I'm reading Fisher (1997, Journal of Monetary Economics). From the intermediate goods produced ($Y_t$), the final goods firm allocates into consumption ($C_t$), business capital investment ($I_{b,t}$), and household investment ($I_{h,t}$) s.t....
$C_t + (I_{b,t}^K + I_{h,t}^K)^{\frac{1}{K}} \le Y_t$
Fisher claims when $K>1$ there is complementarity in production, but my intuition is failing me. If $K>1$, $I_t = (I_{b,t}^K + I_{h,t}^K)^{\frac{1}{K}}$ is maximized when I invest all savings into either business or investment capital, while $I_t$ is minimized when I split my savings equally between the two. To me this sounds like anti-complementarity.
Can someone point one where my intuition is going awry? If it helps, on the utility side of things is log-utility w.r.t to $C_t$, $K_{h,t}$, and $L_t$ (leisure).