The Theory of the Firm
Meaning of function
 The word function is derived from mathematics. It
establishes the relationship between two variables. It
explains the extent to which one variable depends
upon another. For example demand and price ,output
and input, expenditure and income.
Production Function
Meaning of Production Function
 Production function analyses the physical relationship
between input and output.
 Production function means functional relationship
between physical inputs of factors of production and
physical output of a firm. It indicates maximum rate of
output that can be obtained from different combinations of
productive factors during a certain period of time and for a
given state of technical knowledge.
 “The production function is a technical or engineering
relationship between output and input. As long as the
natural laws of technology remain unchanged, the
production function remains unchanged.”
Prof. L.R.Klein
Production Function
 States the relationship between inputs and outputs
 Inputs – the factors of production classified as:
 Land – all natural resources of the earth

Price paid to acquire land = Rent
 Labour – all physical and mental human effort involved in
production

Price paid to labour = Wages
 Capital – buildings, machinery and equipment
not used for its own sake but for the contribution
it makes to production

Price paid for capital = Interest
Production Function
 Mathematical representation
of the relationship:
 Q = f (K, L, La)
 Output (Q) is dependent upon the amount of capital
(K), Land (L) and Labour (La) used
Production Function
Inputs
Process
Land
Labour
Capital
Product or
service
generated
– value added
Output
Characteristics
 It establishes relationship between physical quantities
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of output and inputs
This is an engineering problem
No change in technology
Production function should be considered with a
particular period of time
Inputs can be easily substituted
It can be related to short period or long period
Divisibility or indivisibility of factor should be taken
into account.
Kinds of production function
 One variable and two variable production function
 Production function for a firm and for an industry
 Short run and long run PF
 Homogeneous and Heterogeneous PF
PF= production function
Analysis of Production Function:
Short Run
 In the short run only one or two factors can be changed by
keeping other factors constant.
 Reflects ways in which firms respond to changes in output
(demand)
 Can increase output up to a certain level.
 It is associated with law of variable proportions.
Analysing the Production Function: Long
Run
 The long run is defined as the period of time taken to vary all factors of
production
 By doing this, the firm is able to increase its total capacity – not just
short term capacity
 Associated with a change in the scale of production
 The period of time varies according to the firm
and the industry
 In electricity supply, the time taken to build new capacity could be
many years; for a market stall holder, the ‘long run’ could be as little as
a few weeks or months!
Analysis of Production Function:
Long Run
In the long run, the firm can change all its factors of production thus
increasing its total capacity. In this example it has doubled its capacity.
 The Production function expresses a functional
relationship between quantities of raw materials and
output. It shows how and to what extent output changes
with variations in raw materials during a specified period.
In the words of Stigler “The production function is the
name given to the relationship between rates of input of
productive services and the rate of output of product. It is
economist’s summary of technical knowledge.” It is
expressed as follows.
__
Q =F (L,M,N,C,T), where Q stands for the output of a good
per
Unit of time, L for labour, M__ for management of
organisation, N for land or natural resources, C for Capital
and T for given technology and F refers to the functional
relationship.
Basic concepts related to
production or law of returns
 Short run
 Long run
 Fixed factors
 Variable factors
 Levels of production
 Scale of production
Total product, Average Product and
Marginal
Product
 The total product of a factor identifies the
total volume of goods produced by a given
amount of factors of production during a
certain period. This can be displayed in
either a chart that lists the output level
corresponding to various levels of input,
or a graph that summarizes the data into
a “total product curve”. The diagram
shows a typical total product curve. In
this example, output increases as more
inputs are employed up until point A. The
maximum output possible with this
production process is Qm. If units of
input are increased after this point, TP
starts to decrease.
Average and Marginal product
 The average physical product is the total production
divided by the number of units of variable input
employed. It is the output of each unit of input. If
there are 10 employees working on a production
process that manufactures 50 units per day, then the
average product of variable labour input is 5 units per
day.
 The marginal physical product of a variable input is
the change in total output due to a one unit change in
the variable input.
Average and Marginal Physical
Product Curves
Mutual relationship between TP,
AP and MP
 As the quantity of variable factor of production is
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increased, TP also increased
TP is maximum when MP is zero.
TP and AP never can be zero
If the quantity of variable factors of production is
increased after MP has become Zero, it will not
increase TP rather it will start to decline.
