Download Production function

Introduction to Economics
Theory of Production
Lecture#7
Theory of Production
• It deals with the supply side of the market
• It explains the behavior of the producers
• Shows how firms can produce efficiently, and how
cost of production changes with the change in input
prices and level of production
Factors of Production
• A factor of production is any aspect of environment
which has influence on production
• Economics classified the factors of production into
four broad categories
Labour
Consists of all
working people in
economy such as
carpenters
laborers, clerks
etc
Land
Consists of all
natural resources
like agricultural
plots , forests
water reserves
like rivers and
oceans etc
capital
Consists of all
produced means
of production like
machinery,
buildings etc
Organisation
Enterprises which
assumes the
responsibility of
risk
bearing,organising
the business
activity,
The Firm
• The firm may be defined as the business enterprise involved in
producing goods and services
• It is a technical unit in which inputs are converted into output
for sale to consumers, other business firms and government at
different levels
• The main objective of the firm is to maximize its profit which
may be defined as the difference between its revenue and its
costs
• Π=TR-TC
• Thus in order to maximize the profit, the firm will have to
make this difference as large as possible
Production Periods
• The short run is defined as a situation in which the
firm has at least one fixed factor of production. The
short run is such that the firm does not have sufficient
time to vary all its inputs
• The Long Run is the time period during which the
firm is able to vary all its factor inputs. There are no
fixed productive factors in long run
The production Function
• The Production function shows the maximum level
of output that can be produced from all specific
combinations of inputs, given the state of technology.
Alternative
Input
Combinations
Production
Function
Different
Quantities of
Output
The Short Run Production function
• If we assume that a firm uses capital (K) and labour (L) to
produce output(Q) Than the production function will be
• Q=F(K,L)
• It means production depends on capital and labour
• As one factor of production is fixed in short run, suppose
its capital than production function will be
• Q=f(L)
• It shows how output varies as units are labor are added to
fixed amount of capital its relationship will also be known
as law of variable propotions
Important Concepts
• Total Product
TP refers to the total output of the firm per period of
time.
• Marginal product=∆Q/ ∆L
MP is the change in total product resulting from using
an additional unit of variable factor
• Average Product= Q/ L
Average product is the total product divided by the
number of units of variable factor. This is simply
total output per unit of variable factor
Law of variable proportions
Units of
Labor
TP
Marginal Product Average
∆Q/ ∆L
product
Q/ L
1
10
10
10
2
25
15
12.5 Zone I
3
45
20
15
4
60
15
15 ZoneII
5
70
10
14
6
75
5
12.5
7
75
0
10.7
8
72
-3
9
9
63
-9
7
MP> AP
MP=AP
ZoneIII MP< AP
d
40
30
Total Product
c
Slope = TPP / L
= APP
20
TPP
Maximum
output
b
10
Number of workers (L)
0
Average and Marginal Products
0
1
2
4
5
6
7
8
b
14
12
3
Zone I
Zone II
10
Zone III
c
8
6
APL
4
2
d
0
-2
0
1
2
3
4
5
6
7
8
MPL
Number of
workers (L)
Relations between MP & AP
• When the marginal product is rising the total product increases
at the increasing rate till the point b
• When the marginal product is positive the total product is
increasing. As it means that every additional worker would
positively contribute in total output. TP is increasing till the
point d.
• When the marginal product is negative the total product falls.
It means every additional worker is negatively contributing in
total product
• When the marginal product is zero the TP neither rises nor
falls means reaches at its maximum. It is the point when seven
workers are being employed
Relations between MP & AP
• When MP is greater than AP, Average product
will rise till the four workers
• When marginal product is less than average
product, AP will fall after the employment of
fifth worker
• When MP=AP average product is at its
maximum
Three Stages/zones of production
• Stage 1 is characterized by rising APL. this is the stage of increasing
returns
• Stage 2 is characterized by the equal APL And MPL. It is known as
constant returns
• Stage 3 is characterized by the fall in both APL & MPL. This is known as
diminishing returns
• Analyzing this situation economists argue that first stage is not suitable for
production as total productivity is increasing and still has the more
potential to increase by using additional workers
• Third stage is also not suitable as its showing the diminishing returns duet o
decrease in total productivity
• Thus second zone is quite suitable for production as TP is maximum and
AP & MP are also equal here.
