Production Function is known as Input-Output Model. Input is the liability of the management which is reflected in the employment of the factors of production, i.e., land, labor and capital etc which are playing important role in the generation of output. On the other hand output is the asset of the firm as it is the result of the productivity of the different factors of production which are employed by the manager into the existing production process. Therefore Production Function is examining the nature of relationship between the input and output of the firm. Production function is important econometric model where we get economic analysis, statistical technique and mathematical model.
Production function is given by the equation,
y = f (x1, x2)
where
y = total output of the firm (dependent variable)
x1 = total employment of the labor (independent variable)
x2 = total employment of the capital (independent variable)
therefore the hypothesis is of production function is that output is mainly contributed by the important factors of production like labor and capital.
In the underdeveloped or developing country like in India we observe that labor is playing important role in the generation of output because in such economy capital is very scarce. In such economy most of the projects become labor intensive where rate of employment of labor is always more than rate of employment of capital. Therefore labor output is apways higher. In such situation production function model is,
y = f(x)
where
y = total output of the firm (dependent variable)
x = total employment of the labor (independent variable)
in this situation we observe that the manager is considering the hypothesis that output is mainly contributed by labor and therefore the manager is considering the normal equations in order to know actual contribution of labor in the generation of output. The normal equations are:
∑y = Nx + b∑x … (i)
∑xy = a∑x + b∑x2 …(ii)
where
y = total output (dependent variable)
N = number of combinations
a = technological parameter (constant)
b = labor share in output (actual contribution of labor in the generation of output)
x = total employment of labor (independent variable)
EFFECTIVENESS OR RELEVANCE OF DIFFERENT TYPES OF PRODUCTION FUNCTION:
In managerial economics generally we get the existence of following two types of production function –
A. COBBS-DOUGLAS Production Function
B. ACMS Production Function
Where A – Arrow
C – Chenery
M – Minhas
S - Solow
A. COBBS-DOUGLAS Production Function
COBBS-DOUGLAS Production Function has been jointly contributed by two economists in Cobb and Douglas. This production function identifies the nature of contribution labor and capital in the generation of output.
The COBBS-DOUGLAS Production Function is given by
y = K.LαCβ
where
y = total output of the firm (dependent variable)
K = technological parameter
L = total employment of labor (independent variable)
α = labor share in output
C = total employment of capital (independent variable)
β = capital share in output
In this model it is observed that
α + β = 1
If α > β, then it means that performance of labor is more satisfactory than performance of capital and in this situation a personal manager can employ more labor in the project.
On the other hand if α < β, then it means that performance of capital is more satisfactory than performance of labor and in this situation the strategic manager can employ more capital in the existing project.
B. ACMS Production Function
This production function is jointly contributed by 4 economists, i.e., Arrow, Chenery, Minhas and Solow. This production function examines the nature of relationship between average productivity of labor and the real wage of the labor.
Average productivity of labor = (total production of labor) / (total employment of labor)
and
Real Wage = (money wage) / (consumers price)
The ACMS production function is
logQ/L = b logW
where
Q = total output of the firm
L = total employment of labor
Q/L = average productivity of labor (dependent variable)
b = substitution parameter
W = real wage (independent variable)
If the value of b is significantly high then it implies that the relationship between average productivity of labor and real wage is highly satisfactory and there is no need of substitution of labor by capital.
On the other hand if the value of b is significantly lower then it implies that the relationship between average productivity of labor and real wage is highly unsatisfactory and therefore in this situation the manager must substitute labor by capital into the existing production process.
SIGNIFICANCE OF PRODUCTION FUNCTION IN MANAGERIAL ECONOMICS
1.
With the help of COBBS-DOUGLAS Production Function it is observed that if the value of α is more than the value of β the personal manager can employ more labor in the project as the actual contribution of labor is more satisfactory than the actual contribution of capital. On the other hand if the value of β is more than the value of α, the financial manager can employ more capital in the project as the actual contribution of capital is more satisfactory than the actual contribution of labor in the generation of output.
2.
From COBBS-DOUGLAS Production Function the personal mange calculate the value of marginal productivity of labor with the help of α-coefficient. If it is observed that value of marginal productivity of labor is more than real wage parameter, then it is definitely exploitation on labor by the management and in this situation in order to motivate the labor, the personal manager must revise the Money Wage so that rate of increase of money wage more than rate of increase in consumer’s prices and in this situation real wage parameter will increase.
3.
From the ACMS Production Function model, the manager can formulate future policies regarding substitution between factors of production, i.e., labor and capital. If the value of b is significantly higher, the relationship between average productivity of labor and real wagw parameter is highly satisfactory and therefore in this situation there should not be any substitution of labor by capital. On the other hand if the value of b is significantly lower then it implies that the relationship between average productivity of labor and real wage is highly unsatisfactory and therefore in this situation the manager must substitute labor by capital into the existing production process. Therefore it is observed that future policies regarding substitution between the factors of production can be determined with the help of ACMS Production Function model.
4.
It is finally observed that both COBBS-DOUGLAS Production Function Model and ACMS Production Function Model make an attempt to identify the nature of contribution of labor and capital into the existing production process and therefore with the help of these production function models the manager can formulate future policies regarding employment of labor and capital into the existing production process.
Thus it is concluded that production function model is the most important economic model through which the relationship between input and output can be studied and for this reason production function model is accepted as input-output model in managerial economics.