Page 121 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Mathematics for Economists

Note 7.3.2 Economic significance of Cobb Douglas Production Function
Cobb Douglas Production Function has a very importance role in economic area. At present many
economists are using Cobb Douglas Production Function in various economic areas. The use of this
function is day-by-day is increasing especially in various industries and agriculture. This bring
important information for these sectors. This also helps in framing various policies.
With the help of this function, we can also determine the Marginal Productivity and similarly it
helps in determining principle of wages. Production function describes production technique. With
the help of this function we can also determine whether any factor is paid the value with respect to
its equality with the marginal productivity. In a same fashion it helps in agriculture to find the
elasticity of economy. By this function we also display elasticity coefficients. These elasticity
coefficients help us in comparing the international and internal areas.
As has already be described when function is linear and homogeneous and a + b = 1, then production
would be under the constant result, when a + b > 1, then increase in production happens, and if a +
b < 1, then decrease in production happens. This way this function helps us in studying the rules of
various results. Besides these it also fetches important information related to substitutability of
various factors of production.
In short, this function plays an important role especially in agriculture and industries. This is used
in determining the labour policies, inter-area comparison, substitutability of factors and degree of
homogeneity.

7.3.3 Limitation of Cobb-Douglas Production Functions

Although Cobb Douglas Production Function is used widely in economic areas and its use is
increasing in especially in various industries and agriculture, but some economists criticize this
production function. Among them are Prof K.J. Arrow, H.B. Chenery, B.S. Minhas and R.M. Salow.
Their main criticizes are:
1. The main demerit of this function is this that it considers only two factors of production i.e.
Capital and Labour, whereas in reality other factors also have important role in production.
In other words, this function does not apply to more than two factors. Besides it can be used
only in construction industries. This way its use becomes narrow.
2. This function works under the constant result of formula. Rule of increase and decrease in
result also apply to production function. But this function does not work under these rules.
3. Function is based on the assumptions that technical knowledge remains constant and no
change in techniques happen in production. But the same can change in production. This way
assumption of constant technique is irrelevant.
4. Cobb-Douglas Production Functions assume that all inputs are homogeneous. In reality all
units of a factors are not homogeneous. For example some people are skilled and others are
not in a labour population.
5. This does not determine any maximum level of production. Prof M. Chand says “Since, this
does not ascertain the maximum level of P (Production), it would be practical and convenient
not to use this function beyond a certain limit for statistical measurement of its values.
6. a and b of the function reflects the proportion of labour and capital in production. This
becomes true only when market has a complete competition. But in case economy has a
incomplete competition or monopoly, then above relation can not be obtained.
7. It takes into account only positive marginal productivity of factors and ignores the negative
marginal productivity. Whereas marginal productivity of any factor can be zero or negative.
8. Last, the function is unable to produce information related to inter-relation of factors.

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