Because the scale of these advantages is similar to those given to legacy applicants at some colleges, the paper suggests that socioeconomic integration across two- and four-year colleges is achievable, Professor Friedman said. “This would take a lot of concentration and focus, but it is not something that is wholly beyond our capacity.”

The other authors are Raj Chetty of Harvard, Emmanuel Saez and Danny Yagan of the University of California, Berkeley, and Nicholas Turner of the Federal Reserve. The paper was peer-reviewed and will be published in the Quarterly Journal of Economics and by the National Bureau of Economic Research.

The research is based on anonymous federal data linking parental tax returns to students. The SAT “bonus” scenario is far from a concrete policy proposal. It does not consider student qualifications other than standardized test scores, and does not delve into how public policy might change to make college more affordable — a major issue in the Democratic presidential primary. Nor does it address how such a strategy of income-based affirmative action could affect university budgets. Colleges might have to recruit students who are currently not applying, then provide more financial aid.

The authors present their system of income-based preferences as a counterfactual. In their model, they hold constant the total number of students at each college, the racial composition of the student body and the proportion of students on each campus from each state.

On race, the implication is that some white students with lower incomes and somewhat lower test scores would be admitted instead of some higher-income, higher-scoring whites. Lower-income black or Asian-American students would similarly take the places of some higher-income black or Asian-American students.

The study does not wade into the debate over whether the current racial makeup of elite colleges is fair. That is a subject the Supreme Court may take up, as cases challenging race-based affirmative action at places like Harvard and the University of North Carolina wend their way through the federal court system.

The authors of the new paper do not state who should lose the seats others would gain. In reality, enrolling more low-income and middle-class students while holding constant the total number of spots could mean that some other currently favored groups — such as athletes, legacies or the children of donors, and black or Hispanic students — would be admitted in lower numbers.