I'm a bit confused - do these values represent the largest amount that
can be earned? In other words, can a household of 1 earn up to (and
including) 1037 and still be regarded as "Free", or up to 1476 and be
"Reduced"? If so, you need this amended formula:

=IF(A10<1,"Not valid",IF(L4<=VLOOKUP(A10,N1:O8,2,0),"Free",
IF(L4<=VLOOKUP(A10,N1:P8,3,0),"Reduced","Paid")))

This will cover households up to 8 - extend the table and amend the
ranges as described earlier for more.

Pete