The fashion brand Kate Spade is most known for luxury handbags. But it is also banking on gold-accented staplers, monogrammed planners and $30 ballpoint pens to help buoy sales during the increasingly important back-to-school shopping season.

The discount retailer Dollar Tree is also expecting students and their parents to lift sales, particularly after an unusually weak second quarter. But instead of fancy notebooks, it is focusing on the other end of the price spectrum, like $1 packs of tape, glue sticks and pencils.

As the income gap in the United States has turned into a chasm, luxury and discount retailers have become increasingly deft at attracting people at the separate ends of the income spectrum. Stores positioned for the middle, like traditional department stores, have struggled by comparison.

These days, that divide extends more than ever to what students wear and carry with them to their school lockers.