If the initial level of labor input, L(0), doubles why does the steady state cap
ID: 1168593 • Letter: I
Question
If the initial level of labor input, L(0), doubles why does the steady state capital stock, K* double? that is steady state capital per worker K* does not change. How does this result depend on constant returns to scale in the production function?
Does population growth N>0, lead to growth of output in the long run? does it lead to growth of output per worker in the long run? what is the meaning of the term convergence? how does absolute convergence differ from conditional convergence? Also, Variation for the growth rate of capital per worker K is given by (change K/K)=S*(y/k)-sS-n.
Is this equation still valid when s is not constant ?
Explanation / Answer
A production function has constant returns to scale if increasing all factors of production by an equal percentage causes output to increase by the same percentage. Mathematically, a production function has constant returns to scale if zY = F(zK, zL) for any positive number z. That is, if we multiply both the amount of capital and the amount of labor by some amount z, then the amount of output is multiplied by z.
In the steady state, we know that technological progress determines the growth rate of output per worker. At the steady state , net investment equals zero and the capital stock remains constant at K*.
If the production function has constant returns to scale, real GDP will double when labor and capital inputs double; because output and inputs all double, capital per person, the ratio of output to capital, and output per person do not change. When capital and labor inputs double and the autonomous growth factor also doubles, however, real GDP increases fourfold. In this situation, there is still no change in capital per person, but now the output-capital ratio and output per person both double.