Hi, I am trying to replicate this paper. I am wondering where the naming of capital utilization is the same. Eq (8) uses a[u] while eq(43) uses a(u).

Yes, they are the same and the brackets should be consistent.

Thanks @jpfeifer. I really doubt this paper. Or perhaps my understanding is still unclear. For example eq 42 shows that in SS q= 1 ( i.e Q=Lambda). In eq 43 this seems contracting. Twisting the parameters to force the SS eq to match will collapse other eq.