But sec8 office does not pay the difference in this situation

Because they told me the maximum voucher is $1700 if the teant has no income.  The maximum they can pay in this situation is $1400.

The house is 4bd and the tenant has 3bd voucher. She has 4 kids and would like to stay in 4 bd room house.  Section 8 office basically says "no" to her desire even though she is willing to pay me $600, section 8 office would not sign the contract of $2000. They told her to find a 3bd house.