Production Function
When most people think of a company's essential tasks, they first think of production. The
production function, an abstract way of expressing how the firm derives output from its
inputs, is how economists describe this process. It expresses the firm's technological
capabilities in mathematical terms. The production function refers to the technological link
between a company's inputs and outputs. The production function depicts the functional link
between a firm's physical inputs and physical outputs during the manufacturing process. To
quote Samuelson, "The production function is the Technical relationship telling the
maximum amount of output capable of being produced by each and every set of specified
inputs. It is defined for a given set of technical knowledge."
According to Stigler, "the production function is the name given to the relationship between
the rates of input of productive services and the rate of output of product. It is the economist's
summary of technical knowledge. The translation of inputs into outputs is known as
production. The factors of production, such as land, labour, and capital, as well as raw
materials and commercial services, are referred to as inputs.
The technology used determines how inputs are transformed into outputs. Only a small
number of inputs will result in a small number of outputs. The "production function" is the
relationship between the quantity of inputs and the greatest quantity of outputs generated.
But, as the input quantities change, how do these outputs change? Let's have a peek at a
production function in action. In general, we would allow for varying amounts of land, labour
and capital. However, in this example, labour will be the only input, for the sake of
simplicity.
The main theme of production function is to get the maximum production with the present
given set of variable.
For example, a firm can use the more labour and less machines OR it can use less labour and
more machines to get maximum production. Here which is suited best and how to find the
best substitute choice is the main aim of production function.
,In a general mathematical form, a production function can be expressed as:
Q= f(LB, L, K, M, , t)
Q=output/quantity
LB = Land & Buildings.
L = Labour.
K = capital.
M = raw material.
T= time.
Production Function as Graph
On a graph, any of these equations can be plotted. Under the premise of a single variable
input, the following graphic depicts a typical (quadratic) production function (or fixed ratios
of inputs so the can be treated as a single variable). All points above the production function
are technologically impossible, all points below are technically achievable, and all points on
the function represent the maximum amount of output possible at the particular level of input
utilisation. The production function rises from the origin to points A, B, and C, demonstrating
that when more units of input are employed, the amount of outputs rises as well. Beyond
point C, adding more input units provides no further outputs (in fact, total output begins to
drop); the variable input is being exploited too heavily. The company is suffering negative
returns on variable inputs and diminishing total returns due to an excessive use of variable
inputs in comparison to available fixed inputs. The falling production function beyond point
C and the negative marginal physical product curve (MPP) beyond point Z in the diagram
indicate this.
, The firm is witnessing growing returns to varied inputs from point A to point B. As more
inputs are used, the output increases at a faster rate. Both marginal physical product (MPP,
the production function's derivative) and average physical product (APP, the output to
variable input ratio) are increasing. As may be observed from the falling MPP curve beyond
point X, the inflection point A defines the point beyond which marginal returns drop. The
firm experiences positive but diminishing marginal returns to the variable input from point A
to point C. The output increases when more units of the input are used, albeit at a slower rate.
The dropping slope of the average physical product curve (APP) beyond point Y indicates
that there are diminishing average returns beyond point B. The average physical product is at
its greatest because Point B is tangent to the steepest ray from the origin. Beyond point B, the
marginal curve must be lower than the average curve due to mathematical necessity.
Short Run Production Function
In the short run, the technological conditions of production are rigid, resulting in set
proportions of the various inputs used to produce a certain output. In the near run, however,
increasing the quantity of one input while keeping the quantity of other inputs constant can
result in more output. The Law of Variable Proportions describes this element of the
production function. In the situation of two inputs, labour and capital, with capital being fixed
and labour being variable, the short run production function can be stated as:
Q = f (L, R)
Where K -refers to the fixed input.
When most people think of a company's essential tasks, they first think of production. The
production function, an abstract way of expressing how the firm derives output from its
inputs, is how economists describe this process. It expresses the firm's technological
capabilities in mathematical terms. The production function refers to the technological link
between a company's inputs and outputs. The production function depicts the functional link
between a firm's physical inputs and physical outputs during the manufacturing process. To
quote Samuelson, "The production function is the Technical relationship telling the
maximum amount of output capable of being produced by each and every set of specified
inputs. It is defined for a given set of technical knowledge."
According to Stigler, "the production function is the name given to the relationship between
the rates of input of productive services and the rate of output of product. It is the economist's
summary of technical knowledge. The translation of inputs into outputs is known as
production. The factors of production, such as land, labour, and capital, as well as raw
materials and commercial services, are referred to as inputs.
The technology used determines how inputs are transformed into outputs. Only a small
number of inputs will result in a small number of outputs. The "production function" is the
relationship between the quantity of inputs and the greatest quantity of outputs generated.
But, as the input quantities change, how do these outputs change? Let's have a peek at a
production function in action. In general, we would allow for varying amounts of land, labour
and capital. However, in this example, labour will be the only input, for the sake of
simplicity.
The main theme of production function is to get the maximum production with the present
given set of variable.
For example, a firm can use the more labour and less machines OR it can use less labour and
more machines to get maximum production. Here which is suited best and how to find the
best substitute choice is the main aim of production function.
,In a general mathematical form, a production function can be expressed as:
Q= f(LB, L, K, M, , t)
Q=output/quantity
LB = Land & Buildings.
L = Labour.
K = capital.
M = raw material.
T= time.
Production Function as Graph
On a graph, any of these equations can be plotted. Under the premise of a single variable
input, the following graphic depicts a typical (quadratic) production function (or fixed ratios
of inputs so the can be treated as a single variable). All points above the production function
are technologically impossible, all points below are technically achievable, and all points on
the function represent the maximum amount of output possible at the particular level of input
utilisation. The production function rises from the origin to points A, B, and C, demonstrating
that when more units of input are employed, the amount of outputs rises as well. Beyond
point C, adding more input units provides no further outputs (in fact, total output begins to
drop); the variable input is being exploited too heavily. The company is suffering negative
returns on variable inputs and diminishing total returns due to an excessive use of variable
inputs in comparison to available fixed inputs. The falling production function beyond point
C and the negative marginal physical product curve (MPP) beyond point Z in the diagram
indicate this.
, The firm is witnessing growing returns to varied inputs from point A to point B. As more
inputs are used, the output increases at a faster rate. Both marginal physical product (MPP,
the production function's derivative) and average physical product (APP, the output to
variable input ratio) are increasing. As may be observed from the falling MPP curve beyond
point X, the inflection point A defines the point beyond which marginal returns drop. The
firm experiences positive but diminishing marginal returns to the variable input from point A
to point C. The output increases when more units of the input are used, albeit at a slower rate.
The dropping slope of the average physical product curve (APP) beyond point Y indicates
that there are diminishing average returns beyond point B. The average physical product is at
its greatest because Point B is tangent to the steepest ray from the origin. Beyond point B, the
marginal curve must be lower than the average curve due to mathematical necessity.
Short Run Production Function
In the short run, the technological conditions of production are rigid, resulting in set
proportions of the various inputs used to produce a certain output. In the near run, however,
increasing the quantity of one input while keeping the quantity of other inputs constant can
result in more output. The Law of Variable Proportions describes this element of the
production function. In the situation of two inputs, labour and capital, with capital being fixed
and labour being variable, the short run production function can be stated as:
Q = f (L, R)
Where K -refers to the fixed input.
