Reference no: EM13181143

In this question we are going to incorporates investment in human capital by agents, in a form similar to physical capital. Labor units are replaced by human capital units

Y = AK?(?H)1??

where

• H ? Units of Human Capital

• ? ? [0, 1] ? Fraction of time spend at work so 1 ? ? is the fraction of time spent a school.

(a) Determine the output per worker, y = Y/L?

Additionally we have the laws of motion:

K' = sY ? ?KK

H' = B(1??)H ? ?HH

where

• B = is a parameter which captures the efficiency of the Human Capital accumulation tech- nology

• ?K = Depreciation of Physical Capital (K)

• ?H = Depreciation of Human Capital (H)

(b) Assuming the that population growth rate is n show that the laws of motion in per capita

terms are

k' = sy ? (?K +n)k

h' = B(1??)h ? (?h +n)h

We want to show under some reasonable conditions that this Human Capital model delivers the same dynamics as the AK model, hence endogenous growth.

(c) Given the per worker production function from part(a) calculate the marginal product of physical capital per worker and the marginal product of human capital per worker.

(d) Now imposing that in equilibrium the marginal products of the factors from part (c) must be equal, then give an expression for h in terms of k.

(e) Now plug your expression found in part (e) into the per capital production function and show that it reduces down to an AK model.