Question

How scarcity and constrained optimization differ?

Answer 1

It's analogous to "cause and effect". Here scarcity is cause which lands us in doing constrained optimization to be as better off as possible under given scarcity(Limitations).

Answer 2

scarcity is the fact that we must choose among alternatives. Constrained optimization in how we go about making those choices. We always want more and the best but due to scarcity we cannot have all that we want. We can have what is within our resources to have we try to make choices to benefit us the most.