Understanding section 8 rent

Section 8 office limits rents of section 8 tenants.  In a way, they can't live in a very nice house.

In my case, the section 8 tenant has a 3bd voucher.  If I would like to charge the rent of $2000

1) Section 8 would pay maximum of $1700 - 30% of tenant income.  Assuming income is $1000.  Section 8 would pay $1400, and tenant would pay $300.

2) Section 8 office limits the tenant' rent to 40% of their income. So the maximum tenant can pay is $400

3) Thus section 8 pays $400, tenant pays $400.  The maximum amount I can charge is $1800, not $2000

So Sunshine MM, Does the section 8 office limits the amount of rent the tenants can pay based on their income in your area?