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?

When the college price discriminates:

Total Cost = Fixed Cost + Variable Cost

Total Cost = $10 million + (1,000 x 5,000)

Total Cost = $15 million

Total Revenue = (500 x $20,000) + (500 x $10,000)

Total Revenue = $15 million

The college is able to break even currently when operating with full occupancy since total revenue is equal to the total cost.

When the donor offers to contribute the fixed cost on the condition that the college does not price discriminates, the college has the option to either charge the lowest price it can from all students or charge the higher price from those who can pay.

When the college doesn't price discriminate:

If the college charges $20,000 without price discrimination, only 500 students will enroll. This will generate a revenue of $10,000,000 for the college. The cost of operations, in this case, is equal to $10,000,000 + (500 x 20,000) i.e. $20,000,000. Since fixed cost is donated by the rich donor, the college ends up paying $10,000,000 of its total cost and breaks even. There are zero economic profits when the highest price is charged.

If the college charges $10,000, 1000 students enroll. This causes an operational cost of $10,000,000 + (1,000 x 10,000) i.e. $20,000,000. The college generates the same amount of revenue of $10,000,000. Since fixed cost is donated by the rich donor, the college ends up paying $10,000,000 of its total cost and breaks even. There are zero economic profits when the highest price is charged.

In both cases, the college generates zero economic profits. The pricing decision will be indifferent. If the college chooses to charge a higher price, the social welfare will be reduced since the market will not produce the socially desirable quantity as 500 students will not enroll. There would be a deadweight loss equal to the loss of social welfare.