Answer :
The steady state investment equations for both physical and human capital are as follows:
a) Output per worker = (Physical capital per worker)^(1/3) * (Human capital per worker)^(2/3)
b) Investment in physical capital per worker = s * Output per worker
c) Investment in human capital per worker = δ * Human capital per worker
d) Output per worker = Investment in physical capital per worker + Investment in human capital per worker
In the steady state, output per worker is determined by the levels of physical and human capital per worker. Equation (a) represents the Cobb-Douglas production function, where output is a function of both types of capital with specific exponents. Equations (b) and (c) denote the investment in physical and human capital per worker, respectively. Here, 's' represents the savings rate and 'δ' symbolizes the depreciation rate of human capital. In equation (d), output per worker is equated to the sum of investment in physical and human capital per worker. This equilibrium condition illustrates that in the long run, the output per worker depends on the investments made in both types of capital.
To find the equilibrium conditions in per worker terms, we substitute equations (b) and (c) into equation (d). This yields:
(Physical capital per worker)^(1/3) * (Human capital per worker)^(2/3) = s * (Physical capital per worker)^(1/3) * (Human capital per worker)^(2/3) + δ * Human capital per worker
Solving for (Physical capital per worker)^(1/3) * (Human capital per worker)^(2/3) and rearranging terms, we arrive at the equilibrium condition in per worker terms. This condition reflects the balance between investment in physical and human capital to achieve optimal output per worker in the steady state.
