What Is A Production Function? Describe The Three Production Stages Indicating The Most Efficient And Profitable Stage Of Production For Any Profit Maximizing Firm?

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This is usually described as an abstract way of how a firm converts its inputs into outputs. It is also said that it includes all the possible combinations of inputs in a given economy. Generally, in mathematical terms it is explained as follows;
Q = f(X1, X2, X3,X4...Xn)
Where Q is the quantity of output and X1, X2, X3....Xn are the input factors like (capital, labour etc)
The linear form of the above function would be;
Q = a + bx (This is the general equation)
For simplicity, economists divide the whole process into three different and distinct stages;
  • In the first stage, the variable output is used with an increased efficiency and accompanied with it the quantity of fixed inputs also increases because here the efficiency throughout is increasing and the curve will be upward sloping. For a profit maximizing firm, this stage is highly important. In this stage the fixed inputs are usually being utilized below their effective rate/quantity. So a firm should try to beyond this stage to maximize its profits
  • The average rate of increase in output slowly declines and marginal physical product decreases. In this stage what usually happens is that the companies try to add new variable inputs while it affects two ways. In positive ways it affects the productivity of fixed inputs while due to the increased number of variable inputs, their productivity decreases. Usually what economists claim that the maximum production efficiency point, should lie somewhere in this stage
  • over utilization of variable inputs and fixed inputs. The quantity of both fixed and variable inputs is very high but their production capability is low. So the efficiency in production declines throughout this period
For a profit maximizing firm, stage II is highly important and to cross the barriers of stage I and maintain the status-quo of stage II. To employ a balanced quantity of variable and fixed inputs and make sure that no inputs are being over/under utilized.

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