THEORY OF PRODUCTION1
The theory of production explains the physical—both technical and technological—
relationship between inputs—labour and capital—and output. The nature of
relationship between inputs and outputs is studied with the aid of production
function. However, the following definitions are made before looking at the
production function.
1. Definition of Terms
i. Meaning of production
The term production refers to a process by which a commodity (or commodities) are
converted or transformed into a different usable commodity. In other words,
production means transforming inputs, (labour, machines, and raw materials) into
output. This kind of production is called manufacturing. However, production does
not only refer to manufacturing activities. In the process of production, an input
may be intangible (service) and output may be intangible too. For example, in the
production of legal, medical, social and consultancy services both input and output
are intangible: lawyers, doctors, social workers, consultants, hairdressers, musicians,
are all engaged in productive activity.
ii. Input and output
An input is a good or service that goes into the process of production. Inputs have
been classified in economics as a) labour; (b) capital; (c) raw materials. These inputs
have been further classified as (i) fixed inputs and (ii) variable inputs. A fixed input
is one whose quantity cannot readily change during the period of time under
consideration such as e.g. plant, building, machinery, etc. is inelastic in the short run-
run, while a variable input is one whose quantity can be changed as the supply of such
inputs (as labour and raw materials) is elastic in the short run.
An output is any commodity or service that comes out of the production process.
1
The theory of production is the 4th topic in ECN 201, and the lecturer is Dr. C. O. Ibukun.
, iii. Short-run and Long-run
The short-run refers to a period of time in which the supply of certain inputs (e.g.,
plant building and machines, etc.,) is fixed or inelastic. In the short run, therefore,
production of a commodity can be increased by increasing the use of variable inputs,
like labour and raw materials. It is worth noting that the short-run does not refer
to any fixed time period. While in some industries it may be a matter of weeks or a
few months in some others (e.g., electric and power industry), it may mean three or
more years.
The long-run refers to a period of time in which the supply of all the inputs is elastic,
but not long enough to permit a change in technology. In the long run, therefore,
the production of a commodity can be increased by employing more of both variable
variables and fixed inputs.
The Very Long-period—economists use the very long run to refer to a period in which
the technology of production is subject to change. In the very long run, the
production function also changes. Technological advances mean that a larger output
can be created with a given quantity of inputs.
2. The Production Function
The tool of analysis used for explaining the input-output relationships is the
production function. The production function describes the technological
relationship between inputs and output in physical terms. It specifies the maximum
quantity of a commodity that can be produced per unit of time with given quantities
of inputs and technology. Besides, the production function represents the technology
of a firm, of an industry or, of the economy as a whole in a relevant case. The
production function can be presented in a table, a graph or an equation. The general
mathematical form of the production function is:
𝑄 = 𝑓(𝐾, 𝐿, 𝐷, 𝑅)
Where Q = Output
K= Capital input
,L = Labour input
D = Land Input, and
R = Raw materials
To make the derivation of economic principles easier, raw materials and labour input
are lumped together as capital; hence, the mathematical illustration of a production
function of a firm employing only two inputs—capital (K) and labour (L) to produce
output (Q)—is presented as follows:
𝑄 = 𝑓(𝐾, 𝐿)
The production function suggests that Q is the maximum output that can be
produced by the firm given its level of capital and labour. The increasing output will
necessitate increasing the quantities of capital and labour. Whether the firm can
increase both K and L or only L depends on the time period it tables into account for
increasing production, i.e. either short or long term. By definition, the supply of
capital is inelastic in the short-run and elastic in the long-run. In the short-run,
therefore, the firm can increase output by increasing only the labour, since the
supply of capital in the short-run is fixed. In the long run, however, the firm can
employ more of both capital and labour. Accordingly, the firm would have 2 types of
production functions:
i. Short-run production function—the study of the short-run production is
the subject matter of the law of diminishing returns which is also called
the law of variable proportions. This production period refers to when
output can only be increased by increasing the variable factor of
production.
ii. Long-run production function—this forms the subject matter of the law of
returns to scale. Generally, the terms constant and increasing returns are
used with reference to constant and increasing returns to scale.
, THE SHORT RUN PRODUCTION FUNCTION—SINGLE VARIABLE UNIT
There are three concepts that are normally used in the study of the short-run
production theory. These are (1) Total Product (2) Average Product and (3) Marginal
Product.
i. Total Product
The total product of an input (factor) is the amount of total output produced by a
given amount of the input (factor), other factors held constant. As the amount of a
factor increases, the total output increase. This can be illustrated with the aid of
the table below.
Units Total Marginal Product Average
of Product (KG) Product (KG)
Labour (KG)
L Q ∆𝑄 𝑄
∆𝐿 𝐿
1 80 80 80
2 170 90 85
3 270 100 90
4 368 98 92
5 430 62 86
6 480 50 80
7 504 24 72
8 504 0 63
9 495 -9 55
10 480 -15 48
From the above table, it can be seen that when with a fixed quantity of capital (K),
more units of labour are employed while total product increases at the beginning.
Thus, when one unit of labour is used with a given quantity of capital, 80 units of
output are produced. With two units of labour 170 units of output are produced, and
with three units of labour total product of labour increases to 270 units and so on.
