This question requires that you use the law of motion of capital, the production function, and the national income accounts identity. Suppose that a nation’s production function is Y_t = F(K_t, L_t) = K_t^{\alpha}L_t^{1-\alpha}
You have the following information:
The share of income paid to owners of capital \alpha = \frac{1}{3}
The rate of depreciation, \delta = 1
The savings rate s=.15
The initial capital stock K_0=1
The labor supply, for all t\geq 0 is L_t=5
Assuming that L_t is the number of workers, What is the long run level of output per worker?
Please give an exact answer. This question will accept any answer within .1 of the exact answer