Imagine we live in a world with two types of skill sets: people with high ability and people with low ability. A diploma will cost a high ability person about 8K and will cost a low ability person about 20K. Businesses use education as a screening tool and they intend to pay 25k to workers without a diploma and $X to those with a diploma. In what range must X be to make this an effective screening tool?

Your answer will include a set of equations showing the dollar range for both low ability and high ability people.