After 8 units of employment of labour total output declines with further increase in
labour input. But the rate of increase in a total product varies at different levels
The theory of production explains the physical—both technical and technological—
relationship between inputs—labour and capital—and output. The nature of
relationship between inputs and outputs is studied with the aid of production
function. However, the following definitions are made before looking at the
production function.
1. Definition of Terms
i. Meaning of production
The term production refers to a process by which a commodity (or commodities) are
converted or transformed into a different usable commodity. In other words,
production means transforming inputs, (labour, machines, and raw materials) into
output. This kind of production is called manufacturing. However, production does
not only refer to manufacturing activities. In the process of production, an input
may be intangible (service) and output may be intangible too. For example, in the
production of legal, medical, social and consultancy services both input and output
are intangible: lawyers, doctors, social workers, consultants, hairdressers, musicians,
are all engaged in productive activity.
ii. Input and output
An input is a good or service that goes into the process of production. Inputs have
been classified in economics as a) labour; (b) capital; (c) raw materials. These inputs
have been further classified as (i) fixed inputs and (ii) variable inputs. A fixed input
is one whose quantity cannot readily change during the period of time under
consideration such as e.g. plant, building, machinery, etc. is inelastic in the short run-
run, while a variable input is one whose quantity can be changed as the supply of such
inputs (as labour and raw materials) is elastic in the short run.
An output is any commodity or service that comes out of the production process.
1
The theory of production is the 4th topic in ECN 201, and the lecturer is Dr. C. O. Ibukun.
, iii. Short-run and Long-run
The short-run refers to a period of time in which the supply of certain inputs (e.g.,
plant building and machines, etc.,) is fixed or inelastic. In the short run, therefore,
production of a commodity can be increased by increasing the use of variable inputs,
like labour and raw materials. It is worth noting that the short-run does not refer
to any fixed time period. While in some industries it may be a matter of weeks or a
few months in some others (e.g., electric and power industry), it may mean three or
more years.
The long-run refers to a period of time in which the supply of all the inputs is elastic,
but not long enough to permit a change in technology. In the long run, therefore,
the production of a commodity can be increased by employing more of both variable
variables and fixed inputs.
The Very Long-period—economists use the very long run to refer to a period in which
the technology of production is subject to change. In the very long run, the
production function also changes. Technological advances mean that a larger output
can be created with a given quantity of inputs.
2. The Production Function
The tool of analysis used for explaining the input-output relationships is the
production function. The production function describes the technological
relationship between inputs and output in physical terms. It specifies the maximum
quantity of a commodity that can be produced per unit of time with given quantities
of inputs and technology. Besides, the production function represents the technology
of a firm, of an industry or, of the economy as a whole in a relevant case. The
production function can be presented in a table, a graph or an equation. The general
mathematical form of the production function is:
𝑄 = 𝑓(𝐾, 𝐿, 𝐷, 𝑅)
Where Q = Output
K= Capital input
,L = Labour input
D = Land Input, and
R = Raw materials
To make the derivation of economic principles easier, raw materials and labour input
are lumped together as capital; hence, the mathematical illustration of a production
function of a firm employing only two inputs—capital (K) and labour (L) to produce
output (Q)—is presented as follows:
𝑄 = 𝑓(𝐾, 𝐿)
The production function suggests that Q is the maximum output that can be
produced by the firm given its level of capital and labour. The increasing output will
necessitate increasing the quantities of capital and labour. Whether the firm can
increase both K and L or only L depends on the time period it tables into account for
increasing production, i.e. either short or long term. By definition, the supply of
capital is inelastic in the short-run and elastic in the long-run. In the short-run,
therefore, the firm can increase output by increasing only the labour, since the
supply of capital in the short-run is fixed. In the long run, however, the firm can
employ more of both capital and labour. Accordingly, the firm would have 2 types of
production functions:
i. Short-run production function—the study of the short-run production is
the subject matter of the law of diminishing returns which is also called
the law of variable proportions. This production period refers to when
output can only be increased by increasing the variable factor of
production.
ii. Long-run production function—this forms the subject matter of the law of
returns to scale. Generally, the terms constant and increasing returns are
used with reference to constant and increasing returns to scale.
, THE SHORT RUN PRODUCTION FUNCTION—SINGLE VARIABLE UNIT
There are three concepts that are normally used in the study of the short-run
production theory. These are (1) Total Product (2) Average Product and (3) Marginal
Product.
i. Total Product
The total product of an input (factor) is the amount of total output produced by a
given amount of the input (factor), other factors held constant. As the amount of a
factor increases, the total output increase. This can be illustrated with the aid of
the table below.
Units Total Marginal Product Average
of Product (KG) Product (KG)
Labour (KG)
L Q ∆𝑄 𝑄
∆𝐿 𝐿
1 80 80 80
2 170 90 85
3 270 100 90
4 368 98 92
5 430 62 86
6 480 50 80
7 504 24 72
8 504 0 63
9 495 -9 55
10 480 -15 48
From the above table, it can be seen that when with a fixed quantity of capital (K),
more units of labour are employed while total product increases at the beginning.
Thus, when one unit of labour is used with a given quantity of capital, 80 units of
output are produced. With two units of labour 170 units of output are produced, and
with three units of labour total product of labour increases to 270 units and so on.
After 8 units of employment of labour total output declines with further increase in
labour input. But the rate of increase in a total product varies at different levels
