Need help for the summation of time varying variable in terms of time varying variables and a constant

18 Views Asked by At

Let's say I have a time varying variable, $b_{t}.$
If $z_{t} = \min(c, b_{t})$, for $t = 1 \ldots T.$
Can I say anything about $\sum^{T}_{t = 1} z_{t}$ ? (Any Inequalities, upper bound ,lower bound etc)