Harvard announced on Monday that it plans to offer free tuition for students whose families earn $200,000 and below, making it the latest elite school to expand financial aid after the Supreme Court banned the use of racial preferences in college admissions.

The plan with the new income cap will take effect starting this fall. Previously at Harvard, only families with incomes under $85,000 were offered free tuition. The median household income in the United States is about $80,000.

In addition to boosting diversity, the move could serve to improve the school’s image as higher education is under assault by the Trump administration and growing unpopular with Americans who have lost confidence in education.

The University of Pennsylvania announced last November that it would offer free tuition for students from families making under $200,000. The Massachusetts Institute of Technology also announced a $200,000 cutoff then, similar to a plan offered by Caltech. Other universities have also increased their financial aid limits in the past year, including Dartmouth, the University of Virginia and the University of North Carolina.

The Supreme Court decision banning affirmative action led to declines in the number of Black and Hispanic students at many schools, including Harvard. Last fall, the proportion of Black first-year students enrolled at Harvard declined to 14 percent from 18 percent the previous year, while Hispanic students’ enrollment increased slightly.

The ruling has posed a dilemma for schools that have argued that diversity is important, but that are now under intense scrutiny from the Trump administration, which is seeking to eliminate diversity efforts.

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