  In the envy-free perfect matching problem, $n$ items with unit supply are
available to be sold to $n$ buyers with unit demand. The objective is to find
allocation and prices such that both seller's revenue and buyers' surpluses are
maximized -- given the buyers' valuations for the items -- and all items must
be sold. A previous work has shown that this problem can be solved in cubic
time, using maximum weight perfect matchings to find optimal envy-free
allocations and shortest paths to find optimal envy-free prices. In this work,
I consider that buyers have fixed budgets, the items have quality measures and
so the valuations are defined by multiplying these two quantities. Under this
approach, I prove that the valuation matrix have the inverse Monge property,
thus simplifying the search for optimal envy-free allocations and,
consequently, for optimal envy-free prices through a strategy based on dynamic
programming. As result, I propose an algorithm that finds optimal solutions in
quadratic time.
