Timing of capital in two sector model


#1

I saw Timing of capital in two sector economy before , but I still have some quetsion on it.

Case1:
k(-1)=kT+kN
yT=AT * NT^(1-a) * kT^(a)
yN=AH * NH^(1-b) * kN^(b)

Case2:
k=kT+kN
yT=AT * NT^(1-a) * kT(-1)^(a)
yN=AH * NH^(1-b) * kN(-1)^(b)

Would it produce the same output ?


#2

No, it would not. In case 1, at time t when you produce, you can still decide how to split the capital stocks for production. In case 2, you use the capital stock split that was decided at t-1.


#3

Thanks for response, and I think Case1 is reasonalbe than Case2.