A new analysis of President Biden’s proposal to cancel student debt suggests that the program may cost nearly twice as much as previously expected and possibly as much as $1 trillion depending on how it influences the borrowing habits of students in the future.

The University of Pennsylvania’s Penn Wharton Budget Model, which analyzes the economics of public policy, initially estimated that Mr Biden’s handout would cost around $300 billion over the next 10 years.

After the White House released more details on the proposal, however, the think tank said the plan to cancel up to $10,000 for borrowers who earn less than $125,000 — $20,000 for low-income Pell Grants recipients — will cost between $469 billion and $519 billion over 10 years. About 75 percent of the benefits would fall on people earning less than $88,000 per year, according to the model.

Other components of the plan include extending the two-year-old moratorium on student loan payments for all borrowers, which the Penn Wharton model estimates will cost an additional $16 billion, and changes to an existing income-based repayment program, which will add another $70 billion to the plan’s cost.

New features proposed for the income-based repayment program could change that $70 billion number considerably, however, Wharton said. Future borrowers could have an incentive to borrow even more money than before to take advantage of those changes, it said, and institutions of higher education might have an incentive to raise prices as well. If the Department of Education opted all eligible borrowers into the program, its total cost could exceed $450 billion, the analysis suggests.

The program at issue, also known as the income-driven repayment program, allows borrowers to make payments that are based on their income instead of the standard, fixed monthly payments paid on most loans. Currently, borrowers must pay 10 percent of their take-home pay on the loans and the debt is forgiven after 20 years of payments. Mr. Biden wants to cut that 10 percent in half, to five percent of discretionary income, and eliminate the debt after 10 years of payments.

An analyst at the progressive-leaning People’s Policy Project, Matt Bruenig, said that the number of students enrolled in the income-based program has tripled in the past decade and could grow even faster under Mr. Biden’s proposal. Students enrolled in the program are incentivized to borrow as much as possible, he has written, and schools have every incentive to continue raising the cost of tuition as more students opt in to the program.

“Imagine if Medicare and Medicaid did not dictate the prices of covered services, but instead reimbursed medical care at whatever price the provider and patient agreed to without any cost-sharing,” Mr. Bruenig said. “An IDR-dominant college sector, absent separately-imposed price controls, would be basically the same thing.”

Mr. Bruenig said many law schools across the country have already created so-called Loan Repayment Assistance Programs that help students who, after graduation, go to work in the government sector. Because the students’ future payments are the same regardless of how much money they borrow, he said, they are encouraged to borrow the maximum amount possible. Amounts borrowed beyond tuition and fees are distributed to the students as cash for living and other expenses.

Many law schools make the deal even better for these students by allowing them to set aside some of the money they borrow to be used for the later monthly income-based payments. Essentially, their payments after graduation are zero, and the debt — regardless of the total amount — is wiped out after a decade.

“Through this roundabout process, the law schools effectively use student debt to pay off student debt and make their schools free or nearly free, at least for these particular students,” Mr. Bruenig said.

“If we are going to make the leap into an IDR-dominant college financing system, then we may need the government to also play a much bigger role in setting college prices, something it probably should have been doing even before the Biden policy change,” he added. “Otherwise, we may very well see more unwanted cost bloat beyond what we already have.”