Economic growth is measured by the rate of increase in national output, GDP. The output depends on inputs -labour, capital technology etc. the theories of economic growth bring out how and to what extent each input or factor contributes to the growth process. For understanding growth theories therefore, it is important to understand how the relative share or constitution of each theory therefore it is important to understand how the relative share or contribution of each factor to the growth of output is determined. The answer to this question is provided by the production function. In fact, theories of economic growth use production function to explain the process of economic growth some economists call it growth accounting.
The production function used widely in growth analysis is of the following form.
Y = f (L. K. T)
Where Y = total output L = labour K = capital and T = technology
To begin the analysis of growth accounting, let us assume cob-bugles type of linear homogenous production function. A linear homogenous production function, also called homogenous production function of degree I, is one n which all the inputs (L and K) increase in the same proportion and this proportion can be factored out. Given these conditions the production function can be expressed as
KY = f (KL, KK)
KY = K (L, K)
For example, if both L and K are doubled, ten total productions, Y, are also doubled. In that case, production function can be written as
2Y = f(21. 2K)
2Y = 2(L< K)
From the growth accounting point view, estimation of the relative share of labour and capital in output growth (?Y/Y) is required.
In case labour and capital are increased at different rates, the relative share of L and K in income growth rate (?Y/Y) can be estimated as follows.
?Y/Y =. ?L/L + (1 -α) ?K/K
Where α denotes the share of L and (L - α) denoted the share of K in total input, and
α + (1 -α) = 1.
For a numerical example, suppose labour growth (?L/L) is 3 percent, capital growth rate (?K/K)is 5 percent and α = 0.75 then,
?Y/Y = 0.75 (3) + (- 0.75)5
= 2.25 + 1.25 = 35
Given the parameters, the GDP growth rate (?Y/Y) turns out to 3.5 percent of which 2.25percent is the share of labour and 1.25 percent is the share of capital.
Inadditons to the growth resulting form increase in L and K. there is another factor that adds to growth rate, the total factor productivity measured as ?T/T. the total factor productivity is the increase in total production due to improvement in technology, all other inputs remaining the same. We have so far assumed technology to be given. Let us now suppose that production technology is improved over time along with increase in L and K, it implies that technological improvement contributes to growth rate of output in addition to growth resulting form increase in L and K with addition of change in technology (?T/T).
?Y/Y =α. ?L/L + (1 -α) ?T/T
Suppose technology productivity is estimated to be 1.0 percent ?T/T = 1. Then growth rate can be estimated by applying Eq.as
?Y/Y = 0.75. 2 + (1 - 0.75)2 + 1.0
= 4.5 percent
Thus, with addition of total factor productivity GDP growth rate rises from 3.5 percent to 4.5 percent, this given an idea of growth accounting.