Long Run Production Function
• In LR both K and L are variable
• For LR production function we use ISO quant
curve and ISO cost line for analysis
• An Iso quant curve is the curve that shows the
various combinations of inputs that will
produce the same amount of output
An isoquant
45
a
40
35
Units
of K
40
20
10
6
4
Output
is I000
meter
clothes
Units of capital (K)
30
25
b
20
Units
of L
5
12
20
30
50
Point on
diagram
a
b
c
d
e
I000 meter
15
c
10
I000 meter
d
I000 meter
e
5
0
0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
ISO Quant Map
• ISO quant map contains infinite number of ISO
quant curves representing different level of
output.
• ISO quant record successively higher levels of
output, the farther away they are from the
origin.
• A typical ISO quant curve is convex to origin or
in northeasterly direction
An isoquant map
Units of capital (K)
30
20
10
I5
I4
I1
0
0
10
Units of labour (L)
I2
20
I3
Slope of ISO quant Curve
• The slope of ISO Quant curve is called the
Marginal Rate of Technical Substitution (MRTS).
• MRTS is the amount by which the quantity of one
input can be reduced when one more unit of
another input is added while holding the output
constant
• MRTS of labor for capital is the amount by which
the capital input can be reduced, holding the
output constant, while using one more unit of
labor
Marginal rate of Technical substitution
14
g
12
Units of capital (K)
DK = 2
MRTS = DK / DL
MRTS = 2
h
10
DL = 1
8
6
4
2
isoquant
0
0
2
4
6
8
10
12
Units of labour (L)
14
16
18
20
22
Diminishing MRTS
• Along any ISO quant the slope becomes flatter
and the MRTS diminishes
• When relatively large amount of capital is
used the producer will forgo less amount of
labor for production
Diminishing marginal rate of technical substitution
14
g
12
Units of capital (K)
DK = 2
MRTS = DK / DL
MRS = 2
h
10
DL = 1
8
j
DK = 1
6
MRS = 1
k
DL = 1
4
2
isoquant
0
0
2
4
6
8
10
12
Units of labour (L)
14
16
18
20
Production Functions---- Two Special cases
• Two extreme cases of production function shows the
possible range of input substitution in the production
process
• If the two inputs are perfect substitutes for each other
,here the MRTS is constant at all points than ISO will
be linear
• If one unit of output can be produced with fixed
proportion of inputs than the ISO quant curve will be
L-shaped
Returns to Scale
• Returns to scale is the rate at which output increases
as inputs are increased proportionately
• Increasing Returns to scale happens if output is more
than doubled , when inputs are doubled
• Constant returns to scale means output is doubled if
inputs are doubled
• Decreasing returns to scale applies when output is
less than doubled when inputs are doubled
ISO Cost line
• ISO cost line shows the budget constraint of
the producer
• ISO cost line shows the different combination
of two inputs that producer can purchase
within the given cost.
• The budget constraint of producer can be
shown as :LPL+ KPK=C
• The slope of Iso cost line is defined as price of
both inputs symbolized as w/r
An isocost
30
Assumptions
25
PK = £20 000
W = £10 000
TC = £300 000
Units of capital (K)
20
15
a
b
10
5
TC = £300 000
0
0
5
10
15
20
Units of labour (L)
25
30
35
40
Finding the maximum level of output
35
maximum
level of output will be there when highest ISO quant will touch the lowest
Iso cost line
30
Units of capital (K)
25
s
TC = £500 000
20
15
TC = £400 000
r
MRTS=w/r
10
t
5
TPP1
0
0
10
20
30
Units of labour (L)
40
50