Suppose the standard household maximization problem.
Household has lifetime utility function and maximize it
(1) cash in advance: $c(1-s) \leq m$
(2) budget constraint: $c+q\int_0^s \lambda (c,i)di + \omega '=(1+r)a +m+ w$
where $\omega '$ is tomorrow's wealth
and $s$ means the fraction of consumption purchased by credit
and $q$ is the fee of financial service $\lambda (c,i)$
$i$ is the continuum of consumption
In textbook it says CIA constraint binds if
$w+(1+r)a -\omega ' \geq 0$
How can I derive that solution?