Question

In a Cobb-Douglas/Solow growth model, what does alpha x K/L represent?

I am supposed to "decompose the growth in output per worker into contributions from TFP and capital per worker," but it is claiming that capital per worker equals alpha x K/L -- why times alpha?

Answer 1

In Economics and Ecotromics the Cobb-Doughlas production form in a particular functional form used to represent the technological relations between two inputs, example physical capital or labour and the output is produced by those inputs, In its most standard formulation production of single goods with two factors we represent the function as

Y= total production actually it is the real value of total goods produced in a year.

L= total labours hours actually this is total man hours worked for a year.

K= capital input the assets invested divided by the cost of the assets invested in a year

A= Total factor productivity

P & Q = Total output elasticities of capital and labour respectively and these values are constant

therefore output elasticities helps us to measure the output in respect to the changes of capital and labour used in production this means doubling the K(capital )+ L (Labour) also will double Y (Output)

Therefore the output per worker equals Alpha when total output/ total Input . The golden rule of capital stock is K when it maximises consumption due to a huge population growth.

The solution concept used is per the steady state where the level of capital per worker does not change.