Timing error in model with 2 stocks of capital for the firm

Stochastic simulations
1

Hi everyone,

I’m working on a model where firms can invest in two different stocks of capital Kd and Kc. I can’t run my model with two equations of accumulation. I’ve seen the subject on " Timing of capital in two sector economy", however, I’m not sure that the rationale is the same for a two sector economy and a representative firm relying on 2 stocks of capital.
Should I use the same resource constraint k(-1)=kc+kd in my model?

Thanks a lot.

2

Often, the answer is yes. But in the end, it depends on how you want to model your setup. Can the total capital stock from the previous period be freely allocated across the two stocks in the current period?

3

Thanks for your answer.
In my initial settings, the production function is a CES with kc(-1) and kd(-1), each one following an accumulation process. But, there was a timing error.
But now, I’m not really sure of what it means to have kc and kd at time t in the production function and the ressource constraint : k(-1)=kc+kd. The choice between the two stocks depend on their prices in the first order conditions. Do I need to move all the stocks of my model at period t?

4

It means that the aggregate capital stock is accumulated and predetermined by total investment in the previous period. However, the split into kc and kd is decided in the current period.

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5

Hello again, I’m back on my model. Thanks for your wise advices.
I think I made a mistake, it is not the case that K can be freely allocated to Kc and Kd at each time.
I believe that each stocks Kc and Kd should be accumulated and predetermined and not only the aggregate. The firm is not able to reallocate directly all Kd into Kc or the inverse. It can choose to invest an amount Ic or Id, but all Kd cannot be switched into Kc at time t. However, i’m still not able to have two equations of accumulation, do you know why?