At the initial stage TP increases at increasing rate and
at the ultimate stage TP increases at a diminishing
rate.
Laws of returns or Law of Variable of
Proportions
 Production of a commodity is the result of combined
efforts of various factors of production. These factors
of production can be classified as fixed and variable
factors. To increase the quantity of production,
quantity of the factors of production will have to be
increased. But the increase in production in response
to a given increase in factor of production is not always
same. Such behavior if production is explained by
Laws of Returns.
 If one input is variable and all other raw materials are
fixed the concern’s production function exhibits the
law of variable proportions. If the number of units of a
variable factor is increased, keeping other factors
constant, how output changes is the concern of this
law. As per Leftwich “The law of variable proportions
states that if a variable quantity of one resource is
applied to a fixed amount of other input, output per
unit of variable input will increase but beyond some
point the resulting increases will be less and less with
total output reaching a maximum before it finally
begins to decline.”
This law is based on the below postulations.
Postulations
 It is feasible to alter the proportions in which the a
range of factors are collective
 Only one factor is erratic while others are held
invariable
 All units of the changeable factor are standardized
 There is no variation in expertise
 It presumes a short run condition
 The produce is calculated in physical units, in
quintals, tons etc.
 The price of the produce is specified invariable
Types of laws of returns
 Prof. Marshall propounded three types of laws of
returns Law of increasing returns
 Law of constant returns
 Law of diminishing returns
Law of increasing returns
 When increase in output is in greater proportion
than increase in input, it is known as law of
increasing returns. In other words –
 When proportionate change in production is more
than the proportionate change in the quantity of
variable factors of production by keeping the fixed
factors constant, it is called the law of increasing
returns.
Units of
TP
AP
MP
labour
1
10
10
10
2
24
12
14
3
45
15
21
4
68
17
23
5
95
19
27
Causes to apply laws of increasing
returns
 Economies of division of labor and specialization
 Saving of time and improvement in the technique of
production
 Economies of the use of Specialized Machinery
 Economies of Buying and Selling
Law of constant returns
 Law of constant returns states the situation when
increase in production is just equal to the increase in
input so, AP and MP remain constant.
Units of
labour
TP
AP
MP
1
10
10
10
2
20
10
10
3
30
10
10
4
40
10
10
5
50
10
10
Law of diminishing returns
 Law of diminishing returns occupies an important place
in economic theory. This law explains the stage of
production in which the quantity of one input of
production is increased with a fixed quantity of other
inputs and the resulting increase in production decreases
after a certain point
 Law of diminishing returns states the situation when
increase in production is less than increase in input so,
AP and MP will eventually decline.
Law of diminishing returns
Units of
labour
TP
AP
MP
1
10
10
10
2
19
9.5
9
3
27
9
8
4
33
8
6
5
37
7.4
4
Assumptions
 Technology remains same
 Organizational structure and managerial efficiency of the firm
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remain unchanged
It is also assumed that there are some inputs which quantity may
be kept fixed and the quantity of other inputs may be changed,
as required. This law will not apply if all the factors of
production are proportionately changed.
All the units of variable factors are homogenous
This law is related to the physical quantity not with its value
It is essential for the operation of this law that the optimum
combination of resources of production must have already been
achieved because this law applies only after this stage.
Causes of the operation
 Fixity of one or more factors of production
 Scarcity of productive resources
 Going beyond the optimum combination
 Factors of production are not perfect substitute for one
another
Significance
 Universal application
 Base of Malthusian population theory
 Base of Marginal Productivity Theory
 Base of Determination of Standard of living
 Responsible for migration of population
Explanation
of
the
Law
 To explain this law more clearly, let us construct a
sketch.
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The TP curve first rises at an enhancing rate upto point A where its slope is
highest. From point A upwards, the total product increases at a diminishing
rate till it reaches its highest point C and then is starts falling. Point A where
the tangent touches the TP curve is called the inflection point upto which the
total product increases at an increasing rate and from where it starts increasing
at a diminishing rate.
The average product curve AP and the marginal product curve MP also
raise with TP. The MP curve reaches its maximum point D when the slope of
the TP curve is the maximum at point A.
The maximum point on the AP curve is E where it coincides with the
MP curve. This point also coincides with point B on the TP curve from where
the total product starts a gradual rise.
When the TP curve reaches its maximum point C, the MP curve
becomes zero at point F. When the TP starts declining the MP curve becomes
negative, i.e. is below X axis.
The rising, the falling and the negative phases of the total, marginal and
average products are in fact the different stages of the law of variable
proportions which are discussed below.