How does output per capita change through time

Reference no: EM13189469

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 "effective units" of labor. Due to effective educational policy, the stock of human capital per worker grows through time:

Derivative of b = (1 + f )b

where f > 0 is the growth rate of human capital. At the same time, population N grows at the rate:

Derivative of 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, Derivative of 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?

Reference no: EM13189469

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