Question

Consider the two countries A and B above, but modify the model along the lines of Mankiw, Romer and Weil (1992) so that human capital, H, is included as a factor input.  For simplicity, labour efficiency is assumed to be 1 in both countries.  Output in country i is thus given by 

 

Yit=Kαit Hβit Li(1−α−β)

 

 

 and capital is accumulated according to 

 

 

∆Kit+1= sikYit−δKit

∆Hit+1=shYit−δHit

 

where we note that sh is the same in both countries.

 

a.  Let y ≡ Y/L denote GDP per worker.  Derive an expression for the steady-state value of the ratio yA/yB in terms of sAk, sBk, α and β.

 

b.  Suppose that β= 0.5.  What must α be in order for this model to fit the facts stated in Question 2?

 

 

 

∆Kit+1= sikYit−δKit

∆Hit+1=shYit−δHit

 

where we note that sh is the same in both countries.

 

a.  Let y ≡ Y/L denote GDP per worker.  Derive an expression for the steady-state value of the ratio yA/yB in terms of sAk, sBk, α and β.

 

b.  Suppose that β= 0.5.  What must α be in order for this model to fit the facts stated in Question 2?