Timing of capital in two sector model

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

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

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

Would it produce the same output ?

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.

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


I am trying to solve a similar model (total capital is predetermined, its allocation is not).

I therefore use the timing of the above Case 1 for production and aggregation, but how should I treat capital timing in the two agents (entrepreneur and household in my case) budget constraints?

I use

c^h_t + q^k_tk^h_t=w_t^hl^h_t+q^k_t(1-\delta)k^h_{t-1}+f(k^h_t)
c^e_t + q^k_tk^e_t+w_t^hl^{d}_t=q^k_t(1-\delta)k^e_{t-1}+f(k^e_t,l_t^{d})

but I have 14 eigenvalues larger than 1 for 12 forward looking variables.

Any suggestion would be really much appreciated.



The timing for the two individual capital shocks needs to be shifted by one period to the future relative to what you have in your equations.

Thank you Professor, I will try it.