Reference no: EM13188833

Suppose that the production function of an economy follows the formula
Y = F(K, bN)
where b denotes the number of units of "human capital" per worker and bN the "effectiveunits" of labor. Due to effective educational policy, the stock of human capital per workervgrows through time:
b' = (1 + f )b
where f > 0 is the growth rate of human capital. At the same time, population N grows at the rate
N' = (1 + n)N
In this economy, all production output goes to either consumption or savings. The saving rate is fixed at s where 0 < s < 1. All savings then contributes directly to increase the capital stock (that is, S = I). Suppose that the capital stock depreciates at rate d from period to period.
a)Write down the law of motion equation that shows how capital stock changes from period to period (use K to denote capital today, K' capital tomorrow).
b) Assume that the production function F(K, bN) exhibits constant returns to scale. Rewrite the equation in part a) into a law of motion with respect to capital stock per effective unit of worker (k = K/bN)
c)Write down an equation that determines steady state level of k, denote k. Based on this equation, draw a graph that determines k.
d) In steady state, how does output per capita (Y/N) and capital stock per worker (K/N) change through time?