The first order condition of my maximization problem is the following:
$(1-t_{i})(1-\gamma \frac{S_{i}}{B_ {i}}) -\lambda$ for all i=1...,n
Solving for S should give:
$S_ {i}=(\frac {B_ {i}} { \gamma (1-t_ {i})})\frac {\sum_{k\neq i}^n (\frac {B_ {k}} {1-t_ {k}})(t_ {k}-t_ {i})} {\sum_{k=1}^n (\frac {B_ {k}} {1-t_ {k}})}$
I found the solution in a paper, however I do not know how one goes from the first equation to the second. Can anybody explain the steps required to solve it?