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Concept of Production Function

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Production:

Production is the process of creating utility in goods and services or process of transforming inputs into output. 

Concept of Production Function:

In simple words, production function refers to the functional relationship between the quantity of a good produced (output) and factors of production (inputs).
The Production Function shows the relationship between the quantity of output and the different quantities of inputs used in the production process. In other words, it means, the total output produced from the chosen quantity of various inputs.

The production function is generally expressed as
Q = f(Lb , L, M,T, t)
Where,
Q= Output
Lb = Land and Building
K= Capital
T= Technology
f= Function
L= Labor
M= Materials
t= time  
For the sake of convenience and simplicity, we consider only two factors: labor(L) and capital(K). Now, the production function can be expressed as, 
Q= f(L,K) 


Types of Production:

1. Short-run Production Function: 
The short run is the period of time during which at least some factors of production are fixed. The short-run production function is the technical or mathematical relationship between inputs and output when quantities of some inputs are kept constant and quantities of one input are varied. The input and output relationship in the short-run is studied under the law of variable proportions. It is also known as the production with one variable input. It can be expressed as 


2. Long-run Production Function:
The long run is the period of time during which all factors are variable. The long run production is the technical or mathematical relationship between inputs and output when all inputs or factors of production are variable. The input and output relationship in the long-run is studied under the laws of return to scale. It is also known as the production function with two variable inputs. It can be expressed as