Questions about capital accumulation

Dear all,

I feel confused about the capital accumulation function.I know its general form is “I_t=K_t-(1-delta)*K_t-1”.The question is why not added the capital price in this function.

If I have two different kind of captials like K_1,t and K_2,t with different prices.How should I write these two capitals into one capital accumulaiton function and how to write the correspongding market clearing function?

Thank you.

The capital price would show up in the budget constraint, not in the capital accumulation equation.
Regarding two sector problems, search the forum. See e.g. Timing of capital in two sector model

Dear Professor ,
Thank you for your reply.I have had seen the “Timing of capital in two sector model”.But my problem is a little different from it.
First, the two different capitals are in one sector. My production function is like

Second, when I am trying to construct the sector of “capital goods manufacturer”,I feel confused about “putting two capitals into one capital accumulation function”. If I write just like
the equation means these two different capitals have the same price as the final goods. How should I tell the difference between these two capitals in the accumulation equation?

Thank you.

You first need to decide whether there are one or two laws of motion for capital accumulation. That is a matter of the setup you envisioned.

Dear Professor,

You are right. To set one cumulative equation or two makes me confused. One thing can be confirmed is that I need to set two different types of capital in my model.

As for setting "one or two " cumulative equations, I have the following attempts:

First,if there are two cumulative equations (I_1 and I_2) corresponding to these two different capitals, it seems easier to find steady state than one cumulative equation.But the problem occurs to the market clearing equation. It becomes to I=I_1+I_2. And it is unsolvable to find the steady state of “I_1 to I” and "I_2 to I "by calculation but not calibration.

Second,if there is only one cumulative equation corresponding to these two different capitals, the problem goes to" how to tell the difference between these two capitals in one cumulative equation "as we have mentioned before.

Above all is my question. Looking forward to your reply.

Thank you.

There must be an Euler equation that tells you about the relative supply of capital given the return to capital. Similarly, there must be a first order condition governing the optimal factor use. Those should provide the solution.