Entrepreneurs' first-order guidance to capital

I recently read a document in which a first-order condition caught my attention. Households hold capital, while businesses also hold capital and have the entire economic output, while paying wages and capital gains to households. In the first-order condition of the household sector, we derive the capital Kh,t, while in the first-order condition of the enterprise, we derive the capital Ke,t held by the enterprise and the household capital Kh,t-1 at the same time. I would like to ask whether this is right, and what kind of economic thinking is contained in the final derivation of Kh,t-1.Could anyone help me to answer it?
Thanks a lot

Your description is incomplete, so it’s impossible to answer. Which paper are you talking about?

Iacoviello(2015):Financial Business Cycles.The relevant equations are in the appendix.

The equation of derivation of capital by household department and enterprise department is B.4 B.21 B.24 respectively.

The idea seems to be that households decide on the amount of capital present in the economy via investment. But once that capital stock is present for use in the current period (the t-1 period one), the entrepreneurs face a static input choice, i.e. they have to decide how much of that capital to use.

Your answer suddenly enlightened me, thank you!