The discount rate and items about the closing

On Thursday (2/16/2017) Saint Joseph's College hosted an admissions fair for their students. Seventy four schools were listed as attending They filled the ballroom and spilled over into the hallway around the ballroom. The picture below shows about half of the ballroom.

This week I met three people recruiting students who were former faculty members at the College and had a nice chat with each.

Most of the Indiana Colleges were at the fair. DePauw and Notre Dame were among the exceptions. There were also many schools from Illinois, Michigan, Ohio, and Missouri. The University of the Ozarks came from Arkansas and the University of Houston-Victoria came all the way from Texas. I asked the lady at the UHV booth why a student would consider her school. She said that its tuition was low and that SJC students might enjoy the warmer weather.

In other news about the closing, the Alumni Board is trying to raise $20 million by April 1 to keep the school open. Donations will not be kept unless enough money is raised to be successful. Details are on the Involved for Life website.

There is a petition for the state Attorney General to investigate the Board and administration for fraud. Personally I think this is a terrible idea and nothing good can come of it. It reflects the anger stage of grieving. As the saying goes, never attribute to malice that which is adequately explained by stupidity.

(The rest of this post is about the economics of the discount rate, so if economics traumatizes you, you might want to stop here and go to your safe space.)

In the discussions about the suspension of activities at Saint Joseph's College, there has been frequent mention of the discount rate. The College says that its discount rate is about 65%, which means that on average students pay only about 35% of the listed tuition of $31,000. In some of its financial reports the College lists as revenue what it would get as tuition if there was not discount rate and then as an expense the scholarships that it gives.

As an economist this way of treating the matter seems odd. Colleges seen as businesses have a lot in common with airlines, hotels, and cruise ships. They all have large fixed costs, that is, costs that do not depend on the number of consumers, and low marginal costs, that is, the additional cost of adding one more customer. As a result of this cost structure, all these industries find it useful and in many cases necessary to charge different customers different prices.

The easiest way to explain this situation is with a very simple numerical example. Suppose that it will cost a business $100 to offer a product and that the cost does not depend on how many customers (within some range) use the product. Perhaps, to make the example a little more concrete, the product is flying people from Jasper County International Airport to Lafayette. Suppose there are two people who want the service and each are willing to pay $60 for it. In this case any price between $50 and $60 will work to make the business profitable. At a price of $55, for example, the air taxi will collect $110, yielding a profit of $10 and both persons will find that they benefit from buying the product.

However, suppose that one person is willing to pay $80 and a second person is willing to pay no more than $40. The total potential value of the flight remains the same at $120 ($80 + $40), but there is no single price that will yield a profit. Any price above $40 and below $80 will result in one passenger and a loss. To get the second passenger the price must drop to or below $40, but at that price the revenue is still below the cost of the flight.

However, there is a way to solve that problem by charging the two people different prices. If the airline could charge the first person $75 and the second person $35, the total revenue would be $110. The flight would be profitable and both customers would benefit from the flight. The problem, of course, is to figure out a way to charge the higher price to the person who values the flight more and the lower price to the person who values the service less. If this cannot be done, the plane will not fly and everyone will be worse off.

Hotels, cruise ships, airlines, and colleges have found ways to sort people into groups by how much they are willing to pay. The sorting is often crude but even crude sorting can be worthwhile.

What colleges should be trying to do with their scholarship programs is giving aid in just the amount needed to get the student to enroll in the college. Many, many years ago I tried to explain this idea to the director of financial aid. He was insulted at the very thought that scholarships were part of a pricing strategy. At the time there was little interaction between the admissions department and the financial aid department--I wonder how many more students the College could have had it if had known what it was doing. After spending a lot of money on various consultants, the College eventually got the two departments working together.

Viewed as a pricing strategy, financial aid is not an expense. Rather the revenue is the tuition that the college actually collects so there is no need to deduct aid as an expense. Different students are charged different prices for college education because they are willing and able to pay different amounts. A question that the situation of Saint Joseph's College raises is was there a way to charge prices that would have made the institution viable but the College never found it, or was the demand for their product such that no winning pricing strategy was possible.

Here are some links to videos that explain or illustrate price discrimination, the term that economists use for charging different prices to different people. The first is an explanation of the sort you find in an economics textbook and uses pricing of drugs as its example.
http://www.mruniversity.com/courses/principles-economics-microeconomics/price-discrimination-examples-airlines-arbitrage

The second is a continuation of the first. It ends with an explanation of how colleges can sort potential students by willingness to pay.
http://www.mruniversity.com/courses/principles-economics-microeconomics/price-discrimination-social-welfare

There are two videos linked on this page that illustrate pricing strategies for several products.
http://ingrimayne.com/econ/Monopoly/videos15mi.htm

The second video on this page is a bit of British humor in which the seller tries to figure out how much the customer will pay and then asks for that amount.
http://ingrimayne.com/econ//TheFirm/videos09i.htm.