Answer
There exists a person who is happy and does not have a large income.
Work Step by Step
Recall the definition of necessary:
"$\forall x$, r(x) is a necessary condition for s(x)" means "$\forall x$, if ~r(x) then ~s(x)" or equivalently "$\forall x$, if s(x) then r(x)."
In this case r(x) is: person has a large income.
s(x) is: person is happy.
The necessary statement stated in if-then form is: for all people, a person is happy, if that person has a large income.
Recall the form of the negation of a universal conditional statement:
$~(\forall x, P(x) \rightarrow Q(x)) \equiv \exists x$ such that $(P(x) \land $ ~$Q(x))$
In this case the negation is $\exists$ a person such that s(x) and ~r(x) which is, "there exists a person who is happy and does not have a large income."
