Production Function Models

A production function model, in particular, explains the interaction of variables in production. They treat production or growth as a function of such interactions. These types of models are used to examine, assess and estimate the relative weights of different variables and sub-variables in their interactive functioning and contribution to economic growth. A few economists from the Chicago School of Economics, U.S., used this approach in the late 1950s and early 1960s to examine the sources of economic growth in the United States.

One of the landmark studies in this genre was by Edward F. Denison in 1962. In a simplified framework, the technique adopted may be described as follows. Using the growth accounting technique, Denison explained the sources of economic growth in the United States during the period 1929 58. He accounted for the recorded rise in national income by balancing the factor shares of production with the total output produced. Since the effort was directed at accounting for growth over a period of time, the technique came to be known as the growth accounting approach. The Cobb Douglas Production Function Equation (known so for its development by Cobb, a mathematician from Cambridge, and Douglas, an economist from the United States) was used for the purpose.

The production function equation assumes that the quantity produced in a country is determined by the interplay of labour (L) and capital (K). Although these two, i.e. labour and capital, are considered as the main factors, there are other factors or variables which influence the relationship. As they could not be accounted explicitly, they are treated as a constant. Hence, Q, the quantity produced is the outcome of the interplay of ‘L’ and ‘K’ along with ‘other factors’ denoted by a constant ‘A’. The capital used in production included fixed capital such as land and circulating/perishable/consumable capital such as raw materials, machines, electricity, etc. In equation form, the relationship was expressed as:

a”1 -  a

Q = A . K . L  where

the symbol a (alpha), a constant, stands for the contribution of the capital K to national income. Since the total contribution of L and K is one (a unit), the contribution of L is (1 – a). The contribution of capital and labour as well as that of ‘A’ can be determined by solving for the parameters/constants (i.e. A and a) when time series data on the three variables L, K and Q are available.