In Mankiw's Macreoconomics, how come capital is assumed to be fixed while investment is assumed to be variable?
It seems that Mankiw has implicitly assumed that all the investment is used to replace the depreciated capital. See the second sentence in the Investment section of Chapter 3-3:"Firms buy investment goods to add to their stock of capital and to replace existing capital as it wears out. "

Usually, the law of motion of capital is written as
\begin{equation}
K_{t+1}=I_{t+1}+(1-\delta)K_{t}
\end{equation}
where $\delta$ is the depreciation rate of capital. By assuming capital to remain at a fixed level $\overline{K}$, I believe that Mankiw is trying to only discuss the steady state in which capital is remained at a constant level, while avoiding introducing any more details. Since this is just the beginning part of textbook, everything is made as simple as possible. There is even no time subscripts for variables!