixed rate as indicated by
the straight line isoquants (which have a constant
slope and MRS)
Ie. Honey and brown sugar are often nearly perfect
substitutes, Natural gas and fuel oil are close
substitutes in energy production
Isoquant Maps for Perfect Substitutes
and Perfect Complements
Substitutability of Inputs
c) Imperfect Substitutes – and the rate at which input b
can be given up in return for one more unit of input a
while maintaining the same level of output (the MRS)
diminished as the amount of input a being used
increases
Ie. In farming, harvestors and labour for harvesting
grain provide an example of a diminishing MRS, and
in general capital and labour are imperfect
substitutes.
The Marginal Rate
of Technical Substitution
Marginal Rate of Technical Substitution
? The absolute value of the slope of the isoquant is
the marginal rate of technical substitution, MRTS,
between two resources
? Thus, the MRTS is the rate at which labor
substitutes for capital without affecting output ?
when much capital and little labor are used, the
marginal productivity of labor is relatively great and
the marginal productivity of capital relatively small
? one unit of labor will substitute for a relatively
large amount of capital
Law of Diminishing Marginal
Rate of Technical Substitution:
Table 7.8 Input Combinations
for Isoquant Q = 52
Combination L K
A 6 2
B 4 3
C 3 4
D 2 6
E 2 8
AL AK MRTS
-2 1 2
-1 1 1
-1 2 1/2
0 2
Marginal Rate of Technical Substitution
? If labor and capital were perfect substitutes in
production, the rate at which labor substituted for
capital would remain fixed along the isoquant ?
the isoquant would be a downward sloping
straight line
? Summary
? Isoquants farther from the origin represent higher
rates of output
? Isoquants slope downward
? Isoquants never intersect
? Isoquants are bowed toward the origin
Marginal Rate of Technical Substitution
? Anywhere along the isoquant, the marginal rate of
technical substitution of labor for capital equals
the marginal product of labor divided by the
marginal product of capital, which also equals the
absolute value of the slope of the isoquant
? MRTS = MP
L
/ MP
C
Isocost Lines
? Isocost lines show different combinations of
inputs which give the same cost
? At the point where the isocost line meets the
vertical axis, the quantity of capital that can be
purchased equals the total cost divided by the
monthly cost of a unit of capital ? TC / r
? Where the isocost line meets the horizontal axis,
the quantity of labor that can be purchased
equals the total cost divided by the monthly cost
of a unit of labor ? TC / w
? The slope of the isocost line is given by
? Slope of isocost line = -(TC/r)/(TC/w) = -w/r
Choice of Input Combinations
? The profit maximizing firm wants to produce its
chosen output at the minimum cost ? it tries to
find the isocost closest to the origin that still
touches the chosen isoquant.
Isocost Line - is a line that shows the various
combinations of two inputs that can be bought for a
given dollar cost.
The equation for an isocost line is:
C = P
L
+ P
K
Maximizing Output for a given cost
r
w
MP
MP
MRTS
K
L
LK
= =
Minimizing Cost subject to given Output
Expansion Path
? If we imagine a set of isoquants representing
each possible rate of output, and given the
relative cost of resources, we can then draw
isocost lines to determine the optimal
combination of resources for producing each rate
of output
? Expansion Path leads to Total Cost Curve
? An expansion path is a long-run concept
(because all inputs can change)
? Each point on the expansion path
represents a cost-minimizing combination
of inputs
? Given input prices, each point represents
a total cost of producing a given level of
output when the entrepreneur can choose
any input combination he or she want
Expansion Path
? If the relative prices of resources change, the
least-cost resource combination will also change
? the firm’s expansion path will change
? For example, if the price of labor increases,
capital becomes relatively less expensive ? the
efficient production of any given rate of output
will therefore call for less labor and more capital
Returns to Scale
? Is large scale production more efficient than
small scale production for a certain market?
? Is a market better served by many small
firms or a few large ones?
? The returns to scale concept describes the
relationship between scale and efficiency.
Returns to Scale
? The returns to scale concept is an inherently
long run concept.
? Increasing returns to scale : a production
function for which any given proportional
change in all inputs leads to a more than
proportional change in output.
Returns to Scale
? Constant returns to scale : a production function for
which a proportional change in all inputs causes
output to change by the same proportion.
? Decreasing returns to scale : a production function for
which a proportional change in all inputs causes a
less than proportional change in output.
The Distinction between Diminishing
Returns and Decreasing Returns to
Scale
? Diminishing returns to scale is a short run
concept that refers to the case in which one
input varies while all others are held fixed.
? Decreasing returns to scale is a long run
concept that refers to the case in which all
inputs are varied by the same proportion.
fig
0
1
2
3
4
0 1 2 3
U
n
i
t
s
o
f
c
a
p
i
t
a
l
(
K
)
Units of labour (L)
200
300
400
500
600
a
b
c
R
Constant returns to scale
fig
0
1
2
3
4
0 1 2 3
U
n
i
t
s
o
f
c
a
p
i
t
a
l
(
K
)
Units of labour (L)
200
300
400
500
600
a
b
c
R
700
Increasing returns to scale (beyond
point b)
fig
0
1
2
3
4
0 1 2 3
U
n
i
t
s
o
f
c
a
p
i
t
a
l
(
K
)
Units of labour (L)
200
300
400
500
a
b
c
R
Decreasing returns to scale
(beyond point b)
Returns to Scale Shown on the Isoquant
Map
Economic Region of Production
? There are certain combinations of inputs that the firm
should not use in the long run no matter how cheap
they are (unless the firm is being paid to use them)
? These input combinations are represented by the
portion of an isoquant curve that has a positive slope
Economic Region of Production
? A positive sloped isoquant means that merely to
maintain the same level of production, the firm must
use more of both inputs if it increases its use of one
of the inputs
? The marginal product of one input is negative, and
using more of that input would actually cause output
to fall unless more of the other input were also
employed.
Economic Region of Production
? Ridge Lines – are lines connecting the points where
the marginal product of an input is equal to zero in
the isoquant map and forming the boundary for the
economic region of production
? Economic Region of Production – is the range in
an isoquant diagram where both inputs have a
positive marginal product. It lies inside the ridge lines
Homogeneous Production function:
? If both factors of production are increased by
proportion ?, and if new level of output Q*
can be expressed as a function of ? to any
power v, and the initial output ,
i.e. Q* = ?
V
Q
then the function is homogeneous and v is the
degree of homogeneity.
For example , check the function Q = 4L+3K
2
? If the production function is homogeneous ,
the expansion path is a straight line.
? Check the homogeneity of the following
functions:
? Q = 4L +3K
? Q= 4KL
? Q =4KL+K
A simple production function is the
Cobb-Douglas form
? Three parameters: A, o, and |
? The Cobb-Douglas production function has
CRS if o+|=1
? The Cobb-Douglas production function has
increasing (decreasing) returns to scale if
o+|>(<)1
? If o=|=½, we have the square root production
function
q A L K
o |
= ·
ISOCLINE:
? An isocline is a locus of points along which
MRTS is constant.
? An expansion path is also an isocline.
? An isocline is a straight line if the production
function is homogeneous
Cobb – Douglas Production Function:
? Q =AK
?
L
?
If
?
+
? =
1 , we have CRS
> 1 , we have IRS
< 1, we have DRS
Check Q = L
2
K
2
doc_667027364.ppt