Concept of Production Function

Nature imposes technological constraints on firms; only certain combinations of inputs are feasible ways to produce a given amount of output, and the firm must limit itself to technologically feasible production plans. The easiest way to describe feasible production plans is to list them.

The set of all combinations of inputs and outputs that comprise a technologically feasible way is called a production function. The relation between the inputs and output of a firm is known as the production function.

The production function is a purely technical relation which connects factor inputs and output. It shows the maximum amount of output that can be produced from any specified set of inputs given the existing technology. It is a flow concept, so production refers to units of output over a period of time.

• It refers to the relation between the inputs and outputs of a firm.
• It is a flow concept, so production refers to units of output over a period of time.

Mathematically, the production function can be expressed in a functional form as:

Y = f (X₁, X₂, X₃, Xn)

Where,

Y = Output

X₁, X₂, X₃, Xn = Quantity of factor inputs (Such as land, labour, capital or raw material)

f = shows the functional relationship between inputs and output.

Concept of Product:

There are three important concepts regarding the physical production of factors:

• (i). Total Product of Labour (TP_L)
• (ii). Average Product of Labour (AP_L)
• (iii) Marginal Product of labour (MP_L)

(i). Total Product of Labour (TP_L)

The total product of a variable factor is the maximum amount of an output that can be produced by a given amount of variable factors, keeping the quantity of other factors, such as capital, and land fixed. When the amount of the variable factor increases, the total product increases.

TP_L = AP_L x L

or

TP_L = ∑ MP_L

Where,

TP_L = Total product of labour

AP_L = Average product of labour

L = Labouror Variable factor

MP = MP of Labour

∑ = SumTotal

Total Product (TPL) initially rises at an increasing rate (so the slope of the TPL curve is rising in the beginning) but after a point, TPL curve starts rising at a diminishing rate, reaches a maximum and then starts falling as the usage of variable factor increases.

(ii). Average Product of Labour (APL):

The average Product of a variable factor is the total product divided by the amount of labour (variable factor) employed with a given quantity of capital (fixed factor) used to produce a commodity. It measures the average output per unit of the factor. Thus,

APL = TP_L /L

Where,

AP_L = Average Product of Labour

TP_L = Total Product of Labour

L = Number of labour employed

The Average Product (AP) is an inverted ‘U’ shape curve. The AP curve first rises, reaches a maximum and then falls thereafter as the usage of the variable factor increases. The average Product at any point on the total product curve is the slope of the straight line from the origin to that point on the total product curve.

(iii). Marginal Product of Labour (MPL):

The Marginal Product of a variable factor is the addition to the total product by the usage of one more unit of a variable factor. It measures the rate at which output changes as a variable factor changes. Thus,

MP_L = ΔTP_L /ΔL = Change in Total product / Change in Labour

or

MP_L for nth unit = TP_n – TP_n-1

Where,

n is the number of units of labour

It measures the slope of the total product curve. Marginal Product (MP) is an inverted ‘U’ shape curve. The MP curve first rises, reaches a maximum and then falls thereafter as the usage of the variable factor increases. When the Total product starts falling, the Marginal product becomes negative. The Marginal Product is the slope of the tangent line to the total product curve.

Some of the special Production Functions are:

1. Cobb Douglas Production Function
2. CES Production Function
3. VES Production Function
4. Translog Production Function

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