A small college has space for a maximum of 1,000 students

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A small college has space for a maximum of 1,000 students. The college can identify 500 of its students who are willing to pay $20,000 per year and 500 students who are willing to pay $10,000 per year. The college gas annual fixed costs of $10 million, and the variable cost for each additional student is $5,000. To continue operating, the college must receive payments equal to its total cost (that is, total fixed costs + total variable costs).

Suppose a rich donor offers to pay all of the fixed costs at the college to make sure that it can stay in operation. However, because he opposes price discrimination on moral grounds, the donor places one condition on his offer: From now on, the school must charge all of its students the same amount. That is, it should ask everyone to pay the same tuition and offer no financial aid.

Assuming the college chooses the price that maximizes its profits, would this condition lead to an increase in social welfare, as measured by the sum of consumer and producer surplus?